In this lecture, Erik Olson demonstrates more varied and complex examples of drawing objects
using reference planes, reference points, intersecting planes, shapes, and surfaces
meeting with seams. Erik will create a simple scene with a blimp, an archway, and a 1940s
type race car related to the cone of vision and constructed using all of the above methods.
Erik will do a digital draw over on top of a wooden rowboat scene to review
and demonstrate all of these concepts.

Now we’re going to do an intersecting rectangular plane like a block shape intersecting a large
curve shape, but we’re also going to take this opportunity to still talk about the cone
and setting up another set of vanishing points in a more casual manner for the actual block
shape. So the block shape will not be coming into the curve shape, as you can see lightly
drawn in here, at a 90-degree angle or a right angle; it will actually be at a steeper angle
or more shallow if you want to look at it that way. We’ll just start drawing it up
and making it a reality. I will mark the cone for you.
We have our center of vision. We have our horizon line eye level, and there would be
our one-point vanishing point, which we’re not using, but I just want to get used to
the setup again and start relating things a little more again to where we are within
the cone or reaching outside of the cone. That would have to do with how close or far
we are with our station point. Our station point, of course, is right down here. Our
vanishing points for our big curved shape block idea will be kind of 45 and 45 to this,
but then the more rectangular long block will be turning to another set of vanishing points
as we’ll start going with here.
I just wanted to make it clear, so I’ll go ahead and mark our cone. In this particular
case it’s here. I’ll just put it in a couple places here. It makes it easier to
conceive of where it is without having to draw the whole thing out. That would be our
cone continuing up out of camera space.
Okay, so I’m going to start drawing in my idea for my first shape will be along this
line here. I usually get my top and bottom plane to try to compose where I’m going
with these ideas, and the bottom shape as well will be running along this idea here.
Then I think I want to stop it back around here, so what I’ll do is draw vertical in.
Just feel out the shape and go ahead and follow my lead, kind of just drawing the idea here.
Do the back shape here. Then it would be coming forward basically like this. Then between
these two ideas about here I decided to draw on the idea. I’m going to have the block
lead a little bit from the left vanishing point a little bit and then start curving
down. I don’t quite know how long necessarily I wanted it. I just mark it out. I pre-draw
these a lot in a simple manner to make it really clear when I talk exactly what and
why we’re doing it because, again, these diagrams are supposed to be longstanding examples
in your own notes with your own explanations; your own arrows and shaded planes; with color,
blue and red, why this stuff works.
Each little one has a little difference that might help you understand it more, but also
we’re trying to combine different ideas and be efficient here. So in this one we are
talking about with the relationship again of the cone, the station point, even though
it’s off camera. It’s right here. And, you know, the eye level and how to get this.
The view we’re going to have is pretty much going to be pushing the cone, like a wide-angle
lens, which is very, very common these days.
Other people a lot of times tend to draw only these type of diagrams with sectioned planes
and stuff very much well within the cone of vision, which makes them very conservative
and also makes all the shapes from end to end look the same. We’re also moving quite
a ways across the cone, so as the shapes diminish and go farther back in space they actually
change in nature because of how they foreshorten as they come forward or become more steep to us.
So let’s go ahead and start this shape. And as I did it here I just basically started
angling this one out like here, coming down, turning like this and just plummeting down
toward here like that and look straight up and down there or close to it. Alright. What
I’m going to do is I’m going to say, well, there’s the point where it starts turning
away from being straight. We’ve got another one at the peak of this. I’ll put another
one right here, another one right here, and then of course we have our end. So we have
really our first end here; one, two, three, four, five, six. It’s not that important
because we’ve done a lot of these shapes. Now I’m going to draw it back some ways here.
Now, we don’t quite know where we want our other shape intersecting it, so I’ll just
make a nice dark line here in this shape. And I’ll go back here just to try to get
our other shape nice and dark and obvious. We want to make sure and say this is an actual
block we’re thinking of. So if we’re talking about a block let’s do that.
Alright, we’ll make that end nice and dark again just to make it clear.
Okay, so there’s the beginning of that shape.
We’ll continue that shape, but now we can also figure out where
we want our other shape intersecting.
This brings up an interesting point. What I’m going to do is make a lead line from
my block which I believe I want to intersect here. That’s why I stopped the line; that’s
just me making it up. Then my first line I’ve drawn is a long one saying this is not going
to be at 90 degrees. Because again, 90 degrees would be a vanishing point right there, and
then the other 45 coming up and being over here to the vanishing point. We’re going
much further out to the left than that conventional vanishing point which this plane and this
plane follow. So it is at another set of two-point vanishing points.
I’m going to set my idea here, and then I’m just going to continue it on like that.
That’s the line that leads way out meeting up with this eye level eventually for the
left side vanishing point of this new block shape. I want it at about this high so I’m
going to start the corner here. That’s still a vertical.
But now I have to kind of decide how do I set up maybe quick diminishment guides
or just doing it by hand if I was doing it that way.
We’re doing it more formally, but you could easily just kind of feel out
the diminishment guides for the second set of vanishing points. We have our first set
to this block going to our left vanishing point here, coming down to the 90 to our SP
and going back at an angle up to find our second vanishing point which are these lines.
This block we’re going to draw in is obviously at a more shallow angle way off to the left.
Therefore, it’s night or its right degree or its right angle counterpart for its ends
are going to be actually somewhere within here. So the idea is if I go way off here
and I’m meeting up way out there, I’m just estimating just by eye and a little bit
with a ruler way out here where this line meets this line I’m saying, hey, that comes
way back to our SP at a particular angle. And to do that all I’m saying is, alright,
I’m going to go way out there and project but just guess like I do when I’m doing
a larger painting or working on a piece of paper with the vanishing points way off. We
could make diminishment guides and remind ourselves how to do that. In this case we
can do both using this line as a base here and then the straight line of this. But I’m
also just going to guesstimate, where does this meet if I take this and run it way out
to my left. I’m just going to do a really good educated guess where it comes down and
runs into my SP. Then I’m going to bounce back from my SP which is right down here from
where I’m guessing that slowly diminishes right in and just take a really good guess
at how this runs into our SP and comes back up at a 90 degree angle from our SP, which
is has to represent this new block’s idea. And yeah, I come from the SP into the picture
and mark a vanishing point there, just estimating it because way out there coming back to our
SP and bouncing up at 90 degrees gives me a possible other vanishing point right here.
That’s for the long rectangle, the long block. So that’s the right VP for that.
That’s for this object that’s going to be running into this object. This object,
again, is using the conventional two points that are pretty much at a 45 and a 45 from
our station point down there. So now, how do I guess that? I can say, alright; we’ll
pull out a red pencil and little bit and just do a really mini, mini diminishment guide.
We have our first line here which we already put in.
So that will be our first line guide here, so I’ll also put that in red a little bit.
Then also we’re using the eye level. If I take a piece of paper here, which I’ve
already done and get half this space. Remember, you take a piece of paper and fold it in half
and you can get that. This space cut in half with a piece of paper marking the piece of
paper as you remember them folding the piece of paper down and finding the half leads to
this being the half between here and here on the center of vision. Also, I take a random
space also—about here I took and found the half there to be right about there, between
here and basically here. Found that half. That just gives me a little bit of a diminishment
guide idea. I’ll put that in red not to confuse myself later. I have an idea of a
diminishment guide for the block object off to its distant left vanishing point.
I’m not drawing it in that dark. There’s the lead object we got originally to set the
angle we want the bottom of this long block to be at, but I did go ahead from here. Take
that distance right at the center of vision, cut it exactly in half, and got that point.
I also just took a random place as you’ll remember from how we find distant vanishing
points in our initial lecture. You take a another small, random vertical place still
connected to this plane and the truly horizontal eye level, and you’ll find another halfway
point in the smaller space. That gives you that division. You connect the division and
you get a diminishment guide now from the horizon line and this middle line
down to our original baseline.
You could keep going through your picture with more and more of these by just repeating
these increments here down more and up more and come up with a complete set. They would
lead you very dutifully to that left vanishing point. I only need about this, but I find
it helpful. Let me now draw in the top line of that object because I want it this high.
Now we can complete that shape a little bit or start to. I’m going to take it back,
and I’m just to line it up and diminishment properly a little bit in. So a little bigger
space here, little smaller space to my red. That’s what I’m going to do. So just about
there would be about right. I’ll draw that back. It’s going to come out somewhat, and
then I’m going to do it lighter all the way back here because I’m going to do it
transparently. So now the top of this block goes all the way across. This is my other
vanishing point, my right vanishing point. Let me make that clearer.
It’s not drawn too well.
That’s vanishing point right. And the left one, again, is out there. That’s
a second set of vanishing points for this object as opposed to the traditional vanishing
points we started with for this object.
Okay, so here we go. We’ll feel out that shape. How deep do I want it? Well, I can
basically cast my lines from here now to my vanishing point back a ways. The bottom and
the top like this. Then I can decide, okay here I’ll make it this deep about, so I’ll
make a little mark there. I’ll also just follow the feeling of my diminishment guides
about like this. Go ahead and draw this back like this. That’s the idea of the bottom
of that plane. Also, know I have this mark. I can go from my vertical to get my top plane
at the other side going across to the left vanishing point, so I’ll pop that vertical in.
Connect up here, the corner. Go ahead and put another good guesstimation on my diminishment
guides where that goes. Probably be about something like that, so I’ll go ahead and
draw that it in nice and dark as the object. I’ll have to stop a little bit with the
dark line not knowing exactly where it intersects with the curved block. I’ll go ahead and
just draw the rest in kind of lightly like that.
Then I can also finish out the outside parameters of my rectangular shape like that just to
make it clear that that’s the edge of the actual object. Go back to the VP, make that darker.
Alright, so we start seeing that object, and I won’t darken any more of that in, nor
this object until we start figuring out where the intersection. Because the thing we’re
looking for is the seam that’s created by the meeting of these two objects, which will
be different than the seam that would be in there by itself. Again, it’s not going to
be that huge of a change, but I just wanted to kind of play this out a couple
more times just to get the feeling of it.
Let’s go ahead and finish out our block shape a little bit if we want and say I want
it this long; from here to here now. I’ve got the bottom and the top. I can just finish
out my perspective by drawing in a vertical for the back of the block now.
As you'll notice they’ll be quite a difference between the back of the block and front of the block
because of the foreshortening that’s happening to it because we are—I’m going now to
my right vanishing point or the block. We’re seeing through the block now,
kind of making a transparent version of it like this.
I’m coming back down with a backside of that block.
At the end of the block over there to the left. Then the actual part of this object
we’d see come through the back of this object we can make darker. We want to use our line
weight and say that’s coming out of there as an actual object, and so is this line here
leading into that. Then we have the back edge of it as well right about there. So just draw
it in about there. A little higher actually, like this.
Alright, so there’s the back of that block. Coming out of intersecting with this object
eventually. Then we’re just going to concern ourselves with the seam. We can also drop
the ideas of the curve, and we’re going to make two ideas of repeating this scene
or this idea of this edge as a seen here and here. We’re going to use this point here
to start with, where the two shapes or objects intersect. We’ve done that a lot before.
Then I’m just going to pick an end which I randomly picked back here.
I’m going to go ahead and pick points on that curve or pick the points of having this
curve now to help me bring this shape accurately to where these intersect. I’m just going
to pretend this shape is unaltered at the point of intersection very lightly. Then we’re
going to see how much it changes because of the block surface meeting the surface of this
curve shape. But first, I’m going to draw in a light version of the seam how it would
be here, uninterrupted at first, as well as the end of the shape.
I’m going to drop these points to the ground here and cast them all the way over, so that
I can get my referencing a little bit easier for getting that curve shape in the middle
and then at the right end there. I’m going to drop it down here, just to there. Drop
it to there…to there, and just the idea of dropping it there.
Of course, we have our back as our corner right there. So we have our front, back; we’re
dropping these ideas. So I’ll make little dots of those points because they’re important,
and we’re going to go ahead and cast one, two, three, four of those drops to our traditional
right vanishing point for this object, not the right vanishing point for the block.
That's here. We’re doing it to a vanishing point right off camera there for this block. Okay.
I’ll just cast those lines back quickly all the way through our object, fairly lightly, all the way back.
All the way back,
and then that little one right there from that little drop there all the way back.
Okay, so now since I decided to have this shape end here I’m actually going to go
ahead and draw back to my vanishing point over here.
Then I have to meet this back corner plane here
by drawing that idea back again here to intersect with that line, which makes
the corner about right there. So here to here is back here, is here to that dot. This goes
to that dot and then has to go up vertically so we have the back of our shape.
Let’s draw that up.
Now we meet our object at the top. There’s that back corner of
our object. This back corner, that back corner. This bottom back corner, front back corner.
I’ll make that line a little darker going through the back, but not too much. I don’t
want to interfere with the idea of the block and stuff. Now I’ve got this front corner
here, this front corner. I’ve got the various points. This point is back here.
This point is back here.
This point is back here. This point, dropped from here, is back here.
And that’s going to bring up the verticals that are going to help me re-create that curve
again. The curve from here all the way back there. I’m just doing this because—I’m
not doing it just by rote guessing. I’m doing it like you might when you’re hand
drawing. We’re doing everything in context of explaining why the perspective helps us
reference the space properly regardless if we can draw it freehand or not.
This point here runs back all the way to here and up to here. This stretch here runs straight
back to our right vanishing point for this block, so to here. I can do the same traveling
with this to my right vanishing point like this. Straight over.
We know that this little run here is the same right back here. I can connect it do just a very, very light block
scene like this. Okay? Like the top of a piano or something. Then I’m simply re-creating
this curve dutifully back here, you know, gauging how this behaves to its new perspective.
It has a curve down right here, and we have to transfer these links now before we understand that.
Let me not get ahead of myself here.
What we’re doing with these verticals now is we’re catching where these positions
are in height and drawing them all the way across until they hit these standing verticals
here. That’s how we know those points are. We’ve got that point there. We need to bring
this one across here, all the way back to hit here. We need to bring the next one all
the way back to hit here. And then the other one right here all the way back to again hit here.
We already know where that corner is. So now we can just draw on the shape as we
see it this way turning down. This way kind of turns around this way.
This one kind of starts on its way down here.
So again, not that hard to do freehand, but really we’re trying to understand why referencing
works in a simple way for artists. So we’re not going to say we’re going to do it as
complexly as the most complex demonstration on sectioning ever. We’re doing it to be
understood by everyday artists. If it’s helpful for beginning and intermediate designers,
great. But there is, of course, much more complex ways that if we started to do with
some more complex diagrams than this series, but really have to get to a couple more when
we do plan view. Then we’ll get more into really
detailing out a couple of vehicles or something like that.
I’m not interested in going that detailed, in that complexity. We did the little alien
vehicle a few diagrams ago, but really that was still pretty simple. The idea is you’re
gauging these different things. So here’s this shape, and now we’ve just replicated
that shape behind. We have the end of the block here. The block casts this way. We’re
seeing the end of the block. Look at how much wider that is because it’s way over to the
left of our cone of vision. This one is so foreshortened and show close to the vanishing
point. In fact, if we were to extend this out in a very light idea here—I think I’m
going to do that in blue just to make the point—it could still be shown in a wide
angle movie lens to go past the cone of vision to the side. We could just extend the idea
of this shape out like this and transparently see through it. What we’d notice is even
if we went way out here with the shape like this it would still move back to this vanishing
point. We’d need this back scene, which I didn’t draw in here. Let me get that in.

We’d still notice how it would behave if that shape actually extended and we were in
a wide angle lens for film or something very close to that. We’d still have our verticals
come up from these two ends points here, which they’ll do. I just wanted to make this point
now where we’re kind of talking about the cone again and distortion and lenses a little
bit. Lenses behave in a more curvilinear manner. We know this because of the nature of the
lens being round like our eye. But again, this is a good enough approximation for perspective
to help us understand what is kind of happening in distortion space for perspective drawing.
It’s still very helpful. So we have those two points now meeting that. So really, this
would come back like this and then this part right like that. And this part back here.
I don’t want to muck up our work back here, but frankly I just wanted to show you that
if this long block continued and pushed into distortion space, we’d be actually looking
at the end of this, which we can see the actual ending side here in this plane. I guess it’s
a little to the left of that vanishing point. But now this is stretched beyond the point,
and it goes to the right of this vanishing point and we’re actually seeing the inside
of that end plane because what would not be visible if this object was opaque would be
this cap end of the rectangular shape because that’s how it would pass our straight-on
tangent point-of-view and continue.
I just wanted to make that clear that, yeah, pulling it further out like if it was longer
and a wide-angle lens would result in that. So look at how thin this from the end cap
and then looking through the object here how much wider this really is, but it’s the
same object, actually. It’s just behaving very differently way over here to the left
of the cone of vision then over here to the right, and then over here to the right and
then eventually pulled out like this. Always be aware of that as a narrative artist because
you can play with those effects a lot, and so obviously designers when they do more distorted
drawings that are playing with having the vanishing points closer in a sketch. Well,
that’s the same thing you have the flexibility of doing is working right within or outside
the cone of vision if you wish. Or, if you want a more conservative effect where the
ends of things look more the same, you would do much smaller drawings or a smaller framed
area way inside the cone. That still might be your whole huge canvas, but you’d still
be playing the more conservative game, much like when we did the digital draw over of
the Napoleon portrait in his library. Very conservative perspective all happening well
within the cone, the cone being here, this area being very small. But we decided to really
draw right to the parameters of the cone and a little bit out here with the tip of this now.
So we have this shape now, this other end of it. We understand how it’s starting to
work as a curved shape. We’re going to put in this light scene here. We just want to
put in a scene derived the same way as this one right at the intersection of the object,
so let’s do that. Sharpen my pencil a little bit. Okay, so I’m going to do the same thing.
This goes up in the air a little bit like this. I’m going to carry these points over
here to where these intersections are. So that is intersecting there. This is intersecting here.
Excuse me, that’s incorrect. I’m going from this intersection of the plane and then
following the perspective of the block, so we’re doing another seam on the block, pretending
that it is unaffected by the longer rectangular block her by just doing another seam of this
object in the middle. So I have to actually go to my traditional right vanishing point
here through the object like this. So this is a seam going through this object here straight
back to its same vanishing point here. Sorry about that. And so this point would be here,
not where I put it. I was following the longer block’s perspective and that’s incorrect.
This point would be here where this comes and intersects this. That makes a standing
plane. We’re not going to draw the whole plane out yet. This comes here and hits here.
This comes here and hits there. This goes here and hits there. All we’re doing is
saying we’re going to create the same standing verticals that comes to these same points
and make a plane connecting this new scene point right here on this object going down
and making a seam here. Then we’re going to show how the seam between the first object.
We could say this is object number one and this is object number two. We’re going to
say object number one’s normal seam is then affected how by meeting this plane secondly.
So first we want to figure out how it is not affected by the block meeting it. So I have
to come up in a vertical manner just like this part. I have to then go across and come
up between the two to replicate that same back scene if I wish to do that. So there
it is. That’s that point. This point is that point. Then I’m going to go ahead and
make standing vertical from these points here; this, this, this. That’s already got a vertical.
This already has a vertical here for where these two meet her. I have to do a little
vertical here, here, here, and here. So let’s do that.
I’m going to come up and meet that scene properly. I’m going to overdraw them a little
as we usually due. This one comes here to where this is kind of a straight run on a
flat top. Same here. I come out here, up here to that run, and that goes directly back to
the right vanishing point to close that seam off there. The rest I have to carry over this
point, this point, and this point. Carry over to the right vanishing point to find their
counterpart verticals here that we just drew in. Let’s draw in the shorter one here, this point.
We’re going to come from that point and draw over until we hit that new reference vertical here.
Now, again, you can say this is too much work or too confusing to make these planes and
all that just for these simple objects because I’ve been freehand drawing my whole life,
and I’m good freehand drawer, and I’m a good observational drawer. The problem is,
where are you going to get with that when you do more and more complex objects if you
don’t begin sometimes to section or think about the logic of sectioning. You can really
spend more time struggling with an object. Otherwise, if you would have just put in really
soft transparent planes working and basically doubling and tripling perspective, having
the perspective that you’re using, you know, cutting it half and using these planes and
dots, you actually can get a better feel of where the space is taken up by the objects
meeting different points. Much easier and faster than being frustrated with an object
not looking right for one or two hours.
So it all depends. If something comes easily you don’t need to do all the sectioning,
but if something is becoming more difficult and the combinations of the shapes meeting
or doubling or having thickness becomes pretty tenuous, and you’re not getting what you
need, you can go back to seaming and sectioning these things and understanding what things
are doing in actual perspective. That’s why were doing this. It’s to just get good
at this stuff to use it when we need it. Taking this point, dragging it over to its vertical
here. So here it drops down, comes over, comes up. So these are making little sections again.
I’ll be clear about that here. So we could say this is a section for this thing here.
We could say the front little one, this thing drops down, comes over here, drops up, and
comes back over. That’s a little standing rectangular section. Standing rectangular
section. If you want to tone them in on yours that’s fine, but it’s going to get too
confusing. I’m trying to get you to understand how these standing rectangular planes work
without mucking up the diagram too much yet. So here are the points we need to draw in
our natural curve that’s repeated on this shape here so that we can see how that is
altered when we intersect it with the other objects. So first we’re going to draw that
seam like this kind of lightly, not real dark.
That would be that natural standing seam like that on that.
Okay. One then that’s one in the middle, and then the end one. Now, let’s see how
it changes or what the logic is when we actually consider the idea of this shape slamming into
that shape. We need to do a couple of things. We have a pretty complete idea of what our
number two block is doing, what a number one block is doing. I know it’s a lot of work
and a lot of setup. But, it’s the kind of thinking you have to get used to. Then focusing
on the seam area when you need the help.
One thing that’s fairly obvious is we can use the ground plane between these two seam
areas. This is the one that’s of interest, and then the other is following this perspective
of that. So, we’re following the idea, how both of these are different than each other.
Another thing we can do, so I’m going to do it in red. We’re going to come straight
up from this point, which is an important point cause that’s our intersection point.
If you want to keep thinking of it, label that intersection point that we kind of led
off of. We need to come straight up with that actually to be helpful and go up like this
to the true height of our new object touching this one, which is right there. From this
point, this is the top of this block at this point. That’s important because now we need
to make—instead of following the block’s perspective, instead of following object number
two’s perspective back way out to the left, we’re following this plane back at this
height right here. This is the height of this object. So we know we have the correct height
of this intersection point of block two.
What we need to do is take this back to the vanishing point left of this object, number
one’s object until it hits the point on this natural seam we made in the middle here.
This is all part of the same plane here. Therefore, we know that the block is this high at this
point of the curve. But, the block seam on the leading edge is over here. We have to
have the two ideas meet each other.
Meaning once I make this idea of this standing plane here, I can then take—in blue let’s
say-I can go along the perspective from this curve along the surface of object number one
back to the right vanishing point, and I can go further back and forward. I’m going to
line up with the top plane of object number two until I run into that line, which is right there.
That’s the point at which this top plane of this object intersects at the point it
should properly with this curve shape. Also, the back edge of the block runs into it until
it runs into that same place. We found the true height at this point of the picture plane,
and then how to shuttle this back to the perspective of this block to touch that curve. How do
we know where the curve is? We drew in a seam right in on that plane. Therefore, this height
of the block here changing perspective and going back to the perspective of this shape
now shuttles back to the curve. That’s its true height at the curve in red.
We can make a plane out of that.
The important thing is that we take this to the right vanishing point now and slide across
this object and say, oh, where this real seam meets this object at this height projected
back that, the top of the seam starts there. We could also say the back edge is drawn to
here and runs into our curved seam here at these two different points. That’s where
this block number two runs into the two points at the top plane of this curved object. Okay?
Now we have to find some other points that we could carry across from here that come
forward, of course. We’re going to do little planes like that. So the first one is this
point here and the top here. We’re going to make a little plane so it runs into the
plane at the bottom here, which is only a tiny bit out. See this tiny craal right here?
But we’re still going to do that little craal in perspective just to be annoying in
showing why it works. There’s my tiny little plane like that. I come down and that’s
the beginning. And that’s how I know by this little shaded plane, I know that my seam
instead of being here for the standard seam of this shape following that perspective.
The new shape, the block, I just carry forward a little bit up to this point, and that’s
the seam where the dot starts. The second moves here. So if this is number, let’s
say one, we just got number two out here, right there. So it’s a little bit over.
Now we do the same thing with this seam and take this idea here. Do it in red again if
we want. Actually we’ll do it in red again. This idea here has to be carried over across
to run into our new shape again. Why? This is the bottom of the intersecting shape. We’re
taking what we had, a correct plane from this seam here, and we’re shuttling it over as
a plane to run into the base of our new object. We know where that is. I go straight up and
straight back at this same height. I get my second point here, right there. I’m going
to put that in in pencil. That’s another point.
So now let’s work backwards before we’re too confused. We’re saying that here we
know the intersection point is where both of these start at the same place in the ground.
Once we get up to this point the fact that this cube or number two comes in at a different
angle. We have to shuttle from this standard point here and here behind slightly forward.
That’s where the seam begins because we made this plane jump over to the position
of its ground base here. Same thing here. This was the original position we can take
down and make a plane and realize that’s the second seam. Then we found out the third
place they meet is right here because that’s the top seam that we figured out how to make
that meet the curve by expanding this idea out from the original height of this taken
to the perspective of this block back here. It’s just logic. We’ve made another seam
here that’s unaffected by this object meeting it, and then we’ve shuttled the space over.
So what I’m going to do in blue is just draw in the seam as it would actually exist,
like this. Here it curve around and it come around and meet right up here and curve very
close to where it is already. Then it would come down to meet the original generation
point of that seam right there. So the new seam is going to be in blue, just trying to
make it clean as I can here, but dark.
That seam would pretty much come in and meet like that, so the difference here
I’ll shade in in blue between what would be correctly the original
seam basically and our changed seam. It doesn’t seem that big of difference, but let me draw
it in here. But, there is a difference. The original is in pencil; right here I’m drawing
right now. Then by reference we kicked over a little here. Came up, we kicked over a little
here, came up, and we made this true height come straight back, come across, and found
this point. So we know now that’s where that top plane contacts this curved shape,
that plane starts there. We don’t need to draw in the back curve. What’s of interest
here is the fact that we can see whole new seam that’s created from the ground up to
here. Then we know this seam has to go back the entire length from this all the way to
that back there. So that entire length between those blue dots, this and here, has to be
drawn in as part of the top shape. That’s the top shape of this curved object fitting
over the top plane of that block, stopping here at the corner.
Let me draw in this nice and dark. The object now goes in nice and dark this way. This object
completes its journey right here. So there’s the top of the block. I can do the top of
the block if I want in red. That thick pencil line is where it turns down, meets right here,
and that’s the new seam. It seems like a big deal over nothing, but the fact is that
is how shapes meet, and I wanted to show, again, how to rehearse referencing an object
from end to end here as well as the idea of this object. It has its end here, section
here, pulled out into the cone. The important thing is even though this is a little move
that you could easily say, oh, if I did enough of this I could just that by hand and not
have to do all this. Of course you can.
The idea is how do we get used to in a basic way with diagrams and really considering this
stuff and looking at other supplemental information how these seams behave and move when the two
surfaces meet, and what new seam is made on the surface between the two objects. That’s
all we’re doing, that we’ve been doing for a few diagrams now.
There’s the difference shaded in blue.
Again, the pencil seam is the original seam section we drew here. That goes to this vanishing
point that this behaves to, the traditional one just to the left there. But then the new
seam has to behave to this object meeting this object. Of course, this object is meeting
a vanishing point that is a good deal more way out to the left hitting the horizon line
as well as coming to the SP up at 90 and creating this right vanishing point, which these parts
of the block move to. So that’s how we know.
When this block, though, goes under this new shape because it’s parallel to the ground
it moves to, or the intersection of these two shapes because the top of the block is
flush with the ground. That seam moves to the vanishing point of this object, which
is out here, not to that one. It’s only the ends of the block viewed as its true shape
here at the ends and here that follow back and go to that vanishing point. But, all of
this object behaves to the traditional vanishing points that are 45 basically and 45 to our
center of vision of this object. It’s only the seam that meets that we kind of have to
question, yeah, how do we make that new seam with some reference planes
and some reference points. That’s what we’re doing.
Again, we wanted to consider how things look when they get near the edges of the cone then
they really do take on a different shape. This is a quite a bit more foreshortened or
a good deal more foreshortened that that shape, but they’re part of the exact same shape,
and they’re exactly the same shape.
Of course, look at how foreshortened that is compared to how wide open that other end
of the block is, but that’s the pole of foreshortening actually works. So if you were
standing here at a particular distance at this eye level from this exact shape, whatever
it measures to, that’s exactly how it would look and behave in foreshortening in our peripheral
basically. If we just were able to look and move our eyeballs around a little bit from
the seam because we were standing fairly close. If we standing a good deal farther away from
this setup then everything would behave more conservatively within the cone, and we would
have not such a large degree of difference between the foreshortening of these two ends.
But, because we’re getting close and pushing the boundaries of the cone it looks very different.
So that’s part of the point too. So we’re referencing. We’re finding the new seam.
We’re talking about standing planes. We’re doing a whole bunch of stuff here.
So we just want to integrate this now into everything else you’re doing, so this should
be becoming natural as you draw the thicknesses of arches and have curvaceous shapes and how
those curves behave like we did in the curved section of curved objects and planes. Now,
we should really start learning with a few more diagrams what we need to know about basic
sectioning. We’re going to get back to some sectioning after that when we go to obviously
plan view and starts doing some objects drawn from plan and elevation, but we also have
to get to a whole bunch of figure stuff so we can figure out how figures appear and can
grow out of a particular perspective so we know that they’re in correct positions too
when we draw them in perspective generally as mannequins.
So we’ll be doing some of that. Okay? So this is a little step here, but it’s a lot
of understanding to understand why these things change. We want to get good at referencing
for those more complicated situations we might run into when we’re doing shapes that are
confusing us and actually take us longer not to apply some logical planes too.
Okay, on to the next.

For our next diagram we will be doing another curved plane, and then we’re going to have
basically a cylinder, you know, which would actually be a circle if it wasn’t in perspective.
A tube, a circular tube, a cylinder going ahead, and we’re going to move the cylinder
through the plane. You can see the little ghost of it this way. So I’m just going
to try to make this pretty direct and simple, but I wanted to make sure that we step it
out real clear. Again, because we’re going to get the new seam that’s made between the
surface of the cylinders striking, you know, somewhere in the middle here of the curved plane.
We’ll go ahead and draw the curved plane out randomly, you know, from the start for
you guys, so in a sense I went ahead and basically again did the same thing, found the top and
bottom essentially as I wanted it roughly, like this. And the bottom as you can see here.
So we’ll just move pretty quickly in this one. Then I want it basically to start here
and about here. Go back up. There’s an L that way.
I just want to make these clear.
Then we’ll have the curve roll. I’m going to have it come forward from the right-left
vanishing point for a little while, but then I’m going to have it break away and start
curving about here. As you can see, we’re going to just come down nice and easy. Take
a curve this way. Keep going here all the way until we finally hit the bottom there.
So we’ll go ahead and draw that in a little darker. It’s pretty clear stuff so we’re
going to move pretty fast on this one. Alright, oops.
I don’t know quite how far down it’s going to go
yet for that, so what we’ll do is we’ll do it nice and dark on the way
over here like that. And we’ll make some references here.
Got this up here. It should be a little down on this curve just a little bit here.
Where else would be a convenient reference? We could right here as a point. Can do a point
there, point here in the middle as well.
So that should serve us pretty well. So let’s
see what kind of doubling over we can do with this curve at the back end. It depends on
how far back we want to do, and as I remember I picked this spot right about here. We’ll
say that’s the back end. So I’ll move back to my left vanishing point way over here.
Move back. Then I’m going to meet this back plane we have back here. Going from this point
here back. Meet that back corner about here.
Okay. Make sure I get that more accurate. Yeah, it’s probably more like that.
Okay. I’ll make that L. I’ll make the back wall on the other side now over here
from that corner that I see. Okay, it’s about there.
So that goes ahead and meets the same point up here,
which is over here. Now, we can look at the back plane and say,
alright, we’ve got these things we can drop to the ground now. One, two, three, four in
the middle here; we have the ends here and here. We’ve already struck over here.
We’re going to take this, this, this, and this; drive them that way, and drop them to
the ground. Make a plane. These will be standing rectangular planes that tell us where the
opposite corner to these touching are like we’ve done before. I’ll drop these three
points to the ground pretty much just like that. A little arrow there if you need it.
You guys should be getting pretty used to this. Again, the idea is please draw your
own diagrams with me on this same type of paper if you want or smaller. I’m just using
18 x 24 white paper, leaving enough room for you guys to make tons of notes and steps as
you see fit, stopping and pausing, reversing. Play over and over until you get it. Not only
drawing with me, but making all sorts of notes. A, B, C; we did first,
whatever makes the most sense to you.
I’m not going to direct them specifically only because some people need very few notes,
and it’s mostly visual. Other people might need a lot more. That’s totally up to you.
That’s your business. I’m telling you and repeating these ideas over and over. We
first created our basic space. We came over from over the right vanishing point and came
across. We found this basic L. We made our curve. We found the back, went back, decided
to stop, you know, the shape here. Drive back like this so now we are going to replicate
this curve back here by bringing these down and bringing this over as we’ve done before.
I’m going to bring them over now to the right vanishing point. That point right there,
just as a light line. Dark enough for you guys to see. Another line comes over and one
more time right over there.
Okay, so now we have these points made there, there, there. We’ve got the back corner now.
That point, that point, and that point driven, driven, driven over to the right.
Back wall here, here, and here.
Now we can come straight up vertically from those points and then meet or projections
over from our object. So we go up, go up, and we go up.
We’re going to come over from this point, this point, this point, and that point.
And I forgot a point. I forgot that point right there, so excuse me.
I will drop that too. Forgot about our one little point.
I almost left it out there. That might help us a little with the curve. That drops to right there.
And we’ve got it over. Alright, so that’s where we need it here. Good. Right there.
Draw the vertical on the opposite wall back there.
Okay, now we’re going to transfer these points across the surface of the curved object.
Start with that one up there. Okay.
Next. Go to right vanishing point. That makes it right there. So we have those two. Next.
Find its counterpart here. So counterpart there, this counterpart there, this counterpart
here, and the last one down here.
Make sure that’s accurate. There. So we’re just
referencing the same idea of this curve now back here. This goes straight for a little
while here and almost hits our point. So what I’ll do is take this driven from the left
vanishing point almost over to that point. Then we’ll allow the curve come down pretty
much from here, through here, estimating that curve at being about that steep essentially.
That one kind of comes through evenly this way. Add that one as well coming through to
here because it has to land here. So now I get more of a connection. I always, again,
like doing off the points like that before I draw the curves so I can kind of try to
organically feel the curve from the little tick points I make or the little reference
lines I put before through the points.
So now we have our back shape.
And the idea is now we’re going to find a centering point
for our—we’re going to set up a square that’s going to represent the plane that’s
going to hold the ellipse for the cylinder we’re going to have meeting. So we’re
going to have like a clock face, like an old mantle clock, the face of an ellipse. And
then there would be a pipe or a cylinder moving in through here. We’re only concerned about
where the seam meets. We know the cylinder will come back in the backside and all that.
I’m just going to set up the basic square for that. So if we want we could do that in
blue. Why not. Just for the setup of that. So in my case I had to pick a center place
for that, so this will be center line here. Really lightly I can put it on. I can use
measuring points if I wish knowing where my SP is. I can measure a real square’s depth
from this height. So if I’m saying I want, let’s say, at almost the same height as
this reference line I’m saying I want the height of my circle almost there just independently.
I’m going to draw a plane like this and say, alright, that’s going to be the height
of my cylinder. There’s the base.
And I’m just going to take this idea here and say, alright, I think about here is what
I want, or I could measure it using measuring points. If I knew where my vanishing points
come to my center of vision here. I have a very light indication of my center of vision.
Make a 90. I can use measuring points and stuff like that. Come in close. So I’m just
going to say my first wall up here is right about there. And I’m going to double that
over so really lightly I’m going to find the center. Let’s do this.
Coming through there, happens to be right there. Just a hair higher actually. Right about there. I’ll
come through and find that. Come through there. Come right to there. See with that back wall.
So now I’ve got my little square setup, and I’m doing it the simple way. Again,
since this is getting fairly large. If you want to create an ellipse just by drawing
it in this contained space or going by hand, of course, we are talking about this being
the center now because we did hit the center here and drive it to here, as you remember.
So that’s the center. We’re going to have that minor axis coming through from our left
vanishing point, so I’ll put that in real light. Going through like that.
That's our minor axis.
Okay, alright. Remember our major is actually halfway between the front and rear side of
that at 90 degrees. Again, we can X this off now.
Let’s just finish that out first.
This is so we’re clear.
We have our center right about there.
Alright, so we have our standing square.
We know four points are going to be here, here, and here, and then if we want
we can just X this off like that.
Find the center there.
Fix that off. Again, I’m going to find that 8th point there.
Remember how we did that. It was to also take this up,
X that off.
Find that 8th point, so what we’re going to do is I’m going to X that off right
about there. Drive it down. So now we’ve got that point there.
Remember, I’ll show you in red we come down now.
A lot of industrial designers are going to go, oh, you don’t
need to do all this. Just draw the ellipse. But again, I’m going to use an ellipse guide.
I’m just going to find those four other points as well and find the major axis. That’s
the way I prefer to do it. You can do it however you want as long as you’re getting what
you believe is a correct ellipse.
That part there. That part now. We have that point. Then we need one more up here by coming
across, as you remember. Coming across right to there.
Okay, so now we have those points. We have these four at the cross and then at the diagonal
X. We got this one initially, remember, from X’ng off this space, getting the middle
then X’ng off again and slightly inside of that. We have the ellipse so if it crosses
here just inside of that we find the spot here. Right here, right here, and right here.
So that’s basically what our ellipse will be doing.
I’ll still draw it out in pencil, though. I just wanted to show the face of it and stuff.
We still have to do our major axis, which means we’re just going to take a piece of
paper and say what if? Have our actual halfway spot between these two areas basically here
and here.
If I just take what I believe is about halfway optically I usually just do that. Get it to
be about there. Essentially something right around there should be where I have my minor
go through, something like that.
And again, yeah, something like that. So that’s where the minor is going. That would be the
real halfway point between the front and the back edge, remember? On the point of that.
Then I’ll put in a real light one. Major, remember, would be crossing the minor at 90,
so I’m just slowing this down for people to construct proper ellipses. Again, if you
want to do yours more based on just the square and a good ellipse, you go for it. For those
of you hand-sketching, that’s fine too. And with just the assistance of a ruler. As
long as you’re doing it accurately to consistent vanishing points and the ideas coming out
that’s fine. But, I’m going to take a little extra time here. So that’s our major
axis, just to remind everybody. That’s about the climax of the ellipse here and here, so
I’m just going to feel it out. I know it comes through here for a fact. I also know
it has to come through the top. Draw that in. I know it has to come through here. Go
to come through here. Also, the climax comes around almost back here,
so it has to come around something like that.

Come around there, so I’ll start connecting those. It has to come around here. Come around.
Comes around there, climaxes at the top. It tends to pull just up there a bit. Come back
down. Comes through there as we crash down into here and then back down into here. Pretty
good. Alright, so I’ll go ahead and draw that in. There’s the end of our cylinder
or a pipe like a clock face against the curved object which kind of looks like a mantle clock
a little bit. We drew one of those a little bit in a very simple form earlier in the lectures
way back in the old days when we were going a whole bunch of one-point objects, I believe.
That climax down there by the major. Come around like that. Okay, it’s pretty good.
Little flat on the side. We can pull it out a bit.
Okay, so there’s our ellipse. And we now also understand that our center is going to
drive back to this way. I’m going to put that in really light, the idea of that. But
now, what I need to do to reference where this shape here would meet the shape of the
front plane of the curved shape, I’m going to make a center section of this curve coming
from right here going straight back. We know this is the center of the ellipse. That’s
a clue to us we’re going to start right here with that curve, and we’re going to
start by driving back from what we know is the center of the ellipse. We’re going to
go ahead and perspective, center of that. Go straight back there to this. Go back up
vertically and that will give us the top of it. We want to replicate that curved section
again. Now we’re up here. Same here. Same back here. That corner, that corner. We’ve
got that corner driven back from here just like these sides on the ground.
Now we’re starting to make a plane from here to here, but we are going to make this
curve because that’s where we have to meet the shapes and have some rectangular planes
and reference points to understand where the new seam is from this new idea here.
So we can do that.
So, what we’ll do is we’re just going to carry back the idea of these same ideas.
Where do they strike? They strike here, basically right there.
I’m striking these ideas here on that new ground plane area.
We’ve got that here and back right to there.
I'll just take those little verticals up before to make the end piece on the far end
to the right. I’ll also take those verticals up.
So now I have to meet them with these ideas, so I come back. I come across. Hit this vertical here.
That plane right there. It makes a point. There’s the back point. There’s the first
mark of my curve. The second one is here.
Let’s go down, across, up to where that meets it.
Down, across, up; right there.
Next one here at this level; down, across, up, meets that right there.
Next one here; down, across, up. Careful of that one.
We meet it right there so that’s my curve.
Here it comes down pretty steeply. Here it’s about
even like this. Here it’s just coming down a bit through here before it straightens out
up here like this, so that curves down toward that one like that.
It comes down back toward this one naturally like that.
This one starts from here and then meets that, so I have to
remember, okay, slowly sloping through here to finally land almost straight right there,
very close to it. Then that comes down, I gotta make this look like that. Almost trying
to guess here where the natural curve would be between these, about there. So there’s
that middle seam we need to gauge off of. It starts here and ends here, and that seam
goes right down as a center plane, same as the center of the ellipse. Let me make clear
what the center of the ellipse is right here. It’s not the major axis. It’s the perspective
vertical center. That plane drives back and becomes this curve as well. So we’re going
to meet different heights with this center from this shape of the ellipse with a tube
and crash it into just the tip of the plane of that curve with different points.
We’re going to start with this point here. How do we find that point as the new position
of that point slightly back for our seam? It’s going to be close. What we can do though
is say how do we find that? Well, what we can do is we can drive it down to the ground,
and we can drive it over to the center. Let’s take this center point here. Drive it straight
over to here to this reference it makes on the center of the ellipse. We drive it toward
that curve a little bit, just a little distance right there just a little bit, and that makes
a plane. We can come back then, make that plane come out, and then meet that plane going
back to our left vanishing point again. The back corner of that plane becomes the first
part of the seam. The seam starts right here flush where the curved shape meets the very
bottom tip of the ellipse and starts curving around. It comforts for a little bit. There
is a little bit of a straight here. It will comfort a little bit, and then it will kick
out a bit here and meet this, breaking away from that. So where this shape, again, the
shape of the tube going through here meets the curve of this object we’re trying to
find different dots to meet the seam again just as we’ve done before.
Okay, I can fill them in the middle. I’m going to take this one of for the second one.
This point here. Just drive that back to the center again.
Meet is right there in center.
We drive back toward the minor axis, actually, until we meet the curve. We make a reference
right there, and we turn from the right vanishing point again, and we come out to make that
plane. Then we close it off by casting this back to the left vanishing point.
And that makes that little point.
Now we have this point and this point, but I probably want some information of where
the seam falls here, where this tubular circle is meeting this curved plane. I’m going
to put a middle one right there and just invent one. Quickly reference the center line. Do
anything we want. We can make as many as we feel we need. We can do anything we want or
as few as we need, whatever you feel like. I happen to think I want to drive that back.
I’m driving it back from here straight back toward the left vanishing point now until
I hit the curve. Remember, I’m going from the straight blue line until I hit this curve
just like I did here, hit the curve, had to come back and make the plane.
Straight up, over, hit the curve, come back. Here, straight over until I hit the curve, came back,
squared it off. We’re using what we could call the back left corners here as this new seam
where this curved object hits the tube’s edge.
Okay, so basically new mark there. Come back from the right, over, and then meet this point.
Back to the left. And that back corner becomes our reference seam. We could even make another
one if we want. We’ll keep going up. We now have this one.
We have that one. We have that one.
Now I’m just going to go ahead and take this point here again. We’re going to slam
it. We already have a line. We can come straight over to the right vanishing point, make that
reference where we hit the center, vertical standing center of the ellipse. Come back
until we hit the curve right here. We have to come back and hit the curve. I’ll put
little arrows in there, but really it’s about just knowing that we have to come back
from the center seam until we hit the curve and then come back from the right vanishing
point to make that plane. Slide over, then we have to come from this point and then go
back to the left to complete the little rectangular plane,
and we get this point right here. That’s another seam.
Of course, now it’s easy. We can make the center just slam straight back because it’s
already in the center right back to the seam.
We’ve got this, and we’ve got that point right there. That’s where it will start.
Okay, anything else? We can have a little arrow on that one if we want. We’re always
going toward the middle. I don’t want to go crazy with the arrows, but if it makes
more sense. This is a plane here that helped us out. This little plane helped us out, remember?
This bigger plane, and this other plane up here again helped us out. We could still use
two more if we wanted to. We have a pretty good idea where this one is going. Just let’s
say we wanted to do one more in the center here. Same game. We take that, go to the right
vanishing point from that mark we’ve put on just randomly slam into there. Change direction.
Go back to the left. Go back until we hit the curve right there. Come back out using
the right vanishing point and cast ourselves forward like that and take this original shape
or original reference mark we’ve made between these two. Now we’ve made one right up here
just to kind of fill in some idea of space, and we came back to meet it. We have one more
point right there. That makes a pretty legible pattern there.
We still want to make it look curvaceous now. We’re starting here at the top where the
very top of cylinder hits. I’m going to make it nice and dark because it’s a shape
going back there, just a little higher like this. It’s the top of the cylinder.
Here's the edge, entire ellipse. We know the bottom is here. Let’s make the curve first.
We're going to start here. I’m going to come through here. I’m just going to make it light and
try to make it really curvaceous. This and this spirit comes over, and it’s just shorted
a little. Instead of coming all the way over back like this it kind of curves and is shorted
having to come through here. I’m trying to make this the most natural thing I can.
Then it comes around through there, back up following the spirit of this curve it would
do something like this. Steeply go down and then, again, fall into this seam right away like that,
probably even faster than that. Let me erase a little bit of that.
There’s the original bottom of the ellipse. This seam would close in pretty fast right
here to the bottom. There it is going to its new seam there in the red.
Coming through a little like this and dipping down, cupping around, turning a little. Probably coming
through like that. I’m just trying to, again, make this look natural. It comes down where
the seam would be. There would be the seam of the cylinder standing right here thrusting
back and meeting all the surface shapes of this curve here where this turned cylinder
meets them. So that’s how you figure that one out. You could do the other side if you
wanted to. The same idea. You just take the center plane of all these points and double
them over if you wanted to. The idea would be—let me just draw the little planes I’ve
got here. All these planes we have for reference, actually, all you’d do is in perspective
double them over by X’ng them and doubling them over. We would find the counterpoints
over there. I’m not going to bother doing that, but the other side of the curve could
be found by just doubling this over, doubling this over, doubling this over like we’ve
done many times. I don’t want to take the time to do it because, again, since we’ve
done a lot of doubling over with them mini shapes since arches and all the stuff we did
in between, that should be pretty easy to find that same counterpoint sliding, coming
down over here. It would end up right here again, and then come back to the other side.
So you just imagine obviously this entire thing as being transparent. Double all these
planes over, and then, of course, it would start here and end here.
Double over and all that.
Let’s draw the ellipse in nice and dark or the tube. Okay. It comes around like that,
in like that. We’ve got a nice dark seam. The new seam we’ve made by our red reference
points that we’ve circled. It comes back around that. Of course, we have our two edge
shapes here, and then we had our middle seam there, which helped a lot. We can shade in
our middle seam really lightly if we want, which was important. I’ll do that lightly,
not to be too obnoxious. That’s very important that we meet that middle seam, of course.
This middle seam is very important so that we can make all of our references back from
the center line, the vertical standing center line of our ellipse
as we’ve pointed out many times in blue.
So there is that idea.
Remember, we had all these reference lines from the curved drop go all the way back,
but we also intersected on that curve to find these points to make the curve. We made our
standing ellipse. We met the center here. Then we came out to find our edges. We got
our edge reference from coming here, but having to come back, meet that same height of the
curve. Once we had the height we could bring it out to the same plane as this, going back
to our left vanishing point. We found our back left corner and got our seam in there.
So there’s our seam for our cylinder hitting our curved plane as promised. There we go.
Okay, then we’ll darken in the object a little just for good form at the end of the diagram.
Just good, straightforward pencil. No big deal. Nothing wacky or fancy.
Then we have this outside edge too. Might as well do that. Just get used to having heavier line
on your actual object in a sense, a darker line, a little heavier line on the outside
or important parts of your actual object. Everything else is planes, setup lines, whatever.
Okay, so there we have it.
A cylinder touching a curved plane and the new seam that’s created
from the two shapes meeting each other. I believe that’s everything I wanted to do
on that one. Don’t forget about your minor axis and your major, you know, the true half
of the real front and back edge of the square or the idea of the front and back edge of
the ellipse. The true halfway point is the major axis here. This is always at a true
90, so let’s make sure that’s obvious. So here is the minor crossing the major, the
true halfway point between here and here is about here. Then you have that true 90.
Okay. That is it for that one.

We’re back and right now we’re going to—actually, I’ve kind of pre-drawn this idea lightly.
We’re going to have kind of an extruded cylinder through an uneven ground plane or
almost like a thin plane that’s uneven so we can see how it works now vertically. We
kind of did a cylinder into an uneven surface kind of moving in horizontally last diagram.
So now we’ll try like almost a whole being drilled through on an uneven surface. We’re
going to box it or surround it by a box just to try to get the logic.
What I’m going to do is I’ve started the idea of a box. I’ll show you how.
I'm drawing the idea like this, so I’ll just kind of start it like that.
I’ll make the top of the box basically like this.
So it’s down from the eye level. I don’t know if
you can quite see the eye level. If it’s not it’s right off camera or right at the
top of the camera here. Go down a ways, as deep as you can without getting distortion
here. The two vanishing points. We can see some of this top plane here. I’m going to
come down with my verticals here for my corners real quick. It’s the quick idea of a box.
So while you watch me get a start here and you jump in then and pause and build, catch
up. Then we’re going to close this little box off here, about here, just like that.
We’re also going to run the transparent. We can still see the backside. We’re going
to run the backside across and make the back corner obvious as well. The back corner is
about there. Go ahead and raise that up.
Now that we’ve got that box we’re also then
going to set up the idea of an ellipse, kind of a cylinder in here. What I’m going to
do is kind of feel out the box that I want for that cylinder. What I’m going to do
is put again, get in here and do this and draw the idea up here like that.
Come back.
I’d say my 45 is somewhere around there so I’ll shoot it through there. The idea
of the corner being about there. Close it off.
Then I’ll X that.
Right in the middle right there.
Drive that middle back to the back wall of the box and to the front wall
there. So we’ve got two references here and I’ll also go through the X in the middle
to the vanishing point to the left, drive that there. So we’re getting this type of
idea. We’re just taking the T—not the diagonals; we use the diagonals to find the
middle. Once we find the middle we take the T all the way to the edges of the box on the
top. We’re going to drop those vertically. We’ll also find them at the bottoms, so
there’s that one to the bottom right there, also this one right there.
That’s side one there. And then this one there like that.
So go ahead and pause and take a little bit
of time to catch up. Then we’ll just close it off like this. Or you can follow me all
the way to this point and close them off. Then leading to my left vanishing point as
well. Close that off like that. We know now the middle shaft or the minor axis of the
ellipse actually goes through like this. I’ll go ahead and use red for that. It’s always
easier to remember the minor axis if we use a little bit of red here from there to there.
It’s our minor axis if you want to make note. We’ll extend it up a little; call it minor axis.
Alright. We’re setting up for the idea of that box down there. I'll first draw my ellipse
out on top based on just these ideas.
Carefully look at my four points here: right there, right there.
And I know my major axis comes through, so I’ll just be clear about that
to be consistent. We know it’s a little bit in front of the perspective center, so
I’ll just put just a tad forward, the idea of that thing.
So we have the minor coming up through the shaft all the way through the top of the pillar.
We’re going to make and ellipse now. There’s my minor. I’m just going to kind of feel
it out like I know it touches these four points.
Try to feel it out and just feel it out.
I'm not going to do the other point. I’m just going to try to get the right feel to it.
Coming around like this.
It should be about even to that, so it should be coming right around there.
Alright, so tap that one away a little. There we go.
Alright, so we have again those four points right there.
We have our other ones here.
Our diagonals, we found them here. We have one here, here.
Those are other points we can be interested in dropping down when we need them.
So we have our T points here.
Just to make it clear and blue, we have our T points here.
We also have our diagonal points of
the ellipse that are around here, basically. Just the idea of dropping those when we need
to. We know the middle shaft comes to here. This comes down to here. We can see the edges
of the ellipse. All I’m doing is I’m basically just taking this idea and dropping this points
now, the basic four points of the T first as we’ll do together here
down to that area on that T.
Drop the first point here, straight down. I’ll make a mark right there. Drop the second
point here just a little bit in front of that one right there.
Third one there.
Alright and fourth one is about there.
So what am I doing? I’m dropping—let me make it more obvious.
The T that exists here across to here I’m dropping that down to the referenced
same plane as they come down to here. Now I have that same relationship with the ones
in blue. I want to look at it that way in blue. I can also square that out a bit.
I can get my diagonals. If I want to draw the square around that I can do that real quick.
I might as well have them come and meet the edges too because we’re going to be referencing
up the side of the boxes because we’re going to add a blanket shape, almost like a curved
shape, which I’ll explain after we kind of hit the cylinder here and make it a complete
shape at the top and the bottom. Have that coming through there. We’ve got that square
shape here. We’ve got our box. We can max our diagonal like this.
After we make our diagonal we then drop our other points pretty much like this.
Now, we can take our points in red up here and drop the idea of those here, here, here,
and here. We can drop those straight down as well, reference those down to our diagonal.
I have a decent idea of where those go.
Now we kind of have our eight points so that’s pretty obvious.
Again, we know where our minor and major is. We know our minor is here. It
goes through a little bit. It shares the same one with the top. If that’s the perspective
center I want to just make sure I understand and communicate that we’re taking it slightly
forward then our major axis like that. No big deal, just wanted to be official.
We’ll take these four points now along with these other ideas of the eight points drop.
We should be able to get our ellipse filled in fairly nicely here quickly, like this.
Alright, so we’re just going to fill that in as the bottom of this cylinder. That’s
at the bottom plane of this box. We’ll explain further what we’re doing.
The main thing is that we know that there is a solid idea of this cylinder going down.
I'll do the sides even just like it’s made of pure substance like metal or something. We see the edge of
the ellipse on both sides then draw that in. Also see the edge over here. Okay.
Then we'll still drop those other, use these other reference points as we know.
Now we’ve got a box obviously and we’ve also referenced the relationship
with a lot of these things. I’ll go ahead
and put a couple more relationships like this and like that going back.
We get the idea here.
We’ve got a cylinder from the top to the bottom of this box shape. What we’re going
to do now is add an element of a kind of random curve shape from each corner of this box.
We’re going to say it’s almost like a piece of paper. I’m going to draw the idea
of this thin piece of wood or a curved uneven ground surface going from corner to corner here.
So there it’s touching that corner. It’s touching the back corner. Here’s
the back corner of the box here. Then I’m just going to do something,
and I want to bring it up like this like that.
It’s going to have a little bit of an indent here. Come
back down. So now this is the back corner of the box.
This is going to the right side corner, left side corner, back corner, front corner here.
What we’re going to do is see when this cylinder
crashes through and meets the surface of this uneven wrapped kind of
floating Kleenex shape. It’s going to make a particular shape and a new edge, obviously,
the edge between the plane that’s uneven and slightly curved and rolled compared to
the cylinder slamming through it.
Again, we’re stuck in a position where we’ve got to reference our way out of this. One
way to do it is to take the center of our bottom here of the box and also the center
of our ellipse here and here on this side. We could say, oh alright; we know this is
also touching here, touching there, back down over and touching here and touching there.
So now we can kind of describe with the line the shape we think this makes at the crossing
of the T that we design going through as planes through the ellipse. The T shape here and
here and here going through and touching the box. We can kind of draw a line of what we
think the pattern is doing from here to here. I’m also going to draw it over like this
and say I think it’s making a shape like that. I’m going to draw also a shape through here.
Now this meets right here. This is where in our imagination if both are transparent
and can move through each other. This is where the center shaft or the minor axis shaft of
our cylinder is actually touching the very center or crossing of those
seams I’ve put on this bent shape.
We also want to find where the other four edges of this touch. That’s pretty easy
because, again, if we use, let’s say blue, we could say, well, if I know this plane here
represents the cut through the center this way going to the right vanishing point over
there, I can identify where this crashes into this plane. So here is the center T plane
of our ellipse shape or our cylinder, right there. So where this crashes into it and meets
that is where the seam would be at that point. It would be up this far because this plane
here with our shape crashes into this plane coming up here. It makes that point there.
You can say this is in a sense a plane we can say helps us find that there. I just happened
to use it that way. We could go the other direction, but it seems pretty easy.
Then, of course, we could also say the other thing is we know that this projects from down
here, or this comes by. If we follow the center here down, straight through and up, whatever
we want to do, and come down; it seems like this center seam then comes forward and touches
that seam right there. Again, we could say we’re using this center plane here to find
where that touches there. That’s not going to be visible if everything was opaque. We’re
seeing that little plane we can see there. Now we can do the same thing with a side plane.
It’s pretty obvious. If we note this plane going through that goes through to our left
vanishing point as a plane, across, all the way in itself, we can use the miniature versions
of this to find this point. Come across, up, and rise up until we hit that center seam
right there. There’s another seam there.
That’s another little plane we could say we were using.
Again, on this side we can say, oh that’s right; there’s that side going to the left
vanishing point. There’s that side going up the plane. And then, oh right, this center
going through there, dropping down, comes through and touches this right there. It’s
on the other side. These two points are on the other side of the ellipse,
or I should say the cylinder.

And that is still a helpful standing plane right there. Now we have those four. Now we
have to find our other ones that are going to be in our diagonals. There equal to that;
drop that straight down; down, straight down, straight down.
This one is right down here, also that on the diagonals or the X.
Let’s just find out how do we figure that out?
Well, we have to follow the pattern that has already been set by the seams we already set through
the middle. And with the help of our edge we can kind of take an educated guess how
we think that works. Let’s just try and say—if we wanted to we could say if we took
this idea here and came out to our edge like this, went straight up.
I’ll use red for those other four points we’re finding.
Go straight up, just to be official here, until we find this point.
Now we know the edge of this goes right along flush with the whole box. So that’s a point
at the edge here that is parallel and moving to these planes here. So now I have to figure
out how would, if I made another side of that little plane come straight up and connect
these two ideas at top and bottom real lightly this. Make sure it’s accurate. I’ll kind
of make it go up like that. So now I have to say to myself, yeah, how would this pattern
behave at this point coming in? It’s not going to arc as high as this or be as low
as this, but it’s kind of changing and shifting a little probably like this. I’m going to
say, alright, it’s kind of doing something maybe a little lower like this. And it strikes
that plane there or maybe a little lower like right there.
So I’ll just say, okay, that’s where I believe the seam of this would go across maybe
here a little bit and keep going. I’m not sure where I’m saying it’s going to go.
We could then come across to our other side here and keep going and saying, alright, what
we’ll do is we’ll keep going with the idea of this plane between them here.
If I came straight up that way too, where would it meet that shape if I continued it over
here to my left vanishing point all the way to the edge over here, raised it up? I know
it meets the edge over here way on the other side. That shape looks something like that.
Kind of over there doing something like that. It would meet over here. Or, would it be a
little higher. We could say, oh alright, well maybe this actually raises up and raises to
there. Maybe it’s here. So I’m going to say, nope, I think it raises up more.
That’s what we’re saying. We’re just guessing what the surface is doing as we’re
crossing it. There is that plane. I’ll say it does this. We have this plane moving over
there. We have this little helpful plane to that one. So now we’ve got what points coming
up. We’ve got this blue point for the seam. This one.
That one over there. You get these back ones.
Let’s do that. We can still do it to the side if we want. I’ll come through.
There we go. We’re going to go all the way through this one and this one and continue onto that side. We’re getting
those other X points there by just using the side to side referencing. I’ll go ahead
and go through there to the side wall. We’ve got to go up, crawl up the side until we meet
our edges which are here and over there. We can crawl up like that
and meet the edge way up there. That’s raised quite a bit. But, that’s just on the edge. That’s not a
reference. We have to go back and identify our reference, or we eventually make our seams.
It’s the thinking we can do, the complex thinking and not losing track, which corner
of our planes is actually saying it’s the connect-the-dots pattern for our new seam
where this cylinder crashes through, drills through, and meets this kind of uneven plane.
You have to be able to think complexly and not forget which plane leads where with your
work toward the vanishing points and going up. We’re just going a bunch of standing
planes along with points and rods with beads on the end to get our referencing.
So here we go. We have to imagine how these two also connect across here, coming up, coming
up, and then move across. We can say it’s kind of like that, probably. I just want to
say it doesn’t behave all that different, so maybe it’s something like that.
So now I can come up vertically from those points directly here, straight up, and also
that other point right there straight up. Now, where this comes up and meets that plane—cause
that’s where we said the seam was working, just like this one works down here, that’s
another point that our seam will wrap around this cylinder with from our object here.
Then, of course, if I go up from here, over, and I follow that over, I go straight up and then
we went in the back. These would be invisible again. It’s okay. We’re going to treat
the whole object if it’s transparent.
So what we have to do now is identify that’s the one in back. Right there. That’s another
one on the side here. We have another one here. Let me tone in these planes. Not to
be confusing. There’s that little helpful plane. There’s that little helpful plane.
We’ve got this one, this one in red, this one here, and let’s not lose ourselves over
here. We’ve got this one here. As the red comes up and meets this seam moving over,
we decided it was going to be here. Those are those four on the X. The X points raised
up with planes. Now we’ve got our blue points we’ve already done. We come over. We found
that one there. Come back over to the back one. It was way up there. This one across
and up is right there.
So now we can ahead. I’ll just go ahead and use my pencil now and draw in the seam
as I see it. It would come, bottom point would be right here and would raise slightly to
go through here. I have to remember it’s going to be a rounded shape somewhat, so it’s
going to be a little awkward to try and find at first. It’s going to be coming way up.
We’ll do that. On the other side, come up, meet that kind of as a spiral shape. Come
up and meet that cause it’s still rounded. It still has to follow the idea of the cylinder
driving through it. Then also it comes up the back, meets here. It’s a little higher
I guess here and then has to dip down to meet that. I’ve got to make the shape make sense,
reminding ourselves that it is a cylinder shape, a rounded cylinder shape moving through
this uneven surface. It has to still represent both the uneven surface but also the nature
and the trueness of that. There it is.
So that’s basically the shape I’m getting for moving through that. Let me make it real
clear. So here is our bottom ellipse with the bottom of the cylinder. Here’s our top
ellipse. Here’s the weird kind of elliptical kind of shape that is made when this shaft
of a cylinder drives through this random plane that seamed like this and kind of surfaced
as we crossed it. We could even put some more planes on here and move like that. Guess what
it does there too. But the main thing we want to catch these eight points and these eight
points. You can just think of them as dropping down here. If you need to, slow down and go
back again instead of crowding the entire diagram with tons of arrows and everything.
The advantage of these high-def lectures is that you’re doing your own version. If you
want to put arrows and broken lines and descriptions of what you did first the big idea—we’ll
talk about it in a second to review—it’s important to review. I just want to get this
in real dark and even. There’s that new shape created there inside that with that
cylinder driving through.
I’ll go ahead and tone it in with blue lines going this way just to remind us what we have
here. Kind of the direction we’re moving for the pattern anyway, like this. Anyway,
that’s the hole we get through there or the ellipse. Let me the do the outside darker
two of the cylinder so we can make a really clear idea of a really distinct shape there
that’s thick. So this edge is thicker. Draw the outside edge of the ellipse nice and dark.
And then we’ll go through step by step what we did. Define that. And there’s that uneven
shape there so both are moving through each other transparently.
Okay, so the big idea is that if this wasn’t transparent then clearly the cylinder would
be in front of the uneven ground surface until right here where that wrap would happen. But
if it was transparent we could see that that seam connects all the way around or roughly
like that with this cylinder slamming through this curved shape, which we’ve basically
described the surface. We’ve kind of improv’d it, but that’s the feel we wanted to get
to it. Of course, we have the box around it but I’m not going to darken that in because
the real two shapes we’re concerned with are the top and the bottom of the cylinder,
and the entire curved, kind of floating Kleenex shape. Then, of course, the new seam that’s
created between the curved surface hitting the surface of the cylinder here.
So what we did. We made a box first and we boxed out our first idea of where we wanted
our first size and degree of ellipse. We got our T first, our T shapes. We put a diagonal
through. We also got the diagonal by getting the middle. Actually, in reality we did make
a box shape guesstimating where the 45 degree vanishing point was between the two vanishing
points out there and just made a basic guess at a square. That was with this original shape
here just to remind you.
Then what we did is made a diagonal, and we found the center of the square that was going
to turn into an ellipse. We made our diagonals. We made our T. We extended our T to the edge
of the boxes. We created the box first as you remember, and we basically created this
square with X’ng and a T. Extended the T to the edges of the box to start dividing
basic planes. We then made sure we understood how the ellipse turn and find the eight points
by just guesstimating from the crossing of the blue marks, really, and then we formed
the ellipse. Now we understood where the diagonals touched the edge of the ellipse. We drive
all eight of those points down to the other side down here, taking the minor access and
finding that box down here and then matching those eight points down there and creating
this ellipse. So we just had the box with some planes referenced from this top square.
Then we dropped down the idea of the cylinder shape itself to the bottom ellipse, and then
carried these eight points with us. We basically had this ellipse and this ellipse working
fully with the edges of the shape of the cylinder. That’s all we had was that and the box.
Then we completely randomly connecting all four corners of our box with this kind of
floating tissue shape made with might be really balsa wood flap or some type of aluminum.
Really thin. This random shape. Then our interest was how do we put seams to that shape lining
up with the reference planes we’ve already put in and around the box extending from the
ellipse, the minor axis and the crossing of the T’s and the X’s. All that stuff helped
us with basically making what we felt the surface of the Kleenex shape is, and that
helps us start to reference and be logical of where that shape would meet the cylinder
turning because of the lead we got from the outside shape of the curved idea, plus the
solidity of the cylinder. Both come together as a logic, and then we can start referencing
off the sides of the box, this imaginary box, because that is the perimeter of the floating
piece of Kleenex basically. We can come and find the seam.
So we just imaged what the seam would do and then met with transparent planes here. We
just met the idea of those eight points of the ellipse being raised for the cylinder
to meet those seam points. That’s how we connected the dots, the seam points at the
edges of those standing planes became the points. We connect the dots and made the actual
shape of the seam of where the cylinder drives through and meets the surface of the curved
Kleenex shape or that kind of balsa wood or aluminum shape.
Again, if you’re getting lost in this go ahead and just play it over and just keep
constructing and taking your time. Pausing and making sure your reference planes are
logical. After we set the big shape of the cylinder in first in the box. We had both
ellipses working. We dropped the eight points to the ground. We had all of that working.
Then we put in our random shape to corner to corner. We know that these edges are flush
with the edges of the box, and we started our reference planes and our heights in findings
those points which we eventually connect the dots, and we get our actual seam of the Kleenex
shape or the randomly bent shape. It could represent uneven ground. Anything like that,
like some kind of cylinder going through uneven ground. It can even be the idea of like a
golf hole coming through, you know, a golf green, and that’s where the hole or the
flag goes in. Any idea like that is this perfect cylinder being driven through this actual
surface. By just guessing what those surfaces seems are doing we can meet up and match our
referencing and get a very good idea of what this seam would look like.
Again, how much you have to use this stuff will just be contingent upon how complex of
a drawing you’re doing. If you’re inventing things or drawing from something that gets
fairly complex and you just want it to look basically right you can use just a few of
these planes to get your guesses right about the two seams meeting, the two intersecting
planes and shapes meeting each other. Or you can use a lot of them. It’s totally up to
you, as you’ve seen in the last few examples, all the way through the arches and curved
shapes and intersecting planes. You can use a little or a lot of stuff, depending on how
much you want to get an idea of how that seam would really meet. But the perspective does
make it very, very accurate just like the 3D programs. If you’re accurate with your
perspective, and you’re clear about your referencing and your reference point and your
standing planes and corners, you’ll get a very accurate representation of what a seam
would really do in real life with these two ideas actually meeting.
Okay? So that’s the point, just getting familiar with it. But please, take your time
to write your notes and these steps for anything you don’t understand. Use more arrows than
I have. Make the planes really clean, and the idea really neat with A-B-C, 1-2-3 explanations,
as many as you need for that idea. Some of these kind of references get kind of intense
until you kind of get the logic of why they work. Then it becomes easier and easier.
Alright, so we’ll go on to the next diagram.

Here we are. We’re back for another shape that I’ve kind of sketched out that we’re
going to go through. It’s a big curved shape again, and we’re going to have another shape
that is also curved like a flat plane going through. This time it’s just a little bit
different with a little bit different kind of setup than we’ve done before just to
hit these different things with variables. So if you have any questions about why these
planes and why two intermeeting planes or intersecting planes would behave like they
behave with the scene that would be created, or in this case we’re kind of saying that
the simpler curved sheet shape that we’re going to do is going to be kind of possibly
cutting away a section of the rounded shape. But really what we’re doing is we’re looking
at the scene that would be created by both as before.
Okay, so let’s get going. What we’ll do is I’m just going to sketch out the parameters
of the basic box, the rectangular box that I thought would be the right shape. We’ll
do the front edges of that and meet it kind of here where mine is. This is kind of my
center of vision, really lightly drawn in. My horizon line. My vanishing points as usual,
so we’re just going to keep this real simple. I’ll put a slight edge at the front of that
box just to kind of contain it as an idea, as a little transparent box there. We’re
going to make a back edge, also come up from back here. And a little bit of an edge over
here, and that’s where I’m going to say how far back they go like that. I’m going
to take that corner and this corner and this corner. There’s the front corner. I’m
going to cast that back to the left vanishing point for the back right side. We’ll also
come back and do it to the right vanishing point for the back left side. I’ll draw
in a light back corner as well, which would come up just about here somewhere.
All we're doing is assessing the place we want this shape like we did in the last one to have
a shape kind of fit the contours of a box and then come in to it a little bit in this case.
I’m going to start with a shape this high in the back corner, and it’s going to come
down to here, and it’s going to come down to this corner. So I’m just going to randomly
do that so I’ll go ahead and carefully draw what I want. Okay, so that would be that.
This would be riding right alongside the flush side of the backside of the box as well.
Also, this one will come down and make this side come down like this
right to that corner. So it’s going to come
down like this, and we’re going to seam it across and over this way. In this case
we’re going to pick places we want to do the seam. We can say here. I’m going to
make a seam here. Before I do that what I want to do is I want to make sure I have a
plane for that seam. What I’m going to do is I’m going to drop down to the back corner
and come forward to here. Now we know that seam from here to here will be properly
lined up along the same plane.
Alright. So there’s one seam line or section of that curved shape there. Then at the bottom
we’ve decided to break away. Now I’ve going to decide if that’s flush to the box,
what am I going to do? I’m going to have curved edge and then come back and meet this
over here. So this is going to be flush then I’m going to start breaking away and say
alright. I’ll come by over here.
Keep going...
all the way back to there.
I’ll darken that in a little more.
Make that real clear. Just trying to bend myself around that, getting
in the way of the camera. Okay, so that’s that basic shape. Now, we kind of have this
shell shape here. That’s the back arching back fitting in the contours of the box. It
breaks away from the contours of the box. It swings around and ends up back here anyway.
Then I’m going to take a section here, and then I’m going to drop that idea down. Straight
down to the back seam again. Just an idea of how to make a sectional reference plane
that we’re going to be using in a little bit here. Drop the idea of that forward. Then
we’re going to meet it right here. This all connects up just like this all connects
up. This time I’m going to throw it forward like this.
Then one more seam I’m going to put about here.
Drop that straight down as well to the back seam, back corner.
I'm going to come forward like this. Notice that it hits right about there.
We’re going to then come forward with an imaginary seam or section that would follow the surface.
All these sections obviously the top line is following the surface description of the piece.
We can even put another little one right here just to make sure that that makes sense when we
do the seam of two objects meeting. We haven’t introduced the second object yet.
We're just trying to get this simple shell shape clarified.
Say that hits about right there, coming forward from there.
Again, we can do this.
So we could say all these lines follow the contour of what we’ve decided the surface
of the shape would be. That’s fair enough. We’ve done it before. Now we’re going
to introduce the idea of another shape that is starting a particular position, and we’re
going to use the back wall of the box here, the back plane here. We’re going to put
a curve in it. That’s another shape. I’m going to do that in blue just to make these
things a little clearer. I’m going to say that section starts here. I’m going to make
kind of a random curve that will end up somewhere down here. I’m just going to say that is—we’re
going to have a shape that comes through this like a straight plane that’s curved, cutting
through this shell shape. I’m going to do the backside of that curve right now.
It's going to end right there on the corner of our box here a little bit up. Then I’m going
to cast over to my right vanishing point and come forward from that saying it comes into
space this way. This comes into space forward like this.
Now we’ve got to decide how do I match this on the other side if it comes forward and
meets this box plane here? Then that comes forward and makes a plane all the way to the
front like a rectangular plane of our original box. Ends here. This side of the curve down
here is starting there. Also, that’s easy because I know that that plane is out there.
Now I’m going to drop a reference line here to find out how to find the other side over
here. I have to drop, make a plane, come across, come up because I do want the other side of
this curve to still be flush with the other side of this box so the actual curved sheet
shape kind of like a big curved blade comes from the back side all the way forward. Its
curve is flush with this whole plane here going off to the left vanishing point. So
what I’ll do is I’ll drop a little reference line down from that original beginning shape
of our curved shape and say, oh yeah, that’s right. I drop right down here I can come across like here.
Make a reference there. If I come up I get the fact...
that originally went down. Across, up. Down, across, up.
Meeting up with that line right there give us our other idea. Now,
we’re just going to use the other planes as we know that we already have in pencil
so we’ll go back over them and be able to figure out where we find those. How do we
do that? What we do is we notice that the curve now hits this first reference plane
here on the backside right here right above that line. Curve moves through that like this
on the back wall and intersects that. We now know we can project this forward to meet up
with drop down, come back over and meet up with this curve right there.
That's what we’re looking for because it makes a plane. We could say, oh, well, that plane comes all
the way over and up and over, but we’re really interested in knowing this curve already
describes the plane as a hole through our original shell shape. We’re just interested
to see with this height here comes over and intersects here, and then also to continue
on we need that plane to continue over and up.
We’ve got two ideas now.
We’ve got the idea where the curve comes down for its second
point right here, but we also know with this plane of the curve is going to intersect this.
That will be important as well. Let’s finish out the curve and then we’ll go back to
the idea of how this is going to describe a scene from these different points where
this curve and this front curve intersect with those sloping shapes.
So there’s my one point. We could call this zero. That’s on the other side. We can call
that 1. We could call the next one 2, which is back right over here. This curve hits the
next plane. Here, right back here, a little above that line. We can cast that forward
again from the right vanishing point. Just like that we can go down in the ground over
all the way to hear if we want and up until we hit this coming across.
We know that that’s the second point here. Zero, 1, 2; that’s the counterpoint to there. One, zero.
These we did first. We’re getting these second. Then again we could come across. Get one more
shape if we wanted to from this convenient section. Where does the curve hit that section?
This section right here drops down. So the curve hits there on the back wall.
It hits that section there. That’s the height we’re looking for. We know we can drop down. Come
way over. Come back up and come over. I’m going to come over from that point. Shoot
over here. Follow this point across the floor to here. That makes a plane. That makes the
other side of the curve, the counterpoint number 3 here. We can call that 4. We already
have 4 here. We just made 3. Now we have that reference over there. Get used to the idea
of why we’re looking. We wanted this curve, remember, to be on the flush side of this.
But it also interrupts those shapes, which we’re going to get back to in a second.
Those will be where our scene happens in our cut through this curved shape cutting through
and seaming into that shell shape.
Let’s go ahead and draw in our other side of this now from here to here to here to here.
We’ve got our other curve so I’ll go ahead and put the drop there. I’ll just kind of
plan out where it goes through. It kind of feels natural, meeting to about here. I’ll
close that off there. That should fall about like that and keep falling through there.
Basically like that. We’ve got our front side of that curve now, that curved plane.
There’s the end of it so I’ll make it a little more clear. Make that thicker here
just to make it clear, and then the top plane is this, of course.
We already got one section coming across. We got the other section coming across, this
section coming across, and this section coming across. We even put another little one we
could put I if we wish to meet to understand the scene better, but let’s start with the
scene first. Then we put a little extra one in here to help with the scene, but we’ll
explain that in a second. We already said, alright, how about this first section? We
already know we’re starting the 2 seams meeting here because that’s the highest
point with this curved shape from the shell meets this new shape intersecting it. The
idea of these two shapes existing together—what are we going to do here? We’re going to
look and say that’s the first point we’re interested in for part of the seam of these
two shapes, or what would be cut out of the wood if we had this move through and shave
out a piece. More importantly it’s the seam of the two stuck in together. If these things
were fused together like a sculpture then we’d be looking for the seam. We’ve come
down from this part here first and foremost.
We made that plane to come across to here.
Now, we come down to point one and say one goes across here, comes down as an entire
rectangular plane. That’s how we got the other side to curve. But also, it interrupted this.
That’s going to be the first part of our first part of the seam.
Then we can talk about this plane coming across here in making that. Instead of shading them
in I just want to refer them, you know, pretty clearly that we’ve come down and we’re
coming across here. Not this blue line for 3. The bottom of this one is a little bit
above it, as you can see, and comes across to here. That plane there. So where does that plane hit.
This scene from the curve right there because this plane interrupts this curve
for that plane right there. So it’s cast forward, cast forward, and interrupts it right there.
Number 3 as well we can figure out. There’s that plane for number 3 going like
that, or does it come through and interrupt that same curved plane that it’s on.
Right there. Then I’ve added another extra one here.
What we’re going to do is we’re going to drop down and say, alright, where does
that hit the little curve? Right there. Keeps going down. Comes up. What we’re going to
do is that’s going to come all the way over to here and we’re going to come up to the
other side. We’re going to fine the other side of this little plane.
We’re going to hcome across and come up.
We’re going to meet from the right vanishing point and come
over. We basically have this little seam here.
Where does that hit the curve? That comes across.
We’re looking for on this plane, that section of that.
Where does this part of this curve hit that when we come across from this point here?
We can call that 3.5 if we want. No big deal.
That comes across and hits it right there. Then we know where
does number 4 line up; that’s on the back wall and comes up in this little corner. So
we have to thrust 4 this way right over here and hit this last point with a little arrow
right there. That’s the last point.
That’s going to be contacting that. The scene that
would be created from the two would start right here even though the sheet shape that’s
curved comes a little past that to here. That’s where it actually contacts this. We’re talking
about now this, this, this, this, this, and finally right here.
That’s where the seam between the two would be. We can draw it out.
If you want to call this 1, 2, 3, 3.5, and right there is 4.
We’ll go ahead and do that with a pencil actually.
Just draw the seam in. We want it to be kind of rounded and organic
looking. What I’m going to do is I’m going to start from here, kind of round it around
and feel it out through the shape so it looks like a natural kind of flowing spooned out
shape like this. I’ll adjust it as we go. It kind of comes around sharply, comes down here.
Cuts through there. So we’re just doing what we’ve done before, trying to
make this feel natural. Meets up. Comes right back like this.
So that’s my best guess that this comes up a little further like this.
Comes down through here.
So there’s that shape.
That’s basically the seams meeting each other right there.
We’ll shade a couple planes in.
I just want to make this clear and flush it out a little bit. That’s the seam.
So if we were meeting this curved shell shape that originally went through again the
back wall, back wall, back wall, we said this random piece came through it. We’re just
trying to further our conceptual understanding of the fact that when these planes or these
different sections have the two ideas coming out and meeting is that seam right there;
it’s where the two would meet. Especially if that was carved out like that.
That's where it would be. This would be—if this was a solid object this flat object would
be in front of or covering that, but if they both transparent or we were looking at them
from another angle or whatever we were doing, that would be the shape of the seam or where
this is actually touching, going through, and carving through this shell shape.
So the blue shape is a curved blade that’s carving through and making this section as
it comes through and reappears over here. So it’s just the idea of what our concept
of this thing is like this. We can take a little shading.
So there’s the seam line of the two.
I wanted to give examples of just slightly different ways each time, but these
ideas of sections using straight standing in different rectangular sections and reference
points on various corners and ideas running through sections can give us the actual new
seam between two complex shapes. Again, we’ve done a few of these but it’s really that
artists aren’t going to do this exact kind of thing that often. Again, designers have
to do this much more and this happens in the 3-D much more now. But, before the 3-D programs
this type of thing had to be drawn out in sections if it was to understand what a real
thing would have as a seam. It was importantly visually in understanding the construction
of real objects. What we can do as artists is use a little bit of that and some of that
sectioning to understand when two or three things are meeting and possibly a sculpture
or, you know, doing a car or a luscious shape with a lot of intersecting curves, how do
we figure out what those seams are between those two basic shapes we’re combining.
This can help us understand that.
You can use less sections than we are here or more. Again, it’s totally up to you.
These are the concepts that we’re getting down permanently with these diagrams. What
we’re trying to shoot for is just the concept, so let me darken out the idea
of this original shape we had here.
It comes forward.
So that was the original show we had. Then in blue,
of course, we have this complete kind of sharp almost piece of tin or sheet metal that cuts
through the shape, and then we have the seam where the two meet right there, which we found
by reference pointing and standing planes, based on our original sections, which we used
to seam off the surface of our shell shape. That’s really the point.
We have our original shell shape with its seams. We then have this shape cutting through
on the contours of the original rectangle or this front and back side basically going
up. It goes a little bit short of being at the back of this rectangle because it starts
here, remember, on the curve. Not all the way back to the back. That’s the shape where
they’d meet. So it’s just an interesting kind of analyzation of how these two things
with meet with the seam or what the spooned out shape would like if it was cut away.
The blue knife, if you’d call it, cut away a section of this shell.
Okay, on to the next.

Hello. We’re back for another curved object. We’re going to start out with a flat design
on a cube or a rectangular shape, and then throw it back to curve. So we’ll just kind
of start it. I’ve put it in lightly here. The idea would be if we were looking at a
top view of a simple rectangle. We’ll just say that this is a top view.
Right there, we actually will be putting a curve in.
Something like this,
meeting in the front then having it come back out. Something like that.
What we’re doing is we’re having a flat design in front,
which we’re going to do in blue and carry that design to the back as a rectangular
box so that this kind of curved, organic bean shape will go from the front plane to the
back plane. But they’ll be flat. Then we’re going to project that bean shape back to this
curve, which we’ll draw in red, so that we can see how to project an idea as a flat
shape against the side of a box and get that curved surface even though we want that shape
to remain flat for the back shape.
We’re going to start with both flat on the front and the back. Then we’re going to
project back this simple design from the front to this curve, project it back like this.
So we’re going to remain having the flat design as the bean shape in the backside,
and then have the curved shape in the front side by just introducing a curve to the rectangle
as we go here. So not unlike what we’ve done before, but just in a slightly different
way again. So what I’ll do is here is my horizon line so make that clear again.
Horizon line, eye level.
Then we’re just going to draw out the box generally. And at first it’s just we’re
trying to feel it out. This could be an object like a camera shape. You know, anything we’re
designing. So what I did is I just kind of came up with parameters of how long the box
would be like this. Decided on a front corner.
I also projected back to see what kind of
depth I was talking about. So you go ahead and draw a box too once we do it.
We'll have similar looking boxes. And in the end the box is just containing the actual shape
we’re making, so it’s not, I’m not going to draw the box overly dark. It’s just one
of those ideas where we’re starting with a rectangular idea but ending up with more
of a carved and curved object in the end.
Put in the basic idea of this rectangular box. This back edge basically like that.
Then I’ll show a little bit of the backside. Come back from the back corner as well here,
left side. Go up with that backside. So we’ve just got a standing box.
Then we’ll work on our shapes we want to put in and that kind of thing.
Backside there.
What we’re going to do next is introduce a curve, and I’m going to start with that
curve design as if we’re taking this flat wall here in the front, and we’re going
to bend it back to make a curve so it bends back somewhat into the shape. I’ll go ahead
and draw that randomly as I had planned like this.
Starting through here, meeting about here. So you go do something similar.
Then I’ll have it meet, come back over.
Kind of come through and meet it right there again. And I’m going to take where it starts, where
it kind of ends and make basically a point right here where it touches the wall. Those
are three obvious points. I’ll go ahead and make a point here in the kind of middle
part of that curve and go ahead and make one here, let’s say. Well on the way here
So right about there, let’s say. So now we’ve got that bottom curve. I’ll darken it in
a little bit. Again, that’s not our final shape. It’s just the bigger idea of the
curve that our bean shape is going to fit on that we’ll get to in a second here.
So there’s that curve. But I do want to replicate that for a curve up top here. So
what I can do is we’re just going to stick for pencil for now until we start going for
our actual shapes that are put out. So I’m going to bring this forward. I’m going to
bring this point forward here to our front wall. Make a little point, little point. Going
to carry it up. We gotta carry these other points up because we want to replicate that
curve. Nothing we haven’t done before. Just going to extend that up. I want to take that
point and lightly draw it back up there to a point there where it touches up here.
Also, that middle seam or that point there, we’re going to bring that up. Bring it up here.
We also have that point and that point we have to bring up to the top plane of the box
as well to start getting the idea where to begin and end that curve. So lightly draw
up to there. Also, that last point over there at the end of the curve, bring it up to there.
So now we know that this starts up here at the top of the box. This over here and this
is touching that side. We still need to get this and this shot from a little plane back.
So what we need to do is go from the original point and lightly go up, same from this original
point and lightly go up. Now we’ve already driven this plane here up, so we go from this
point back until we meet and make a rectangular plane.
This meeting this projection up makes our second point. First point, second point, third,
fourth, and fifth. We already have the third point. First, second, now third. That fourth
point we drew straight up from that here. We’ve brought it forward, gone up, need
to go back toward the left to connect and make it a rectangular plane like that. That
point would be right there where it meets this plane. So, this point here, number four is
brought up and drawn here to the top plane of the box, and then we end up with number five there.
So I’ll just go ahead and draw it in. I have to kind of bend over here to fit it in
properly here, so I’ll go ahead and draw in that shape just generally.
Keep going forward here.
It’s going to come forward. We’ll make that plane right there straight, back out.
It meets there. We come back. We draw through here and meet back there.
So that’s a simple curve there.
I’ll darken it in a little bit, where it touches the back of the camera space.
But again, not too dark because that’s just the plane I want to
follow when I’m drawing my actual real shape thrown back from the front plane of the rectangle,
which we haven’t started yet.
We have two ideas here now, and I want to just do those in pencil at first. We have
the idea of the rectangular box which has all of its sides and its top as well as this
curve which we can see is just a flat standing plane, which goes from here, curving all the
way, just tickling or touching the front plane of the box. Then going back and ending here.
So we have those two ideas: The curved plane and side of the box.
Next, I have to find out and kind of figure out what I want to do with my kind of invented shape.
I guess what I’ll do is do that in blue. Make sure I’ve got it sharp here.
I started it here. I just said I’m going to go back over like this.
The shape will take up the full extent of the box and
touch different areas. Going to come back down.
Basically like that. Go up to here.
I'm going to meet this point conveniently here.
Sweep past there, come back down, touch the
wall somewhere in here and around there. Come back down.
Go through that point conveniently.
So I’m just going to come up with kind of a random shape here that turns around there.
So that’s flat to the front of the box. So here’s the corner of the box. It goes
back, goes back up, and comes back over. So that shape is just adhered to that front of
the box. I also made a point of, okay, right here it touches, let’s say. Here it touches
the other side. Conveniently we have it going through this plane we’ve already done. I
came up and touched it there. That’s another point we could look at where it touches the
top where that plane comes down. You could also take note that this is right in the middle
of the plane. So these sections we already used to get back to the curved plane will
come in handy to help us a little bit with those same sections that are part of the curve
touching and relating to the front rectangle. It can also help us throw back the curved
bean shape to that curved wall and to back here. Let’s do it back here first, and let’s
make this shape back here on the back wall of the rectangle.
We just have to reference now, so let’s get all of our shapes in order here. We know
it touches here as a reference there. I’ve got that touching the side wall about there.
Touches the side wall about there. Up here we’ll make a plane. In the middle we have
the plane here. So let’s just drop some of that down and throw it to our back wall
now, where we already know we can take this down and over to the corner so that’s easy.
So let’s take all the easy ones. That one touching there simply goes straight back to
the back plane like this. Make a little arrow to that. Makes that point. This one is another
one. It touches the top. Goes straight across. Make that point a little arrow. We also have
this one that touches the side wall in the back. It can go straight across to about there.
Goes to right there.
Obviously, this one at the bottom also is helpful.
That goes right there. We also have
the middle plane, which we know is very helpful so we can drive that forward. We’re just
going to take the middle plane and drive it forward on the other top side as well. This
middle plane now reappears over here in the back. I think that is the whole middle plane.
What other convenient places can we take our curve from?
As we did before, we have our original section from bringing the curve forward to the front
plane to determine the curve, so we can kind of take that and run it down where it splices
that curved shape and it drops right there. That touches. Remember, this blue bean shape
is still flat, as a design, the front face of the box here. That idea.
So let’s draw in the box a little darker if people are getting confused.
That’s the front face of the box.
Make that a little more obvious. Back edge. There we go.
Then the two sides going off like that I’ll do a little darker as well. Just the idea of the box.
Then, of course, we have the back of the box which our other shape is going to take. It’s pretty easy
to see. Okay, so there’s our front of our box shape. Also, we have this plane that we
use to determine the curve here. Coming forward, coming forward. So we’ll go ahead and recognize
how that plane also moved through our bean shape at this plane here. So that’s convenient
because now we can throw those back into space to the back wall as well to there and as well
to there. Might as well use stuff that’s already there. Then I’m going to come up
to where those would crawl up and give us a reading as to how high those points are
at those different places for the bean shape. I’ll just kind of shoot up that idea on
that plane to the top as well as the other one. We carried over from here over.
That's where that touches the top. That touches the top. So now we’ve got numerous points chosen
out here. More specifically that seam that goes across the beam here, that seam that
goes down the beam here, that seam that goes from the center here.
Center, center; that’s our center.
I’m just trying to understand the idea of the three big ideas here.
We had the idea of the rectangular box with its front face, and the idea of the curve put in.
We're trying to reconcile all that in our brain at the same time and then adding the blue
bean shape, passing over certain reference points on the front face of the box. I made
convenient reference points. If you don’t get why I’m making these please go back
and play it again until you get that part. It’s touching here. You can tell on the
center seam in here. So we’ll now slowly bring back all the points we need that we’ve
created here on this flat design here and throw them back to the back wall so we can
re-recreate this same flat shape on the back wall of the rectangular box. Then we’re
going to cast this front shape to the curved plane. As we’ve said, let’s say this is
the design of some kind of camera or some kind of sculpture where you wanted to repeat
this shape back to back and create it, and then carve out the curve as we meet it for
the final shape, which we’ll do in red. But we’ll still project the bean shape back
to the back plane also in blue.
Let’s identify some of our points now. Obviously, with this we can drop down, go over and just
go back to the wall. So that’s going to be that point there for that. We’ve already
gotten this point back here. We have this point here where the curve comes and meets
the middle seam of the front face. We have to actually go through space for that big
plane through the middle and then cast this through until it comes to here. So now there’s
that other one. So we could say here is there. This is for this. And this goes through to
here on that back center plane. That’s a plane. I want you to start getting used to
that. Since we’ve been more careful in the past with the previous lectures to carefully
do the planes, I want you to be able to start being able to think like this and keep up
with the idea of the different planes and why we’re relating them.
Instead of actually trying to tone in all these planes, which will actually become more
confusing, it’s really about following the lead of the diagram and then carefully doing
it yourself. If you want to tone in the middle plane a little bit to make that clear you
should be able to start seeing these things. All it is is about following planes. Even
if you don’t do these diagrams or something like this for two years you can still refer
back to your own notes and go that’s right. What we’re doing is relating the front plane
and all it’s intersecting reference points for this shape back to the back wall. That’s
all we’re doing. Then we’ll hit the curve next in red.
Okay, so that one’s there. Then we know that this also contacts in the middle seam.
The bottom of the bean shape passes through there. I’m also going to project forward
to the left vanishing point and find that point. Now we have this point and this point.
Here and here. Right there and right there. We want to make sure that’s clear.
That is part of the front bean shape hitting the top rectangle. It’s this shape that is actually
this cast back. Then again. We’re going to take this plane here. That goes through
here and recognized where it touches the bean shape here and here. We’re going to also
cast that back to this point and right to that point.
And then we’ve already cast back the bean touching the edge to here.
On that back corner that becomes this point.
So let’s go through it again. We have this point, counterpoint is over here.
Then we have the idea of this shape over here coming down.
We have this one also touching, but we really are looking for this one.
This is over here. We could add in this other one
at the bottom of the bean shape. Not too necessary but might help us. That one would be there.
This one touching the bottom would be over there. Then we have the middle, the things
going through the middle seam here. Right here and here, projected here. That one projected
over there. Next, we have these two projected over for here. These two are back here. This
one at the end is back here. It goes all the way to the back corner of the box there. So
we’ll just join those together as a shape now trying to look at what our shape does
originally here. That passes through like this. I’ll take the bean shape like that.
Just kind of curve it down. How close does it come to the corner, a little more than
I have it there. Something like that. Okay.
Also come through here at this angle so we’re actually wrapping through there trying to
keep that shape alive, coming down here. That flattens out and comes back up. We have to
do that kind of activity there. We’ll do that one.
Not that big of a deal, goes through there.
Next one we can look at. I can go through here too. It starts through here a little
bit like this and then curves up. Curves up and rounds out to meet this. So we have to
round this back and meet that curve up kind of like that. So that shape would be basically
like that. Going back down, going through the curve at that angle and then sloping up
to meet that one. There is its counterpoint so we’ll kind of draw the idea of that coming through.
Okay, then we curve back to meet this one.
So that would be at about that angle right as it meets the wall. It’ll finish out that
curve based on what we see here in this new perspective.
Loop through. Loop through.
About there it starts coming through the wall again. Goes through there.
Alright, so there are the two shapes. I’ll make the front one a little darker. We’ve
got our front shape and our back shape. In the end I’m going to have this back shape
stay as it is for the final shape, but I want the front shape, which is our template on
the front plane of the rectangle to project back to the curve, remember. We’re going
to do that now in red. We already have the curve present since the beginning of the diagram.
There’s the top of the curve, remember, in pencil. We’ve always had the rectangle.
We just made some various points which were helpful to get the curve back and relate it
to the bottom curve to the top curve by using some points, which we then again use to project
back our bean shape once we had common points with those crossing through the middle and
had our sections. We were able to get the back shape. Then we’ll make the whole shape
work and darken it in later when we have the front shape hitting it. I was also going to
introduce the idea of a rectangle, so I’ll do that lightly. That I’m going to do right here.
I’m going to put a little rectangle in here as a surprise like this
on the front face of the box. I’m going to project that rectangle and reference it
back to the back shape as well. So obviously we would just take our four corners
to the left vanishing point lightly.

All the way through cause I’m going to need that to hit the red shape as well. We’re
just going to have to reference its depth properly for that. We’re doing it to the
back wall now. I also have to then reference down to the ground.
I could reference up, but I'm just going to go down here, and it conveniently meets that point.
This one meets the point here.
So all I need to do is say I just move across to there so we know it’s lined up
there, and we know this point here has to go across. We come up from there. So now I’m
just drawing two verticals that will represent the side of the new rectangle on the back wall.
The first one would come up like this from here and meet these two corners, so one,
two, three, four corners. I have to come back and meet these two. There’s that wall coming
back and meeting those. So there are those two corners of the rectangle back there.
Then if I bring this over and make that point too, this side comes down and comes over right here.
I’ll make a vertical go up. Also, with that intersects with the projections
from the corner of the boxes here. Over here. We’ve got one here. Down there, come over,
get that. Now there’s my new rectangle in the back. I’ll just fill in the lines now.
Now as an artist it’s harder to imagine how will I use this, but if you’re doing
sculptures or doing, again, interesting planes meeting from architecture that you have to
make the inside of the architecture transparent so you can have these planes meet to figure
out how maybe the outside of a turret meeting a complicated roof. All the roof and all the
turret and all the stuff meeting the straight walls of a castle would also be made transparent
in the same way, so you can reference where the turrets, you know, the ellipse of the
turret as a cylinder would meet the flat walls and how the roof would peak. Anything you
come across that has shapes meeting shapes and planes and intersecting planes, these
methods you will figure out how to do it. It’s not always immediately obvious. You
really have to think about what you know from these basic diagrams and what we’ve done
together, plus other supplemental resources and then really think, okay, for not my specific
designs and needs, which here’s a million different needs and designs in the world.
We can’t cover them all. You have to translate what you know into what you need for your
specific needs and designs for your art and your project and your painting. So whatever
it is you’re translating this basic conceptual information we’ve done
together in trying to flip it over.
So please, again, on your free space here take lots of notes of what we did first, second,
and third. Use some arrows and be clear about the difference between this original rectangle.
Then we created the curved shape top and bottom. Actually the bottom first then the top. Then
we decided to put a design and project it to the back wall. Then we added a rectangle
in front wall projected into the back wall. We’re just playing around now. Now, we’ve
got this complete idea here in the front, and in the back I’m going to project the
front idea of the bean and rectangle back now to the curved plane to make a new shape,
which would represent how the front face of this new object might be having a flat backspace
right here, coming forward to a curved bean shape we have projected from the front to
the curve. You could project it from the back, but in our case we’ll do it to the front.
Let’s take each point that was important before and project it to hitting the plane
of the curve. So let’s do that in red. I’ll go ahead and sharpen that up. Let’s take
the real obvious ones. Obviously, we have our center plane here with the curve hitting,
so that’s going to be directly contacting that. That’s obviously touching right there.
That’s our front plane. Our curved shape is basically touching right there and right here.
Okay, so we don’t have to go back for that.That’s actually at the peak of the curve. So that’s fully there.
What next do we have to consider? Okay. This common point where the rectangle hits is good.
What we’ll do is we’re going to just lightly put in a red line going all the way up that
because that’s an important idea where the two sides of the rectangle are.
That’s basically just hitting it with a tiny variation there, just a hair back there.
It’s close but not exact. It moves back a tiny bit. The more important thing is the
left side of the rectangle and the plane.
Go down here and hit there.
We’ll put a plane up because we back to hit the curve.
We made a mark on the curve now, and we’re
going up to heights we need all the way up. We also note that the top of the bean shape
touches right there. That has to be projected back also to the left vanishing point
like this to make a plane.
There’s a point.
Then we have to come up to meet that. We know that
the bottom of the bean shape does touch the ground here; therefore, that’s touching
the ground on the curve. We know the bean shape doesn’t quite make it up to the top
of the box. When we project it over there indeed it is right there.
Alright, so it’s this one we’re looking for and this one. We already have these two
here and here. These need to project back—nope, I forgot. They’re right against the front.
We don’t need to project them back. What’s next over here? We have this idea up here,
and this one touches. So obviously this touches this front but needs to go back to the plane
of the curve which is right back here. We’re making a plane like this to get that back.
To get this point we have to shuttle back to the left vanishing point until we interrupt
the curve. We need to go up straight vertically again.
Then where we touch that here, project.
Makes another point on our curve there. Also, we have to take the idea of this projecting
back in here, touching the top. The flat design in the front plane of the rectangle, the bean
shape touches that here. We have to go back there.
Those are two more points.
So far we have basically this one, this one, this one, this one, and the two right here.
We have to also consider then we’ve gotten these two. These two, and we have to get this one.
Well, that goes back and is projected back to the left vanishing point as well, but instead
of going all the way back to the back plane it interrupts the curved plane right there
at the very edge. So that’s obviously another one.
Alright, so now we have this one.
We have this one, this one, this one, this one, this one, and that one.
We’ll tie them together later. We have the middle plane now. We also
have the bottom of the rectangle. We don’t want to forget about that. So let’s carry
our rectangle over as well. We have the left side, but we need the right plane. The right
side of the rectangle comes down and needs to shoot toward the left vanishing point toward
hitting the curve just a hair, the tiniest bit right here. I’m just going to fudge
in a tiny change there, but I’ll just say it’s a little bit. So those corners have
to come forward just the tiniest bit to meet this. Then we know these two corners of the
rectangle have to project forward to the left vanishing point as well to indicate where
the corners of the rectangle are now on the curve right there. Then we figured out the
other ones just come forward a hair. These come forward a hair. So there’s that curved
rectangle. So remember this flat-faced rectangle will have a curve to it when it is cut out
or carving out on the curved surface.
Okay, I also had these so let’s go next to these points here projected back to their
counterpoint plane on the curve. And that is a standing plane doing this. So we have
to come back from here. Why do I know that? Because there’s the curve. There’s that
seam we used originally to project the curve forward to the front plane. We can still use
that to make that a plane there for this point going back to here.
This is now this back in the curve.
Same thing. We have this standing plane, right? We can now shoot this back here
as a point on the original shape.
That becomes a shape now too. Then the last one we project
back is this one here. Straight back against that back wall of the rectangle until it hits
this standing plane of the curve. See how the curve comes around? Comes straight up
in pencil and comes around here again? Well, we have to take this point and have it contact
that wall going back to the left vanishing point, which would be right there. So that
point on this flat bean shape on the flat front plane of the rectangle would be shot
back to hit that wall there and become a point there. There it is.
Let’s see if we can draw this in in red now. We should have all our things together.
Let’s do the bean shape then we’ll do the rectangle. First and foremost, we know
that this one starts here, and then we have to meet these, which represent this to this.
This one goes to there, so I should carve out. I’m just trying to get the angle right.
This one turns right here. Even when I do ellipses I’m trying to get my curves right
even in our new shape, so I can turn them, come through here. This elongates a little
bit, comes and slams through here like that. That’s going to come further down, actually.
Scoop down like that. That’s going to come up and meet that. Nice curvature down there like that.
Come up. We’re going to meet that one where it goes flat through there. It comes down
to meet that. Pretty straight actually. I’m going to have to fit that out and pull it
out like that to meet that one straight. This is going to have to come down even more,
I think, like this. Curve faster like that.
Then I’ll come back and meet that one.
There's that one on the floor. Next we’re coming here and meeting that one right there on the
front plane. That directly connects to that one, turns right there, comes back up to that.
Alright. This moves through here all the way back to that one where it runs through there.
Curves down so that will be turning like that in perspective. This one, again, is meeting
the front plane right there and has to curve back through that one.
So it has to go back to this like that shape.
Then we have to curve this through there, meeting there.
That shape coming down through here.
That one, that one. Now we’re meeting the middle seam of this.
We’re trying to meet up with what we know is here. That one right there. I want to curve up,
come through this one here. There we go and then shoot through that, gotta replicate
that curve. The curve will come up to meet that.
Pretty much to there. So the red shape
kind of inter-tangles with the blue there coming forward. Should be able to flush this
out even a little more actually like that.
That’s a real working way of doing it, but I keep pushing that one out a bit, pushing
it a bit. I’m showing you how I’m actually working it out. If you want to slow down and
do it neater for yours, be my guest. The idea is I’m trying to get the idea of first time
perfection out of your system so you actually have to work at these and push it out. I recognized
this being more flush and straight up and down as a curve, so even though this is bent back I wanted
it to be more flush and straight up and down as it came through here and then has to snap back
and run through here evenly. That’s what we’re doing then the backside comes back.
Now, as you remember, the red is simply representing the curved version on the face of this curve
we originally drew in, that is this bean shape now projected from the front directly back
to that curve but also projected back to the back wall. We have three layers now, the original
bean design projected back to the curve in red. We first projected it back to the back
wall. That’s what we basically have now.
If we wanted the red shape to be the front face of the shape now permanently, and we
were only using the blue bean shape in the drawing of the front plane of the rectangular
plane just for sizing that’s fine. If that was done very, very lightly on your own, and
you’re really only drawing hard for the red bean shape and the black blue bean shape
and then connecting the two, we can do that. If we want we’ll take blue and just connect
the shapes now. We know that the side will come like this and go back to the vanishing point like this.
There’s the actual shape which we’ll do really dark. That’s the
actual shape now. We kind of let go of the idea of the rectangular box. We’ll shade
in now the actual shape, which is the red shape coming back here. We can see the side
there. There’s the top of the shape. That bean shape dips in. We’ll make that blue
darker. Again, we’ll just make anything that’s actually the edges of the object
a little darker, like that. Then we know that the whole red front is the actual object,
so make that nice and dark.
Somehow it’s all standing and balancing on its own, but the idea is we’ve got that
front bean shape we originally drew in blue projected back to the curve now, representing
that curve that we originally put in with pencil. But the pencil lines are lighter and
less important because they’re only setting up everything. The only object we’re actually
left with is the visible opaque part of the back bean shape as well as the projected front
bean shape going to the curve in red, and that becomes her final shape. So in the end
because this curve bends back this curve here gets more extreme and bends out more severely
toward this like this. It does a few interesting things like this and comes down like that.
There we go.
I’ll just shade that in in blue, let’s say. That comes back on there. It’s a little
darker back there. Right to there.
Of course, the red is what we’re looking at for the front plane of the thing.
Do that very lightly in there. It won’t interfere with all the
stuff. We can’t forget about the square. So we have to tighten in the square. The original
blue rectangle that went through the back wall as well, it is right here. Don’t want
to forget about that. The other ends are here. So that line is just a slight bit back from
that original line. Now I just have to connect these through the idea of what the curve does
here right, kind of like that. So I’ll just put it as a curve like that. Same with this.
It has to go back in, take the curve like that. That rectangle just curves a little
bit, throws itself out to that. Like there. So there is that.
The reason is that this—remember, the red front
face of this shape come way back to here, that deep from the original
front face of the rectangle way back to here. But then it curves around and comes up and
meets right here at this seam. It’s meeting the actual front plane of the box, way up here.
That’s why that doesn’t look quite so severely curved yet until it goes really
thrown back here. If another rectangle happened it would be bending back a lot more to
get back to this point that is that far back.
Also, over here at the peak here this gets thrown way back to there. So that’s quite
a ways there to that point there. So that curves back too and would be fairly foreshortened
as we went back. Anyway, there’s that original blue rectangle then the red one.
Okay, so that’s just some more things to think about. How we make planes and things.
I’m just trying to do a variety so artists who are not necessarily designers also understand
this. Designers would go on in some of their visual communication or their Vis-Com training
if they were at a number of colleges across the country, or you can look at this stuff online.
How to create vehicles and objects, industrial design, transportation design,
product design, even environmental design to an extent. They use these sections quite
a bit in the construction of real things that are going to be designed or planned to be
designed in real life. Artists can obviously use this quite a bit, and it’s very helpful.
But, I also want to make the content still stay pretty basic or intermediate so that
the artists also understand that they would really only be applying this method when they’re
drawing things that are more complex as I mentioned with possibly vehicles, cars, you
know, fairly complex modern contemporary sculptures, whatever. If you can understand the individual
shapes that meet in intersecting planes and curves and meeting, you know, starting at
a straight and going into a curve. This will be very helpful. It doesn’t mean you have
to be using it all the time. In a lesser form you’re using it for, you know, visualizing
ellipses, carving through cylinders and that kind of a thing.
All these transparent planes with standing rectangular planes with reference points you’re
going to be using again and again to figure out the more difficult stuff. Other stuff
you’re just going to draw as you always have observationally because you understand
it and it doesn’t provide you with too many problems or difficulties. Again, here we have
originally a rectangular box with a curve set through it top and bottom. Then we went
ahead and drew the blue bean shape in the front plane, projected it back to the back
plane; included a rectangle, projected the rectangle back. Then we drew in and projected
that front bean shape from the front to the curve and drew in red. Then we finally ended
up with the red rectangle added on as well to that front face, and that curving bean
shape as the front face of the red at the point of the curve.
Alright, so that’s that one in that logic. On to the next.

Alrighty, here we are. We’re going start wrapping up sectioning and curved objects,
that type of thing, by doing a scene again. But we’re also going to have a couple side
view elevations of some objects we’re going to do together. So we’ll do a little simple
dirigible. There’s the side view and kind of the front view. That’s all we really
need to build it. We’re going to build that up in this area. I’ve already done a light
indication for myself on film here just to get leads and keep talking efficiently and
repeating things in a good manner for you guys. So we’re going to do a dirigible up
in this area. What I’ve done is I’ve put a frame around this. Here is my center of
vision and my eye level. And these little marks here, you can see this might be slightly
out of camera. But these marks are the cone of vision. My SP is down here somewhere. Of
course, my vanishing points, my two-point vanishing points are, again, off camera a
little bit so we can get bigger with the image. So there you have it. So this frame should
be pretty close to your camera space. I’m just going to, basically the eye level is
kind of in the middle. We’re going to take and analyze these again, kind of like we did
with the stadium and a couple other things back in the earlier lectures. We’re going
to just take the idea of this being one square here where you see the circled corners, and
then so how long is this compared to high. It is one square high. It is 1-1/3 square
long. It is about 2/3 wide. So we’ll just take note as we’re kind of creating the
interior middle plane and silhouette for this as we’ve done before.
And then we’re also going to do kind of a 1930’s simple race care idea. We have
the side elevation as this as one, 2 units and 1/3 so 2-1/3 units long as we can see
by the circles corners too. It’s basically one unit wide according to its own proportions.
Then we’re doing a simple archway that the car will be coming through with a little road.
And that’s just on its own, kind of just X’d off. We’ll just do the same type of
build we’ve been doing with archways and that type of thing previously. But I just
wanted to kind of put together a scene before we do it. We’ll probably have also a digital
draw over of some time. We’re going to do that as well, just to comment on the logic
and the thinking of sectioning. Again, this idea, we haven’t really done many scenic
things where we’ve really composed things out with the cone in our kind of picture plane
device so much because we’re really trying to get the internal operations of intimate
referencing and sectioning down so that you can use it almost, you know, in any manner
you need to when it’s handy. When it’s not so handy or you don’t need it so much
when you’re just sketching you can kind of do phantom movements where you’re kind
of just guessing where sectioning doubles and triples over and things like that. So
it’s all about how do you need to use it, and how much do you need to use. You never
have to always do everything formally. This is just for diagram purposes and a permanent
record of why and how sectioning works. So that’s why we’re doing it more formally, obviously,
in these draw overs together, because obviously they can be used in much more applied and
casual ways as you build up sketches and drawings. Again, just wanted to remind everybody, even
though we’re being pretty analytical about this so we can show the real method of why
the perspective works, your job is to when you apply it to play around and sketch and
draw with more formal and less formal ways of approaching it to see what method helps
you the most to get accurate drawings that you feel with comfortable with. Once you have
that kind of set pattern that you need to use it by then fantastic. That’s what you’re
supposed to do. It’s really fitting it in to your method of whatever type of art you’re
creating. This is just how and why it works in a basic manner. These are more intermediate.
The car will get a little complex. But again, we’re not really going into anything too
complex. It’s mostly intermediate and basic stuff just so we can really be clear on the
idea of how you can pretty much analyze anything with a plan and elevations like we have here
mostly with elevations and then get it in perspective. We’ll go more into this in
plan view later, but we’re still going to get to other things before that. So here we
go. So let’s just space out the basic logic here of what I was doing so compositionally
with the larger object we can start with the archway. I’m just going to draw out what
I decided on as the larger space taken up by the arch, which I’ve decided to basically
make it this large, so we’ll go the vanishing point and kind of draw it out.
And I'm just going to make these very obvious. And it’s going to have a little cap, as you can see.
A little crown molding on the top. But we’re just basically looking for the bigger basic
form, of course. It’s total space it’s going to take up is about here.
And we're going to go back to the right vanishing point. I’ll give you a little bit of lead here.
Then we’ll just, you know, start your diagram off of course. You know, trying to copy this
fairly closely, as long as it compositionally fits and works for the angles we need. We’re
just trying to get a good, simple diagram that works to showcase why we’re sectioning
and what we’re doing with an archway. So again, as usual you’re just approximating
this with your own drawing, because you’ll memorize it a lot faster. Then I’ll get
the depth to this on the other corner. Draw back.
Then we’ll close off the depth knowing the back corner is here.
Going to left vanishing point, which is a ways away. I’ll go ahead
and take that longer distance just to get the idea of where we’re closing this off up here.
We’ll get that back corner in.
I was trying to get the basic space built in out here. That back corner.
Then we know we’d have to have the space generally to get a middle seam.
Then we’ll leave it at that.
That’s just taking up the compositional space, so I’ll make this, you know, these
halfway marks for references later. A little lighter than the outside shapes. Again, we’re
just trying to get the idea of an archway. There’s the middle right there.
Then I'll make that halfway seam, which is close to the back corner so we want to differentiate
that. I want to make that clear that that the halfway point is literally about right here.
So I’ll put that a little above and below. There are four corners, back corners,
and we’ve got a little halfway point. Then the back corner is just a little bit to the
left of that. So that’s the space our archway will take up. And we’ll deal with doing
this as we’ve done before for constructing the arch and repeating, so we’ll probably
do the front shape first and then double over with our referencing to get the corresponding
flipped over symmetrical shape of the arch. We’ll also block out the basic middle section
and height and try to square off the dirigible next, so let’s do that.
I’ve basically decided to have this middle line that goes right through the middle of
the air-filled part of the dirigible here. I kind of composed it as going right through here,
so I kind of started there. I’ll start there and then say, okay, I want the front
leading edge of the dirigible right about there. Then I decided on the height. I decided,
okay, for this height there’s the middle we just put in here. I’ll say about right
here and right here is one unit because I felt it out compositionally how big I wanted it.
We’ll just draw that idea all the way back not knowing how deep I’m doing yet
until we kind of count off what we think our decent squares. So if I take this idea of
the one third, you know, unit here coming forward and the overall square back to that
tail right here. So we’re talking about right through here through there. It’s a
total length of 1-1/3. So I kind of created the 1/3 with a nick here and said if I had
to—let me just feel it out. I had to kind of feel out where that 1/3 would be.
Where would a square be? I kind of felt it out to about here. Now I’ve committed to 1-1/3
standing square. So that’s a square in perspective. There’s the added 1/3. I’m just trying
to feel out what basic space it would take up in basic perspective. We’re not using
measuring, necessarily measuring points. We’re just using good old guesstimation and sectioning.
That’s what we’re doing now.
This would be the middle section, though. Exactly in the middle like we’ve done before
with sectioning. This will be the middle plane, and I’m going to create a silhouette of
the dirigible like this in perspective space as the middle plane just like a cookie cutout
or a paper cutout. Then we’re going to expand it forward and rear into space using this
basic idea of it being 2/3 as wide as it is a whole square for this front shot. So it’s
just trying to think it out that way. So let’s do that next.
We’re also going to do a race car. What I’ll do is we’re going to go down here
to the race car and just block out what block it takes up with the little road coming forward.
Then we’ll leave the block in the road and go back to the dirigible, go back the arch,
and then we’ll finish out with the car and stuff like that. But we do want to kind of
spec out the basic compositional areas things take up. So I’m having the road, I’m guesstimating
where these are. I basically have estimated these at about right here.
And the essential thing for me is at this height then we could just come over across like this.
Come right across. We could keep going up here if we wanted to. Make a little mark there.
Go across to the vanishing point.
Come down just to draw it in and realize that’s the height
right there of where our arch starts right there and then starts coming in there.
I’ll just double that over. Go over in space according to the vanishing point. So we’re
about there. I’m just doing that right now so I know my road is this wide.
I’m going to draw a little extension here coming forward and on the other side. Then
I want kind of a dip in the road, so I’m going to make a little step. Even the road
won’t have a step in it that’s where I kind of want to make my leading angle. I’m
going to drop it down about that far and then continue. We’ll show why I’m doing that
and what the logic is of that. The road will continue but they’ll be a slight kind of
dip. We’re just doing a little bit of an auxiliary idea down to here up to—what we’d
be doing is going to that right vanishing point and a little bit about here above that
right vanishing point would be on auxiliary. I’m just kind of winging it about the idea
of this being a little slope. I don’t want to draw too heavy to interfere with my other
side. I am going to take this idea. I’m going to bring this step over and drop it
straight down from this corner, kind of like this and say, alright. There’s the two points
where that goes. Then I’m going to re-create this step here coming forward very lightly
to the right vanishing point.
Now, I’ve just done a little method of getting that auxiliary slope very lightly here because
I’m not going to really use it through the car. The car is going to be in the way. So
now I have that slope, and that’s what I want my road to do. And it’s the idea of
the road kind of coming forward like this, lazily going up like that and meeting back
up here. And so if we do the same thing and cut the same part and section here, we basically
are just trying to come up with a logical way of the road. It kind of goes flat to about
there, flat to about there. We’re just going to lightly draw the idea of the road going
up. Then it continues through the archway, the bottom of the arch about here. It goes
on for a while. So anyway, we’re just getting the idea of the road now really casually.
So that would be the total width of the road that we’re going to use with just a little
slant. The car is basically going to be in that space.
Then what I wanted to do next was pick a total width that represents this one width, you
know, as a square. Then we have two equal squares here for, one from the front; one,
two and then 1/3. So 2-1/3 of these, this width, will be the length. So first I’m
going to pick my width. Then what I did is I just did a box, kind of picked it there
and said okay, there’s my width which comfortably fits on the road. I did it for my center plane,
so let me not forget my center plane. So before I forget, I basically come in the center plane
of the arch, the little curve of the road. Drop it down to there.
We meet this there and then continue on from our right vanishing point to just get this
little center line going out there through the area the car is going to be in. Continue
it out a bit. I’m doing this lighter so we don’t get really mucked up where we want
to draw our car. So the road basically has a center line now. We know we can connect
this with the auxiliary slope, but we’re going to do it really light again. But the
idea is we’re just coming up with this idea that the dirt here is just basically flat
and then rises slowly. So the car is still on level ground but right past the rear wheels
where we think the box is going to be. We’re going to do that. I’m just guesstimating
now.
So again, I’m going to make the height of my square. So what we’re doing now is we’re
taking this width, which was based on the center line here. We’re going to take it
up, and we’re going to create what I want as my front leading box shape for the rectangular
shape the car fits in, which I’ve decided is this. It doesn’t matter if I draw a little
bit into this car here because we’re not really using the space. It’s only kind of
an invisible box idea. The car will be down below. So there’s my front standing box.
I’m creating this box that is in front, the very front plane of the car, kind of this
invisible idea of a box. There’s that standing box for the front plane.
I’m not going to do it super dark.
Then I’m going to take the bottom of it and draw an unknown distance back to my right
vanishing point just to say how far back does that box lead.
There’s the top of the box for that one unit.
Then I’ve estimated and guesstimated my first increment.
I want to make sure that should be about there. I’m just going to estimate it and say what’s
my first standing box? I want to make sure that I guess that right.
So let’s try this.
Then I have to X it off. That’s my first standing box here. So we’ve done in perspective
what we think is the first box here in this perspective. A little bit longer over to the
right vanishing point. That’s my first standing box here. Then I’m going to double it.
I'm just taking the idea of it very lightly and X’ng it, just the idea of that box will fit in.
There’s the middle. I’m going to drive that middle back. Make that reference
point we know about there so I can diagonally come through and get my second standing box
about right there. That will be it right about there.
So now we have the corner, corner, first unit, second unit. I’ll go ahead and draw out
that second box. According to the perspective it would land about right there. Then I’m
adding about a third, guesstimating another third on or barely a third but right back
to about here. That was my guesstimation there. That’s the total length of the car now.
This is a little added-on part. We have one unit here for we could say our width. We have
unit, two unit, and basically between a third and a quarter or something here. It’ll be
more like a quarter. But, either way, that’s what represents this is is this depth.
Now I’ll kind of make a box of that to try to keep tabs on what I’m doing. That goes across.
That goes across. This goes across to become our, just carefully kind of trying to say, okay,
to our other side. I’ve got to make sure I’ve got the side of the box in on
the back side. We’ve centered this. This was just X’d off this, obviously. We X this
box off here just really quick. Come back to this one, actually. There’s that center.
We can bring that one up. There’s the center of that front box. Something like that.
What we’ll do now is we’ll do the back. I want to make sure I get that back corner right.
I’ve got to bring those other lines over. So meet them. It’s my back line. I’m
going to make the back line here. I’m going to make sure I have the right one and then
go back to that line. So there’s the back corner of the box there. Corner, corner, corner,
corner. Now raise that up just as an idea encapsulating transparent box around the car.
What we’re going to do. There’s that back corner. We’re going to come over from here,
go to my left vanishing point, over. Go back to my right vanishing point in that corner
up there. Okay, so I’ve got a lighter box. I think it should be fairly seeable. I want
these lines to remain fairly light because we can go in with our darker work later. But
now we have the one unit hitting the other side there. The two unit hitting the other
side there, and that back edge again hitting the back corner. So now we’ve set up the
general space of the car. We can raise it to its height of the body later which would
be somewhere around here. I marked there. We can carry that height around saying that’s
the basic bottom height rise of the car from the ground to the bottom of the car. We can
start our silhouette shape of the bottom of the car. What does our middle shape want to
be? That kind of thinking that we’ve done before. I just don’t want to get too dark
with this work in here because I want to, you know, be able to see my imagination and
what the cars should look like for the sections we’re going to do. So that’s about it.
We have now the start of the basic 1-1/3 standing silhouette in the middle we created for the
dirigible or the weather balloon. Then we have our basic space for our archway, our
simple road with the dip that we’ve kind of indicated as a lazy dip going like this.
The car will fit right onto the flat space immediately after the dip in that basic box
shape. Even though the car isn’t as tall as this box it’s something we could make
a good square out of to understand the space. And so we’ll basically just keep taking
proportions and heights from this side view and this front view to basically reach what
we need in here in perspective by counting and just analyzing it.
So now we’ll go back to our dirigible, and then we’ll do our archway, I think, second.
I pretty much want to move from left to right. Then I can get out of the way of the car here
so my head doesn’t get in the way. Let me get a sharper pencil here.

Now, let’s start analyzing what we have in this shape from this middle seam going
through the middle of the balloon shape. This is middle seam here, so that’s an important
shape. Analyze that. That goes through the middle right there. There’s the middle of
the actual box so this is a ways over. If I look at the middle of this standing box.
Let’s do a really light indication of that.
Again, it’s just this thinking. Now you’re
going to say to yourself why don’t we just draw this? Why are we possibly doing all this?
It’s like because we’re showing and doing together sectioning, referencing, and critical
exact referencing of an idea. Then you can interpret that. If you’re making stuff up,
of course you’re still sketching. The idea is if you’re having problems when you draw
with getting good side-to-side continuity with difficult shapes or complex shapes, or
even just the idea of how to move something in the proper perspective that you set up
in the bigger compositional idea of your setup. It’s just this kind of thinking that’s
going to in detailed ways and in less detailed ways it’s going to help you out getting
that side-to-side symmetry. We’re just dong it as an exercise together. So there’s that
middle of that first square here. So now I can kind of estimate where is that middle
seam, and I kind of guessed in perspective would be about there. What I’m doing is
I’m just trying to guesstimate where I think these seams fall on my silhouette.
This one represents that seam that goes all the way down to the middle of the little part
that carries the people and stuff right here. There’s that middle part, which is that
kind of thing there. It’s pretty close to where we are. Then the top.
Anyway, where those other sections are falling. This one falls. There’s the lead line for the front.
That other section is a little bit to the left of that. If I kind of mark that off I’ll
just make note of that and make that another section just in my thoughts.
Just a basic idea. This one is behind the halfway point a little bit.
Again, there’s the halfway mark here and here and a little bit behind that. So I’ll go, okay, that section will
be there. I’m just going to kind of create the idea. Remember we’re just doing that
little section on the silhouette, the flat silhouette that is the middle like cookie
cutter shape or paper shape of that. We’re going back to this seam here as well. So we’re
just trying to find all of them here. If we know that’s the back forward from that, a little
bit of those. Yep, coming forward to that seam right about there. It’s probably that
one right there. We’ll just work it out from there.
Okay. Then one is kind of between the two here, so it’s right about there as that
last seam. We’ll get that going. All those kind of weird lines are like what do they
all mean? Well, now we have to say oh the top meets there. I know that about my dirigible,
so I’m going to draw that in. I’m at the bottom right there. So where is that line?
As it turns out, this is like 1/3, 1/3, 1/3. If I actually draw down the bottom of the
box is 2/3 of the section. So if this is the hole I’ve drawn basically another line here
to say middle seam is 1/3. That bottom seam for the dirigibles bottom of the balloon part
is 2/3 and then another 1/3 down to the bottom. We could basically say 1, 2, 3 or up here
1, 2, 3. Now, I can kind of say that line represents the bottom of the dirigible here.
Right there is that line right there. Again, any time you need these slow down, reverse.
We’re just trying to get a logic of how we construct this silhouette in our mind.
The car we’re going to construct by basically the chassi and the wheels touching the outside
and going across as well as doing our middle sectioning from our middle section out and
trying to meet that idea. We know the chassi, the wheels are flush to the outside of the
box. We know their spacing from their position there, and we know their height. Of course
the basic width being one unit. So we’re going to do a combination for that object.
In the archway we’re just going to do like we’ve done the other archways in here. So
the dirigible we’re doing pretty much from the middle section out front and then doubling
over to being the reverse back. So let’s do that.
Okay, so let’s draw out what we think is the shape here. There’s the top and bottom
of that. That part, and then the front part is smaller so that just goes about here to
about there. Then we already know the length of this because we’ve decided it’s from
here to here in the middle. Then we’ll just kind of draw up as we see the other ones.
I’m just drawing the shape as I see it. Lightly at first just to feel it out.
Again, obviously as we get more used to these ideas you don’t have to take any of this
time to, you know, explain it to yourself. You’ll just start sketching and feeling
out things and building them out. But again, as an instruction of how and why perspective
works, we’re just doing it really slow together.
Then from this center seam down again from
the back here we’re just trying to make sense of how this would come down basically
from the center here. It would come down from right here. The back of this here. We’re
drawing this part here. We just drew this part here, drawing this part there.
Same from here up to the middle and then back down again. So let’s do that.
Just the basic idea of what we're doing.
A little more on that front part. Come down, leave that.
So we might get a little more fullness up here. Alright, there’s the basic idea of that.
We know these are both round shapes in the back and the front, so if we want we
can just kind of draw the squares out for that very simply and say, oh okay, goes to
the perspective, vanishing point, I’m just trying to feel out my ellipse.
If that's my minor axis going through there I can say, oh okay, there’s my exact major going up there.
I’ll just make the idea of an ellipse in there like that. That’s the back one.
We can construct and say oh that’s right. That’s actually a circle in the back. We
can think in terms of those going to the vanishing point. I’m just going to kind of feel it out.
That’d basically be fair to say. Again, there’s the minor axis.
The dirigible itself isn’t an exact circle. It’s a little bit more of a squashed oval,
but at least these end parts are circles.
Again, we’ll just make quick ellipses of these.
There we go. So that basically takes care of those.
Now, we’re starting to flush out a little bit of 3D in that. We still have the dirigible body,
so we have these three kind of supports here. One, two, three.
I’ll kind of space those out like that coming down to meet the ship even in flat space because
they’re right in the middle anyway, even on the actual structure.
They’ll be about here. Then I’m drawing the flat representation
of, again, the dirigible body which basically starts about here and ends there. If you look
at the comparison we’re just trying to make estimates and say alright. Then the flat top
of that would go to about here. There’s the middle. The bottom lasts about that long
here. Just trying to fill out how the seam would come down and flatten. Then we’ll
flush it out later. We’re just being strict about kind of doing this middle silhouette thing.
Okay. Then we’ll decide how wide it is based on that a little later.
Okay, so now we’ve got that silhouette. We’ll worry about the windows later when
we flesh them out and draw them around. Then I want to remind you of the perspective. These
ideas still get crossed like this in depth.
Same with the front and back of that little carriage part
to that right vanishing point in the center because that’s how we kind
of think about our volume coming out this direction and then doubling over.
Now the idea would be how wide is this compared to how tall it is. So if we say it’s this tall
then how do I come out from that center point to kind create my first projection and then
double it over. I’m going straight through the blue now this way. Straight up and down
or straight through, and say, yeah, this is coming out this far compared to its height.
Where we believe that is.
I’d say it’s about here.
What we’re going to do is estimate that out.
If we believe it’s about that far out in perspective. I’m just making a guesstimation now based
on this depth compared to these heights. We’re starting in the center and saying this to
here is that deep in perspective, that part that comes straight through the part here.
So I’m saying, okay. If I do that then I can make a little box around that.
We can start maybe with a little bit of redder-blue just to make it more clear.
There’s the side coming from the right vanishing point. We’re like where’s the
box that takes up there? Again, we’re just doing a box section right now.
Doubles over, right.
If we double a box over right from the center to that corner,
drive that over just in our minds. Again, this is just the slow thinking part.
Again, this does not mean you draw everything out.
We’re just sectioning together. What we need to do is
meet up with doubling that square over. We’re going to extend the top of that onto that.
We’ll do the same type of thinking with the other sections. Maybe we don’t have
to draw them out in red, but I just want to make sure that I kind of just tell you how
I’m thinking here. Now, if we double that over actually it’d be more like there. Kind
of here, that box. So we now find that our box doubled over. The entire kind of imaginary
square around that is basically here. So now we can draw our kind of oval, which isn’t
quite an ellipse. It’s more of an oval. It comes through here following the perspective.
It comes through the bottom. We’re doing the first seam that goes around at the very
center of the balloon part. We kind of did that on our other kind of flying alien vehicle
before. We’re reminding ourselves what the true parallel and vertical and horizontal
is to the vanishing point over here to the right so we get the right start here. Now
I can kind of draw out what I think that bigger shape should be.
Come down here to grab it.
Draw around to there.
That was a transparent rib made of wire inside the dirigible, whatever
we needed it to be. That’s fine. They would flush out to about there. So there’s that first one.
There’s that center point there, there.
We’re just thinking the inside. We’re thinking completely transparently here as
we did before. We want to make sure it doesn’t get too sloppy here because it does get challenging.
We’ll do this next section here, and we’ll do probably three where we do completely transparent
sections. Then we’ll probably just draw a little bit of the transparent reason, the
little body of the capsule here that carries people comes out. Then we’ll just start
drawing on the surface more and doing the fins and stuff as we work around the shape.
There’s the outside of that.
One of those. Let’s take another one now.
What section do we have next? Let’s figure it out here. We have on our square here is
the four corners of our standing original square for our original square there. So just
inside that is a section. We want to figure out, okay, that’s another center point.
We’re going to come out from there. We’re going to do this section here now. We’ve
got to come from my right vanishing point. I’m just trying to place it properly. How
far do we come out? We can also start looking at our center seam. Where does our center
seam come out? Right there. That would be that crossing there. From our perspective
angle. We know it wraps around to have to meet here, right? So this thing in perspective,
that seam in perspective has to wrap around and get a little shallower. My guess is that
it does this. I’m going to go ahead and draw it in like that. Also, then it has to
come around to meet out there on the edge.
That has to draw around kind of allometrically, like that.
We’ll just try to guess it as being about here.
Okay, so what did we decide? That seam is about there and it comes out to meet that
center seam here, that distance out for the new one. Again, that one starts about there.
It comes down to here, down to there, about there. It goes up to there, and we’ll double
it over. What we can do is draw half of it if we want like this.
I’ll draw it up in perspective because it kind of comes around like this and comes around. Proper perspective
because we have to remember how it comes up and around here to meet that seam there.
We just double that section over.
We’re taking this space and doubling over so we can make
a little box again in red if we want. I guess I will use red.
Just to be really obvious about it—a lot of you will be going, okay we get this. But
a lot of people don’t understand why we’re sectioning still in some detailed areas. Now
this little section here we’re doubling over. So in a sense we’re just taking it,
X’ng it off really lightly in our minds. Taking our time, and we’re getting in that
center reference we’ve always needed. That’s where we double over for our next one over there.
Oops, make that a little longer. Okay, then we’re taking that corner or extending this
out to the vanishing point. Going through this center reference from this top corner,
let’s say, through the center reference all the way out to about back here. There.
There’s our side wall now. Now we now that the other half of that section goes to about
outside there. Now, again, these ideas can be drawn out freehand. You can get really
fast at them. I’m trying to make it super clear just to where this particular section
goes. If this is here doubled over it’s right here. So now that meets up and makes
good sense to come around with this. Figure out how to draw that up. Now, you could say
why did you do all that work just to get this space to be correctly diminishing according
to this perspective from this distance. That’s how you’re thinking. Instead of just talking
about it a lot of people go, oh yeah, just double this over and do that. People are missing
that and not doing it correctly, so the diminishment or the correct side to side symmetry starts
falling apart and does not add up in the end in a complex shape. Then people get lost in
the shape. Things don’t meet up in the seams they should. People get lost and frustrated
and then stop or don’t like drawing things that get a little complex. We’re trying
to just take it a step at a time here. I don’t care slowly it goes because you guys can stop,
play back, and get it until you actually get in on your version. I will imply again if
I haven’t made you tired of hearing me say this, but please draw with me along with the
diagrams placing your compositional diagrams and shapes the same way I do and literally
make your own notes as complete as you need to make them on all the space you’d have
on your 18 x 24 paper. If you’re doing smaller paper have some room leftover to do your ABCs
or 123 steps. That’s all you’re doing but you’re mostly learning from the logic
of actually doing the drawings along with me.
Now we have two basic wire structures of the oval, the one slightly inside, the total outside
one in the middle. And let’s do one of the obvious ones in the back now, which would
be this one. Let’s figure out, I think that one was right there. That meets the shape
there in the middle and up here now for this seam back here. Okay, so we’ll do the same
thing. We’ll kind of make a middle section for it to come out and meet it’s center
part which is right here, because remember we did the center seam all the way through.
We guesstimated it but that was based on a really good guess about the original thickness
of the balloon and how the nature of this thing would move at the perspective we’re
at. We can pretty much guess it’s pretty good. So anyway, this section for that new
section we’re going to draw is this wide. We have to go double that in space. That next
section would start about here, go down to about there. Go up to there. Let’s remind
ourselves of the perspective that crosses it. We have to also cross it properly going
down to the right vanishing point here just in our mind so that when we start drawing
up we meet it right here properly. Drawing around and down in that next section.
Also, doing it here and coming in, meeting this section here. Then we’re going to double
that idea over. Also get the other side again. I know it’s getting a little thick in there.
What we’re doing is we’re doubling this space again. If we want we’ll do it in blue
this time. All we’re doing, again, is taking literally this depth.
Kind of making a little square of it going up to the total height of that halfmark just in our minds to say
that’s the kind of work we do when we section. Even though we might just say, oh whatever,
just double it, guesstimate it. The idea is if you’re actually doing a really accurate
drawing or you’re starting to lose control a lot when you do these shapes in your artwork.
Even though a lot of organic shapes are easier to draw.
Let’s say your painting or your image but there’s a few shapes you get nervous about
or the spacing or the overall referencing of people and shapes being consistent sizes
going way back and way forward in space. All these reasons are why we reference off the
formal perspective just when we need it so we can go back to things that are more controllable
and they, you know, a guesstimation method. It’s both. I always use both if I need them.
If I’m doing something more formal I don’t always draw, and I rarely actually measure
things all the time, but when you really need it, that logic does help because it tells
you where things actually belong according to the perspective that you already set up.
So we’ll take that section just in our minds and double it over from the top corner through
that middle reference point here. Top corner, middle reference point basically going down
to here. We’re roughly landing about there.Now we can say that the second wall side of that
is basically there. We’ve doubled it over.
So how does that translate into what we’re doing here?
Now we have that seam meeting here, here, and doubling over.
That’s meeting at the back seam of the same seam. I’m not
going to draw it in quite yet cause the idea would be we’re drawing this one here coming
back, doubling over to here. We’re meeting up here, so we’re coming back down that
same shape to meet it right here. Also coming back around making sure we’re doing the
shape thoroughly enough out here, basically looking like that. So those are those three
rings plus the two end nipples or whatever you want to call them.
Now we’re going to put in the tail or the idea of the tail. We have that back section
here, but we can do one more now, which again is about halfway. So if I put that ring on
I can guesstimate that. But I’m going to skin this thing now, the bubble. Meaning if
we know the top is here but we have the rib that comes out further. The rib comes out
further. Now I kind of connect the rib shapes to the top of where I actually see the real
edge of the shape, which is there and also coming from here. Now I have to figure out
if that’s right. This part here also has a section that comes out more. If this is
the seam middle for this and it’s about, what, roughly halfway that’s going to be it.
That has to, again, come out and be a seam that meets somewhere out here on that
whole thing, which is going to be right about there. So there’s the seam here where the
fins come out of. We’re just going to say it’s about here. I’m just going to draw
that out. There’s an idea and because the seam is here it has to come down and meet
here, go up and meet in our original middle seam there. I’m looking at this silhouette
still and saying where does this meet this there? That means if it starts there it meets
that shape down there and right there and right there. So I kick it out to the seam.
It comes out to about here. Now I can take that out in perspective.
Perspective, and then draw it out as an oval shape like this.
Again, that gives me an idea of how the skin will fit together.
Then I’m just going to skin the rest and say, okay, it meets there. This comes to here.
Meet that down there.
How do the fins come out? Well, the one will come out the seam meeting at that seam right
there. We could basically say it comes out to that perspective like this, like that.
Then let’s do the top and the bottom as well. The fin shape fits right in there.
We'll come down just about that far.

That will meet up right where the thing turns and meets up here.
Have a little thickness there.
Same thing up here.
Like that.
The middle one kind of turns to us like this.
It comes back and has to meet this just about here.
That’s a little sloppy, so let me get that. This pencil gets too thick.
All these meet here. They come around to here so that fin would come out just about like
that and meet, go around that corner seam. Come back just about like that.
The other one is other side, obviously, coming around. These are not quite up there.
So that’s that back tail part. Let me draw in the skin again so that would be behind it.
There is that front edge seam which has that fin right on it, turning around.
The other fin is there. Connecting there and there.
Okay, so let’s go back down and say how much of an oval would this be? There’s that
middle seam. We’re going to draw the thickness of the middle seams and the top to the bottom.
They’d just be ovals again according to what we see from here and here.
I'll go ahead and just draw the idea of the perspective which helps me see where the middle seam is
meeting. If I make it about that wide I’m just guesstimating how wide that comes out
here. I’m going to about there so I’m just going to make that oval. Based on that
and wrap around like this. It’s not that severe. The other side will come around about
like that. Drawing that out. Need a sharper pencil again, hold on.
There’s a thickness that would come out to here about to there. Just a little bit
of the edge we’d see. This goes back. We could say the center seam would be kind of
like that for the side seam coming straight down there, and then the other side can come
back across, meet about there. Again, that shape would come and make a section about
like that. So there’s that middle section of the thing. The body would come back down
like that. Meet the center. Then the bottom again, since we’re under it, is going to
be a little bit of an oval shape, so I’m just going to kind of draw the bottom oval
of that. Now the windows if we say they start about leading out about here. They go all
the way around. We can just make them go in this back lip here.
They wrap most of the way around.
I’ll make them just go straight in like this.
How many of the divisions we have. I’m not sure.
Come around the other side. We really want to see that side than
just see this empty cavity here. Bent glass. The propeller would shaft through middle of
here from about this idea. We could go back with the propeller shaft and then just there’s
that middle back seam here. That and then the propeller would be about that far of it.
We’d have a little bit of screw in there for the propeller shaft.
Then we can just go up until we actually almost hit our balloon, which I don't really want to do.
We have to be far enough away.
The propeller going around the distance about the same height over there. Perspective
of the propeller comes out about there.
Something like that. That probably is a little long.
So again, just having our little propeller coming out there for that shaft.
It's turning around like that. Just a pretty fast little sketch of what things would do. I’m going
to turn this one more here there.
A 6-blade idea.
We’ve got that circle there.
That could be encapsulated in more of a rim thing here. Then we’ve got to show the outside
skin of this still attaching to here in the middle so it departs there. Don’t want to
forget that part of the skin of the dirigible.
There’s that underpart joining the skin together,
making sure our skin connects up here to what we’re doing.
There's the sketch of that. It’s just the idea of transferring that into basic perspective.
There's that middle scene.
We could come out and double over and say then the middle seam would come
out here all the way across here and then connect up kind of like that would there.
I’m going to keep that pretty light because I don’t want it to interfere with everything else.
That middle seam on the other side would be about there.
Alright. What else? That’s about it for that. There’s our dirigible. Now we can
go on to our arch. Again, we don’t know exactly what scale the dirigible is. Once
you decide on a scale of a person compared to a scale of a person here, about how large
that would be then you could double back and estimate if there was a plumb bob dropped
from the dead center of this down to the ground, like a little line with a weight on it, you
could actually figure out where would that drop to going back in space that much. Generally
you could say, oh yeah, if there was a ladder or a little rope coming down to touch the
ground just where it touches the ground, how far would the rope come down in relationship
to the scale of this to that. We’re not that concerned with that this time because
it’s really just about drawing the objects and doing some sectioning again and the logic of that.
Again, this part being more of an oval or round thing we just kind of felt it out based
on our design and didn’t really do that much doubling. We just go this middle section
here and the overall height being sensitive to where our actual silhouette seams would
be as opposed to the flushed out volumetric sides coming out, but a pretty simple idea.
We did three or four sections in our dirigible, the little fans, the little back tailpieces
and stuff like that. That’s the logic of it. Again, you can do a much cleaner version
than I’m doing as far as if you want it really, really clean. These pencils get heavy,
and I want them to be fairly clear on film. I’m trying to move through as much material
as I can so we can be clear about it. You can go back and reverse and pause and play
again until you understand the connection. But remember, you’re just making logical
side-to-side. We built out the front side first from the silhouette. Built it out, doubled
it over and just tried to come around and so the form transparently so we could see
our little framework here in the dirigible. Stuff like that. Obviously, a lot of that
stuff you wouldn’t see behind if you were doing painting, but it’s the idea of creating
transparent volumetric drawings at first.
Okay, so now we can go on to our archway. Again, we have this kind of X’ng. We can
take notes from here and say, alright, I’ve created an arch here at this height there.
That would be right there. Then say, well, where do I think the crossing of this is compared
to this size? I can come down and measure it, but I could also just guesstimate and
say if I drop down about that much from the side here, so if I take note where these are
basically just side to side that kind of thing. Drop down the same proportion I can say, well,
I think those are about here. As long as I commit to right there then I could get an
idea that I’d have to come up a little more for my archway here. That is a corner point.
Just like that’s the corner there. Let me fix this taped part a little bit here.
That point is where this might start, and that goes straight up there. Since I’ve committed
to that top part being there I can kind of feel out the front part of my arch a bit.
I can make a square of it if I need to, or I just feel out the curve of it based on the
original pattern. If I do that that makes that fit there.
Then we could say, alright, that comes up about that far. We decided here to that part
and very close to that we have a little bit of a rise, and we have that part right there.
Draw across and say, alright. Well, I have to get my longer ruler actually.
We scoot across to our left vanishing point to bring this point over to the other part of the X
that I’m referencing to there. This X gives us a little bit of reference room here.
Okay, that reference is typically right there.
Then we meet up here. That works out well. Come down, come down. We’ve doubled over there.
Also, we’re saying now we’re going to try to control these areas. It drops a little
bit down from there. Maybe here. I’ll say how far out is that?
Out there. I’ll go ahead and just draw what I think is the first part of the arch based on that.
Then our job will be to kind of double that over in the other side using perspective.
Okay, so we’ve got that first part. Now the logic is let’s place a reference point
somewhere right around there. A little bit lower. We’ve got this part here. In this
drawing we have that crossing the vanishing point from about here. We’ll do that same
thing here from the corner. We can also then start saying about down here somewhere we’re
going to have a reference point representing that one. Then somewhere up here right around
the horizon line really. We’ll just say the horizon line is a good reference point.
We go straight over to the horizon line so those are those two references.
I’ll go over and cross over from that one.
Then we have our horizon line. Go straight across anyway.
The idea now is we have references. We’re going all the way across. We’re going all
the way across here. Now the good news about this one is it already lands all the way across
on the other part of the X. We know that one. That is there and we can basically guesstimate
this foreshortened part here to around here. It’s pretty easy to estimate. So we'll do that.
Just try to double it over and say okay. It’s doubled over space. How do we kind
of figure this one out? Well, an easy way to do that for me would be to go from this
point and reference it all the way up to the middle seam right here. Make a middle reference
right there. If you want to do it official, come across, get that there. Then when we
come down again in that same motion, the top through here right down to there, we get that
point right around there. So that’s how I doubled that over. I just used this middle
section as a reference going through the X line. Bringing that across to make that reference
coming back down, same way I went back just then. There we go. So that’s that reference
point. We can probably do the same there coming from this point going through to this middle point.
That crosses and makes a little reference there. If I travel across right to there then
I should be able to go right to the idea of we came from here, went through here.
Went through there. Now, if I come through here, through there, I should land on this line
right at the same place across to represent that. There we go.
So now we have our references. Again, it’s just easy referencing. We didn’t really
do it color that time. We did enough arches where I think we all kind of get it. It has
to come through there, come up. It comes up through there. Comes up right through here.
Draw through there lightly. Come back up. I’ll dedicate that one now.
Go through there. Go further out and come back in. There we go. I’ll adjust this one a little. I
think it looks a little. Well, that’s a little too far out.
Let me go ahead and draw that one in again. Alright, so there’s that one.
Now we’ll take those different points.
We need the thickness of the arch. We’ll probably do that in red if we want. We have
the basic arch shape now. No surprise. Now what we’re going to do is drive that arch
back to its thickness. This thick on the other side so we can see it in this side how it
forms. That will be some simple referencing again. We have the first clue here that we
already have the depth. This little seam here is already going back to here and hitting
that right there. This point here is back here. It’s counterpoint is. Then that means
if we know that is standing straight up to be official we can say, well, we know that.
If we make a little point standing straight up on its counterpoint on the backside like this.
We simply meet this height right here. That little corner.
That’s the first move right there.
Same one as that one back on the back wall.
Now we have to start arching in. We take this first reference, but since we can use the
X as we’ve done before, we could also the X if we wanted to. We’ll take the back corner
and the back corner and the back corner, back corner and carefully X it off.
If we want, just as a reference.
There's that X in the back corner.
That's the new X there, and that should go right to our vanishing point if we’re pretty accurate
and it does. There’s the thickness of the arch right there. It seems a little confusing,
but now we can literally take this reference right here on the X and move it to its counterpoint
right back here. I’ll do that with red if we want.
That goes back and hits that point there.
Put a little arrow there. There’s that point. This is there now.
Another easy way we can do this is we can also since this is right on the horizon
line we can draw a red line back like that.
We can still reference that.
Since it's right on the eye level what we’ll do is
we’ll also take notice that this is also right on the X.
All we have to do is bring that back its counterpart on the other side again.
That’s that point right there. Remember this is the back X so I’ve just
projected that back to its counterpoint X. This one we can find from conventional referencing,
meaning that if we draw a line projected back in space from this one we can also then take it--
go to the corner, go back to the back corner here
then come around again until we
meet that plane until about right there. Now this point is right here.
Be a little harder in this one because we, you know, we have no corner on this.
What we have to do here is estimate it on the back
and say, well, if we know this one is in the front.
This one is harder to do because there’s no perspective because we’re flat to the horizon line.
What I’m going to do is I’m going to just say if we know that dropping straight up and
down puts us right on that pretty much, this is right on top of that, very close to that.
We know that this also is very close to that. All I have to do is move that far over in
perspective to about there. It’s a smaller space. That’s pretty good. Again, I don’t
want to get hyper-anal about it.
And then to move on to the corner up here, we have this corner. This point is here. Then
we continue on and move the corner up like this in red.
How do we find that corner space.
We could still go back and very carefully do this reference. Go back to the right vanishing
point to the actual back wall and then come back up to find that spot pretty much to here.
So there it is. If you want an official way we just made a plane between that little spot
corner, came back, went back to the back wall, and came back over to meet that spot right
there. That should be it. Even though it’s pretty easy to draw. Then we can meet the
middle seam as well. The middle seam is important because we can get the back archway that way too.
Very simple stuff.
There’s our back X and we’re just going to make that middle
seam until it goes up and meets there. That is the counterpoint to that here.
That should be pretty easy.
Now we can just take where this meets the middle seam here and make our
final reference meeting there. Pretty simple. Now we can simply say it looks like this goes through there.
It goes through about there, peaks at about here. Runs back through there.
Comes through. I’d say it actually projects to about there.
We know we have that straight shot right there.
We simply have a little bit of a straight, so we draw up to that.
Oops. In our mind we draw back up to that arch like that even though we only see this
part of it. We’re drawing all the way back up there. Then it would double over over here.
All we actually need to see is this part. There’s the thickness of the archway.
Referencing it.
Let me just darken that up a little bit. We know that this part is actually part of
the archway, not the opening. Do the side of the archway.
We’ve got to put our crown molding on top real fast. Little bit of that crown molding,
which will be easy. No big deal. I just want to make it an idea. There’s that corner.
We’ve got the front before the road. A little darker here. Forgot we have crown molding
down here so we can just do that. Drive that back to here.
Okay, so there’s that back wall.
I want to make that darker.
Again, if we add the crown molding just the basic idea would be we came up like this far
just to be official.
A little bit of a crown there.
One seam in the middle may be coming up like this.
Then do it back to here.
So there’s that. Then we have our road that
we’ve already kind of drawn out. What I’ll do before we continue,
we’ll draw a road out here.
We’ve already drawn it through here.
The road just continues out there.
A little slope continues out there.
Alright, so there's our road.

Alright, now we’re going to get to our car. As I mentioned before—let me get a sharper
pencil here. Here’s our box for our car, so we basically, we know it’s one, two,
and a third long. One, two, and a third. We’ve already kind of said, okay, that’s one unit
across by tall. It’s a square. There’s that square represented in perspective there.
We’re just going to take the idea where this car fits in. What we’ve already drawn
is we’ve done the very outside of the kind of transparent Plexiglas box. The idea is
we have a center line, so I want to make that a little clearer.
Here’s the back of the square.
What we’ll do is make sure we understand that the center line hits that back part right there.
We can jump it up because we’re going to want to
know what the center of that is so that we can center the car’s plane. Work it out
from there. We also want to raise it off the ground a certain amount. Then we’ll have
the wheels also. Understand where the wheels are.
First we’ll probably do the wheels, but we have to understand that we’re in the
right position for the box. It’s most important obviously we get the three wheels that we
can actually see. The fourth with be completely behind the car. We can lightly indicate it
with a square or whatever. It’s not that important. For good form we can draw it. We
want to do it lightly because unfortunately it’s right by the cockpit where the driver
would be, so I don’t want to go into too much detail. The wheel will be very light.
Anyway, let’s figure out where we think these heights are now.
If we do that we can, first of all, figure out what height we think the wheels are compared to that in total.
Let’s figure out what about half the space is on those squares if we want to do that.
So again, the total height of the wheels are there. If we look at what is the halfway space
of the actual—about there. So the body is almost exactly the halfway point. It’s a
tiny bit above it. Wheels are a little bit before that. There’s the center of the wheel,
so it’s added about a quarter probably. So essentially if we take about half and put
about half here and then go to about a quarter we’re coming through. The wheels are topped
off at about a quarter. So let’s just draw and estimate where that might be coming forward.
So what I’m doing is I’m just imaging that and bringing this part forward right
about here so there. If that’s about half, and I know where my halfway is.
It's about there, a little under. I’m going to estimate my wheels at about this height here based on that.
Then we’ll try to figure out, okay, where are they following exactly. It’s almost
exactly in the one-half space here, so that’s very convenient. There’s the one-half space
of this square. Remember we X’d it? Make that a little clearer. We’re just trying
to be brief on this. The first square here we’re saying, okay, the halfway part is
exactly where the wheel would start. Right there. We know the height of the wheel, therefore,
we can draw it down here and say all right. Halfway down would be the height of the middle
of the hubcap. We’re just making a mark. I’m just going to feel out what I feel is
a good square. I’m going to lightly put that in, something like that.
Okay, so that’s the position of my first wheel. And then we can go for the second one too. That falls
right almost on the third line too, so that’s fairly lucky. It’s a little forward of that,
a tiny bit. I’m going to follow that center line back from where my other hubcap center
is here just to make a mark back there.
Just trying to feel out according to this where it is.
It’s about where that third mark is plus a little forward. So there that is.
If we wanted to make a basic idea of a square, do that about there.
Just about there really.
Wheel would fit in to about there. I’m just trying to lightly come up with the space that
our basic wheels are in. Then we can move across to the other one too.
That’s the case here.
Four points there just to mark out where those ideas would be.
Then we can take the axle across kind of like this. We’ll do a little thin axle over there.
We know it’s flush against the other side so we can take the idea of carrying this one over.
Taking this side over as well.
The idea here again is to carry the center of this over to the other side.
There’s my mark there, essentially right there from the center here.
The center up. I just want to hit that. That center is about there. Wheel is going to be
about there. Obviously, we want to go the very flush end of the box, so there it is.
I’m making the squares just to make sure my parameters are correct for what I feel.
Since I have this marked right there where it wants to be there, I can also carry that back.
Quarter point over here. Kind of carry the middle of the axle out.
I'm just trying to place it relatively accurately.
Right about there the tip of the wheel back in.
It's about there. We’ll call the square about there. There’s a thickness to the wheel,
of course, we have to consider. That’s just the top part. Obviously, we’re going to
also talk in terms of these corners having a thickness. I’ll draw that thickness out
to our left vanishing point. Again, we’re just doing simple wheels, the idea of them.
Same here. These come in a certain thickness.
We’ll do about the same here.
What we can do is in this case if we know they’re about this thick or so we can also
carry that logic over here, just guesstimate it on that.
We’ll draw an inside box now just to estimate it.
That thickness starts about there. Corner it off just to be clear.
Top box just to shape out the idea of the wheel.
That wheel box will come out about there as well.
So there’s our square over there. Bring our center out right there.
That's about right. We’re just trying to take note where our center is.
That’s where the back of our axle would be,
the beginning of the car would be there. Also, this thickness would
be coming back about here. Again, meeting the car about there.
We’re just trying to figure out for when we
make our flat kind of silhouette on this elevated surface for
the bottom of the car it makes sense with the four wheels. This wheel would have thickness too.
We’ll just draw in the idea of that real quick.
We’ll draw in the back axle idea in the back as well, just really lightly
because we’re not really going to show that last wheel much.
That would meet that about here.
I’m just crossing it just to say, okay, that back wheel would be about right there.
Meet the body about there. I’m just marking where that would be.
I’m going to hold off doing the back wheel first until we do our sectioning of our car too, but I'll do
the front wheels just to see. Don’t want to get too much in the way here.
Okay, so we have, of course, just to remind you, have our minor axis here, there we go.
Minor, minor, minor, and the minor.
We know we want to cross a little bit in the perspective front at true
90 degrees, about like that. Just to remind you. That’s the idea of that.
The wheel will just keep kind of block shape at first. Then we’ll give it some thickness.
Obviously, it goes over to the vanishing point.
Just give it a second here. It comes around like that.
We’re just going to kind of double around our thickness. Now we know that the
little wheels on cars would be more rounded than that. I’m just going to give them their
basic roundness later after we trim out some detail on the car. Not much.
Okay, so there’s that first wheel. We draw out our second wheel as well. What we’ll
do is we’ll just do the same idea. Remember our major is crossing at 90, just a little
bit in the perspective front, like that, just to remind you.
Need it about here or come around.
Also, draw in our thickness here on the top.
Just estimate from the same kind of thickness we had going here.
Come back to that later. So those are our basically two wheels beginning.
Again, they’d be alittle more rounded really, race car wheels like that.
Okay, I’ll hold off on that one. We know the thickness is about there. Again, just
a little past. We only have a little bit of space between the wheel and the body beginning
here, so I just want to kind of say, alright, if we know it’s that thick the body would
begin about there. Same here, just about there.
If we know the outside is right about there,
inside would be meeting about there. Coming straight back from there. It would be about
there, and then this thickness too ought to be about there. That’s where the insertion
would be. So I’m just trying to get that right. Then we have to come up and meet that
into the body. Now the body will actually be lower than this. We decided on a little
bit of a point up here, but that’s about that height. There will be a little bit of
a rounding here toward the top. I’m going to slam that plane into the front here and
just mark it and say, okay, that’s about here. That’s the center where the front
of the car is centered and meets that point there. That elevated point off the ground.
I can kind of put in a light indication of the square of that elevation so that I can
kind of do my silhouette. I’m going to say that’s the car’s height. We’ll go back
to the other vanishing point. Again, that’s just the square. The bottom at the very outside.
It’s actually in from that because the car body doesn’t really touch the actual square
outside except for a little bit. This just indicates the very outside parameters of that
square as a corner that’s raised for the body.
Just as an idea.
It’s important that we get the halfway point properly.
It should be about there. That mark. We’ll go back to our right vanishing
point, just indicate how the center goes all the way back to here.
So that’s that raised corner, raised corner, raised corner, and then the back raised corner
right there as well. The halfway point drives through, touches that back plane just about
there. There’s the center, and there’s the center. Just trying to get an idea of
where all that lays
So now we’ll do basically a guesstimation on our silhouette. Since we don’t have a
top view we’re just trying to say that probably the meeting at the center of the car is probably
the most outright about here. And that at the most still can’t be in the thickness
of the wheel. But what we have to do if we have to come up and kind of meet the center
here and say, alright, just a little bit after that point here we’d come up and meet.
We have to go into the thickness of the wheels toward the vanishing point here and say, alright,
the body of the car is only allowed at this height right here. This is the absolute outside
of the box flush with the outside of the wheels. We have to take the thickness of the wheels
in consideration, but then come in a little bit and say, yeah, the body of the car is
allowed to come out that far about, from there and meet that. We can go across and make the
same estimation, of course, over on the other side. Let’s meet that mark right there.
It comes back and meets right there. We’re just meeting this point here, across here
and saying, okay, it’s right there. And then a little bit in would be where our body
comes out to a max right there with some perspective foreshortening. That’s just an idea.
Okay, so what’s the basic idea of what I want the body to do. It’s going to come
out a little bit here flush from the front. It’s going to wing back, and it’s going
to be a very simple design tapering in slightly like this and coming through so it doesn’t
draw through the tire. Then I’ll also figure out from the back center, just have a little
bit of a rounded shape here. It will start rounding and curving in underneath there,
coming back probably about like that. We’re going to have a little bit of a raised grille,
but we’ll see how that works out. We can just meet a couple places where we know it
comes in, but it’s a pretty shape to reckon because we know that rounds out so we can
start there and say, well, it starts tapering in here, comes by, a bit of a space there.
We have to figure out how far away it is from the car body from right here at this point
and at that point later where the axle meets the car body. What we’ll do is now we’re
going to make what we think is our top silhouette as well. I’m just going to go slightly back
here, that middle section and say where does that middle section hit the top of
where we thought the trunk was.
It’s going to come up here like this. I’m just trying to look at what this does.
So there’s that middle seam there.
Whoops, don’t want to come down too quick. I’m trying to get my head of the way for you.
And just as an idea, this is going to come down like that until about how low, about
that far up. So if we take the middle seam, and we say that’s the middle seam. How far
up is that from the middle seam. It’s a ways up.
The middle seam is only going to come up to about there.
There’s that middle seam, that distance. Go to the middle seam here.
Where do we think that is?
We know that’s there, about to there.
Come up straight up the same height, so it’s almost like this comes across like that.
We're looking for this center point right here where we say it goes straight up like this.
A little bit of indent. It kind of goes up like that. It’s a pretty short back end like that.
It gets wider as it comes out. It also has a back area. I just want to make sure we’re
sitting over the center now. The ground, center, right here. Center, back to there.
There's also a little bit of a funnel thing doing this right from the center here.
Goes back in space like that. Curves back there.
See how that comes out later as well. Then we have a little bit of
the seat coming out here, the center seam of the seat.
See how that works out
Okay, so that’s about what we have there. We have a mark there.
The plane of the tire I’ll do in red. I’ll just come in and make sense of that, center
plane of the tire. It comes up and meets it, that third part.
I’d say at about this height right there we know that’s the height marker of the car.
We take that and we bring it the perspective left vanishing point.
That makes a little plane until we come in and hit our body.
So that’s how far on the body is there, and so that will be repeated on the other
side. We’ll just do some logical seams there. Obviously, this one comes in and tapers.
We could also do another here about in the middle if we wanted to as a section.
We could just drop it from the outside of the wheel if we wanted to. Why don’t we do that?
Take that same section. It’d be right here. Bring that over to there.
It’d be the same idea.
Bring this section in. We’re just trying to get an idea from this original outside
cube section that is the raised part of the car where these different ideas meet it. We
have this little section we’ve already put in here.
It’d be the same idea.
There's that section.We can also put another one.
The center of our wheel here, where the section meets it here. We’re saying
the body of the car comes back here.
So that drops straight down from there again right down to here.
Going back to our left vanishing point for another section there.
And we can probably just deal with that and then come to the front.
We want to take little sections there.
Now we can readjust where we believe the wheel hits the section.
If we’re talking about this center plane here coming to the hub going in. Then the wheel
on the same plane as this hitting the body here. The body is going to go up and curve
so the actual wheel will keep going here and here. It’ll be meeting the body just about
here, a little further in than I thought. And then we’re just doubling it over in
space. So now my job is to meet these sections and go all the way over lightly to the bottom
of that section, bottom of that section, top of this section.
Go all the way over. Top of this section all the way over.
The idea is we’re meeting our center plane right there.
It’s where that section meets that and all this stuff meets on that plane
right there in the center section there. That goes up straight up.
It’s meeting the top of the car there.
Now we have to decide what shape we want that section.
Also, this section at the height of the car meeting here, meeting there, where the wheel
connects about there. Just trying to get an idea of what that section is doing.
That meets it there and I can just make a little vertical there. There we go.
So that’s the idea of that section meeting the middle.
We’re going to double it over after we get a section. We’ll just do that in blue.
I’m going to have a little bit of a body thing here, so I need to figure out
what I want to do. I think I want to come up a bit and then come in like this.
It’s going to come up and come over like this.
There is going to be a taper.
I’m also going to do it here.

Where it meets this body here. This is going to be a little thicker taper, a little bit
more coming down and meeting over there like that. Then we can carve in the grille a bit.
We’ll go a little more around. Maybe if we go—the grille will come down there.
It tapers a bit like that. So that point meets right there for the tapered grille which will
actually come across like this a little.
We’ll probably meet it up in the center or something like this.
The tapered grille might meet in the front, double over. If we take that space
and double it over here, bring it over.
Getting a front grille here will be the idea.
Little vents doing this kind of thing.
And it tapers a bit so the bottom is right there. I’ll do that in pencil.
Then it comes down slightly and meets this curve going back to the car.
We’ve got our two sections now.
So the one is this section here, which has to be doubled over.
This one also has to be doubled over. We agreed that section hit there. It came
over like that. I’ll just very lightly draw them in like that.
This is our section here. That is exactly the middle of the wheel. The wheel slams right
in there to the body. That’s where the axle is attaching to the body and invisible from
the wheel going through the axle, middle of the wheel, like that. It goes that deep. Even
though the wheel is only about this thick here itself, there’s about that much gap
between there and the body, a little more than I have here. Something like that.
Close enough. We’ll just double that over.
But let’s go ahead and build out the seams on the near side to us and just do it slowly
and try to figure this out. If this is the kind of representation of the cockpit right
here, this basic angle, how do we figure out what we want to do? Well, we can come and
just make a section right there. That would be a little hair past that.
Let’s go here.
Here to the middle up here. That section would be a little bit further back, something like this.
I think that has to taper a little more to do this.
Okay, so about here based on where this is and where the cockpit starts, I’m going
to make another section and try to figure that out, where the widest part is to here.
So let’s just do that right where the cockpit starts by the windshield would be a good place
to have a section. I’ve got to come down to that center line, which would be right
here up to about there, let’s say.
I’ve got to come out to the outside of the car at that
point from the left vanishing point, something like that.
Okay, that’s the point. We also have this rise which I’m going to continue. It’s
going to be a little bigger here, maybe. It’s going to taper a little taller. There’s
going to be a little more height than that. I think I want to have this come up and taper in.
Then, of course, this is coming over a bit. Remember, this flat part is only the
flat, middle plane silhouette of what we’re doing. This part, this part, and this part;
it’s like a paper cutout. Now we’re making our section obviously flushed out quite a
bit more. I’m just trying have that kind of perform how I want to do that.
Now we have that plane or section as well.
Then we have to figure out where the cockpit starts. As we know we felt the center was
kind of there to the cockpit. What we’ve done here is—if we take that and go down
to what we think is the seam of the cockpit, about there. We’ve got to come back out
and say where does that happen. Right there.
A little farther back.
That also has a pretty good rise to it.
And we know if that comes around to here the cockpit wants to
meet that above there. I’m just trying to think, yeah, right about the center.
It's about right.
So that actually comes out and just meets it right there on top of that ridge.
Cockpit, that space there. Right as we about get here we’re hitting that there. It’s
going to come around like that and meet here. What it does it comes around here, comes down
and shoots pretty much straight out.
That’s the cockpit right there. That’s how that works.
That’s the point where it basically comes up and straightens out. This straight
section here comes up to here and drops to here. That’s our center section, remember,
right there. Try to think of where that drops and how that’s going to come out and meet.
So I’ll meet that section out there again just past there to meet the outside.
Now we have a little more tapering to that bulge. We have to figure out how wide our cockpit
is at that point. With the seat it comes down pretty much straight down.
So I’m trying to think of, okay yeah,
just about to there like that.
There’s our half-section of our cockpit then.
This is going to go around and meet here kind of in a rounded shape.
In a sense that comes up and does do this.
Section meets that, comes down.
Again, there’s our one little section. Our other little section for
a cockpit just to make sense of that.
Alright, so that goes back. If we go back we can just taper back to the center place.
It’s actually going to be a little further back than that.
Make this thing about halfway behind the seat.
Again, that goes back down so that would be like this.
Around out, pass it later. Okay. Double this over later.
That’s for the cockpit.
So now we kind of basically have our sections. We can double them over. We’ll take our
doubling lines now and just kind of make a basic idea of where to double them over to.
We have a good idea because of where the body falls, but let’s try to be official about
it and say, alright, there’s our first doubling line from here. That distance over here just
to be official about it. We bring a box up to here.
Meet it, cut it in half, just a section real quick.
There’s the middle. We would go for that section just about here.
That would be up there.
It would cross over from here.
We’re just doubling that basically.
Now, we can just make a good guesstimation from how this would behave.
Bring that section across to about there.
Bring this up here. Carry the height over here.
That’s about right where that would land. There’s the second part of that section.
Obviously, the body would have a little more out here, and we’ll just double that section
over too. Again, if we take this as a square straight up, we section this,
X that off at the base at the center line here.
Double over to this footprint here.
Let’s see where the X goes.
Right to there where it should be right there. Double that one over.
Now we can take our section right where it needs to be, perfect in blue.
Double that idea over there. Carry it over.
Double this one over. Now we can kind of see where the skin goes for the car, just right to here.
This fills out just a bit on the side here.
This flare comes out here.
Probably just about to there. Come up.
Meet with this line here. There’s the top of that.
Again, there’s this flare here at the top.
Meet up as that goes out.
Meet up with that back at the body here.
Trying to draw behind the wheel.
Now we can kind of double over the third section here in the cockpit.
It's pretty to guess that because we double over to that side.
That’s what we’ll do there.
See if we can see a little bit of that back wheel. I’ll darker all this in for you too.
We’re just trying to get the idea of the simple idea of the sectioning.
Let’s do this section now. We’ll bring out the base of this section all the way over
to the other side. We’ll go, okay, let’s double that over again.
Bring that as a box over really lightly.
Coming over, let’s X that box off.
We drive the middle to the center and make that reference. We can come back from our corner.
Go through that, down the other side.
There’s where our box should start right over there. There’s our other
box meeting up like that. Just to be official about it. I know it’s annoying. But now
we can kind of say, okay, up about that far.
Over on this side, carry that over, starts turning to about here.
Kind of a broad turn here.
So there’s that section again. Just as good information there. Then we can take
the section, of course, here for the cockpit and take that section over.
The important thing here is to say, well, if that
comes all the way to the bottom there, drive that all the way through.
We can just talk about the seam of the cockpit at the bottom here
and just double this over where the seam meets.
That’s about all we’ll need to double it over.
All we really need to say is, okay, if that’s our cockpit right there, we can make a square
here to that space because this kind of hits that middle seam.
I’m just interested basically in this.
If I can double that over then I can meet the other seam and just realize where
that would be in perspective a little easier. No big deal. It’s pretty simple to do.
Drive the middle over to there. Double it over.
Something over there.
Again, in blue this would be about this square doubled over like that. This part would be right there.
This part would continue out to about there.
The more important thing to me is where’s the
cockpit end, and it ends about right here. Now we know that crawls up like that. That
comes up like this. This comes over like this. Rolls back over that way.
Goes down even further and rolls over that way.
Alright, then we can put in our other vent idea here. Just draw it in. Draw in our seat
because if that bigger vent which is back there, which is taking air in maybe right
there doubles over there to that curve.
Then we can put a seat in. Maybe a little headrest here.
Centered, coming out like that.
Just a little seat in the center.
The center of the seat console.
A simple idea. A little padded headrest, a little rounded padded headrest right there.
Oftentimes I had little tilted pieces of glass
so we can probably say that’s really short.
Just kind of wrap around to there like that. Probably a little tapered.
How would the steering wheel actually come out?
Probably come out around here, the stem of it.
The steering wheel will come out at some angle kind of thing.
Here's the back wheel again.
Just remember the idea that you’re trying to plant your major axis down properly.
Make that wheel behave properly so that one probably comes around just like that.
A little bit of thickness.
That wheel going across might even show up a tiny bit there. I'm trying to figure out if we
had that side of the wheel about that big. Barely.
It wouldn’t even really show. It might be a tiny bit there. That’s about it.
The placement of that wheel back there.
Let’s draw these out darker now. What do we have? We’ve got that vent going a little
thinner. It goes back. Have that wheel come forward.
Kind of a wheel cap, obviously.
It has some thickness.

We have our front wheel here.
Again, the wheel just kind of draw it in here.
Old hubcap, old spokes.
It’s a very weird looking transparent race car, but frankly that’s just trying
to get the idea of the sectioning. There’s the body going back at its thickest point
here where I made that little section. We’ve basically found the bottom corresponding parts
here, having that roll around here to that side. We’ve basically got the idea of where
the second side went for that.
Center line there, something like that.
There's that other side.
That’s the grille, a little lift of that lip coming in
because there is a little bit of a lip here.
That vent going down meets me the back seam
in the center right back there. Center line went back all the way.
Just trying to make the outside dark.
Let me darken this in a bit. Makes more sense. It doesn’t look so confusing.
Just make the outside a little more dark for you.
It’s just the logic of the basic sectioning, again.
Pretty rough drawings as far as the idea is.
You could be using a sharper, cleaner pencil than I am. What I want to do is pound
through these and pretty much emphasize them on camera.
Just the idea of what these sections are doing for the tire back there.
That’s a real simple idea. There’s no guy inside.
I wanted to make it more about the seat and the sectioning for the car. Put a little driver
in there. I will decide against it. It will just be very sloppy and more stuff here than
we need to look through, obviously, just the idea of the beginning of the steering wheel
here, facing out. If it was on a stem about that long, something like that. Little spokes
on it or something. See if I’ve forgotten anything. Yeah, so it’s a simple idea.
Again, it’s coming down this road.
So to recap: Again, we have a basic idea of taking side elevations and a front view; side
elevation, front view; and just a front view of the arch. Just kind of sketching out the
idea of where the planes were. Pencil gets a little soft so it’s dark enough to show
up on the camera. I apologize I get a little bit of lead on my paper here so I need to
clean that up a little bit. The essential idea is you’re just thinking of every object
you come to what would be the most logical way to section it. As we talked out, you know,
in the archways in the initial part of the lecture 14, then going on to curved objects
and eventually intersecting planes, all of that just speaks to the same thing. Am I being
careful to create what I think my plan is? We haven’t gone into really strict plan
view where we follow a design exactly. We are estimating here based on a design or something
we think it wants to be close to it as you really would as more of an artist. When you’re
looking at reference or inventing some things, it totally depends. It’s based on some real
reference, and then you have to have event to make it look real in your paintings or
semi-representational style.
The idea is the sectioning will help you make more sense of the things you have to invent
and then also understand how to turn the angle of the object. You might have good reference
photographically for your painting or what you’re looking at, but you need to turn
it at a different angle. Even though the lighting and the reflections might be basically the
same logic as your reference, you actually have to turn the structural angle. This where
the sectioning can be very, very helpful in perspective.
Again, none of this is that eloquent. The idea is are you understanding how to actually
take something, section it, and make it look correct and believable. As for how believable
the rest of your representational painting is looking for what kind of art you do. So
the perspective is simply helping you understand how to A, set up the entire composition. Again,
these aren’t very eloquent compositions. These are diagrammatic examples that are really
trying to make it clear how and why we create certain things in basic sectioning and referencing.
Compositionally we’ll get to more ideation. We have to still get through 3-point and,
you know, putting figures in perspective. Just basically the good gestural mannequin
of figures and then, of course, the 3-point and a whole bunch of lighting and plan view
and stuff. So ideation is a separate idea.
Of course, you want to be able to sketch and ideate a lot like beautiful ideations like
landscape paintings like Edgar Payne. Really beautiful stuff. But that can’t come before
you understand functionally why and how you’re sketching, sectioning, and do kind of invisible
hand movements to nail your little shapes when you’re actually drawing in perspective.
That comes from understanding how and why perspective works.
Again, I’ll reiterate after this kind of long diagram that it’s about why and how
the perspective works correctly. That’s how you know how to push and pull it more
than it might do because that’s what you want. But, you have to know how and why it
works in more of a straightforward formal manner before you can do a lot of playing.
Again, I just wanted to show you three basic examples of things we’ve been kind of talking
about. How to section a very simple almost like pinewood derby type of car. It’s the
idea of how you’re sectioning and doubling. Of course, we could get more eloquent with
the examples. But I really want to go through why and how the perspective works and get
really far into all the different types of things I mentioned, basic lighting, casting
shadows. To do that much material we want to really make these fairly basic and really
talk about them more. Why did we create the front half? We put all the wheels into place
as little squares so we could get the space correct. Are these the most beautiful drawings?
Not at all. These are just basically working ideas to get you to understand how we kind
of section in different ways. They’re straightforward enough. But in reality I don’t want them
as clean as they would be if you did them digitally because that makes it all about
the cleanliness of digital, which this isn’t about. What people aren’t knowing these
days is why and how perspective works from any angle from any compositional angle.
My idea is I’m going to move through these fairly fast in a pretty simple straightforward
manner. Gets a little heavy in the lines sometimes. The idea is do you understand how to set up
and then proceed with the sectioning of curved objects doubling over in opposite symmetrical
space, almost like a reflection. This side comes forward. It’s opposite goes back and
diminishes properly in perspective.
As we’re starting to conclude this idea of lecture 14, 15, and 16, the main thing
is do I really understand how I can take basically any object, understand it from sketching and
drawing more in my sketchbook normal mode, but then actually be able to do some sectioning
and some logic at the view angle I actually want to use for my composition in my artwork.
That’s when the sectioning is more involved because you’re like, yeah, I have to make
this look like it doubles over like it would in real space. It’s a great way to use it.
You can get very exact with this, as I said, when we go to plan view.
But really, I’m less interested in doing that with people that are beginners and intermediate
people because, frankly, I just want you to be able to understand and use and draw with
the perspective immediately in how you want to apply it. You should be doing all your
homework and the practice sheets or doing more complex composition. If you know how
to light, put all the lighting you want in. It’s the idea of are you using the perspective
in setting up these compositions the way we talked about in the earlier lectures and then
getting more familiar with these different ways to realize objects. Obviously, as we’ve
done in this kind of more sectioning then on lectures 14, 15, and 16.
So again, just keep it clear why are we talking about the cone, the setup, the picture plane?
Because it applies to everything I look at. And then how what position is the subject
matter in. Well, these lectures, 14, 15, and 16 were more about how to attack the subject
matter and understand the sectioning and the doubled over side-to-side symmetrical movement
of those objects and simple objects and stuff. This is still an intermediate object. Again,
if you want to do a really large drawing of a sectioned object without too much distortion
then you wanted more room to get really clean sections and planes to show yourself that
you really understand it then please go a step further. Then do even more complex objects
than this. You’re welcome to. The sectioning and the doubling over doesn’t change at
all. It all stays the same. It’s the exact same concept. The more complex you go with
the object, just the more careful and more focused you have to be that you’re making
the right reference side to side positions, and you’re making your planes equidistant
as they diminish over correctly in perspective. You have to triple and quadruple check the
work. That doesn’t meet any of the logic changes at all. It’s all exactly like this
lecture series has been in 14, 15, and 16. It’s pretty much the exact logic.
It’s just that, of course, really eloquent designs and very complex objects would have
more time put into them and would be very clean with maybe beautiful lines. They can
be done digitally. They are all the time. The 3-dimensional programs, obviously, are
doing all of this immediately. But, the idea is that you’re taking this lecture series,
I’m assuming, because you want to learn how to draw and tackle these things on 2-dimensional
surfaces giving the illusion of 3-dimensional form. This is basically the logic of sectioning
so far. We probably will do a digital draw over next. Then we’ll be on to figures plotted
in perspective in a whole bunch of positions.
Alright. This has been diagram 133.
We’re over and out, and we’ll see you on the next one.

We’re back for another digital draw over. This digital draw over will conclude the diagrams
for the lectures 14, 15, and 16 on archways, curved planes, and objects intersecting planes,
that type of thing. We also have this boat, which is very nice because it happens to be
about exactly parallel to the buildings and then tilting up. It has very clear ribs, and
we can see everything nice and clear. I have to also put in something similar, but not
the same boat, but how the boat basically behaves as a shape from the top view and a
side view. As we can see it obviously bows out and comes back toward the stern. This
one does more of that and is a proportionally longer boat, but the same type of behavior,
but you visualize when we’re talking about the things we are with this boat. Also, we
can see that the bow and the stern are actually higher, and the middle comes down. As it bows
it actually gets lower. Then it comes back as it snaps back to the stern.
Also, that’s important too when we’re analyzing this shape. All we have is this
photograph. I’m assuming the digital draw overs can be helpful is that it puts the lessons
we’re doing and the operations we’re doing into a slightly different context. Since we’re
already looking at a finished shape. It’s very helpful to analyze that shape and be
able to apply perspective to it and understand what’s actually happening here instead of
what you might be assuming is happening. That’s always an eye opener a bit. Also it helps
us practice those same concepts but apply them to things that we already see. We’re
just verifying how and why these operate. We’re going to throw back the perspective
for the entire thing including the cone of vision as usual, just to be able to, again,
rehearse the formal and why it works. So we’re first going to do the formal of where all
the official vanishing points and a couple measuring points are actually for all the
perspective here. Then we’re going to come in closer and actually do the sections and
talk about why the intersecting planes and sections and reference points are happening
as they were in the lectures for 14, 15, and 16.
Okay, so we’ll go ahead and start out. We’re basically just going to be adding layers here
as we go in talking about them. I’ll just make points with the cursor rather than drawing
everything out and taking forever. First of all, we go ahead and lead off and find all
our vanishing points from obviously the planes that are behaving the way they are in the
photograph right here. So the vertical tilt going through the auxiliary vanishing point
up into the upper left obviously diminishes this way.
These diminishments I’m taking from this texture on the concrete, which is evenly diminishing
off to the left. Of course, we have even diminishment here off to the right. When we back off we
see that. These conveniently work toward vanishing points. I put them in kind of a ghosted gray
because they also consistently went to places. As you can see, the auxiliaries work great.
These come to a very, very consistent point as well, and so does the building in these
things out here. I’ve kind of ghosted them in as well as indicating the center of the
picture in the approximated eye level/horizon line from those diminishments off to the left
and the right. No surprise that tilted boat ends up being directly above the left vanishing
point here. We’ll put this in. I also want to point out, though, as well as make these
moves I wanted to show you that our little diagram here will be paralleling those moves as well.
So as we add on things to the verticals here, we can clearly see the idea of these moving
across the boat here as we add these in. We also want to then consider the length and
the widths as well. But, as we critically take these up to the auxiliary vanishing point
to the left, we’re actually adding those on right here as well. If we take them away
they disappear. I just wanted to make that point of we’re looking critically at the
widths right now of where they go in the boat and why they behave that way as well as setting
up our perspective for the vertical leads.
This brings me to second idea here. It’s that now that we’re actually adding the
official horizon line we’re also casting a line from the very top of the bow here all
the way to the stern here straight through where this little peaked arch part comes a
little above. But, this is basically straight up. This is also represented here now on our
diagram of this white line across, as long as the rest of everything that will then be
diminishing to the right vanishing point. The lengths going through the boat are consistently
all going to that vanishing point over there, which we’ll back out and see that now.
And so we’re kind of officially now naming everything. We’ve got our horizon line eye
level now that we’ve derived from being able to find the diminishment to a point for
the vanishing point right, the consistent diminishments leading up to the vanishing
point left. Of course, these projected widths from the tilted boat end up diminishing to
a point straight above vanishing point left. Of course, we’ll call it auxiliary vanishing
point left for the boat widths. That’s what we see here.
Again, these are all paralleled in flat space.
We’ll keep continuing to refer to the simple moves of these ideas here in the flat spaces
we see with the lengths of the boat here, the widths of the diagram of the boat and,
of course, the lengths going this way from the side view. Eventually, of course, we’ll
be adding sections as I mentioned too.
So now we’re beginning to get that setup. It’s important that we get our station point.
So what we can do is we’ll slide on down here, and we’ll look at the idea of the
station point right here. So I came back from our left vanishing point and our right vanishing
point and came down toward the center of vision, which of course is the center of vision here
is the line right in the middle of the photo. The main thing, too, of importance is that
before we went ahead and did that we’ll go ahead and zoom in a little bit on this.
We did find out that the true center of the camera plane is the magenta lines I’m clicking
on and off. We now the camera was being held a slight bit downward because the actual center
and horizon line/eye level of the camera plane, which is represented by the pink line and
the X here in the center, was just slightly below our horizon line we found from our subject
matter in the actual world that was photographed. That way we know the camera was being held
slightly below that or it was cocked down a little bit. Our verticals would actually—instead
of buildings being true vertical would have an incredibly subtle diminishment down to
the center of vision way, way, way down. We’re just going to clean it up and
call it 2-point because this is so close.
We’ve done this before and discussed it before in the draw overs. It’s just always
being aware of what you’re actually doing if you’re an artist using perspective in
a camera and looking at photographs a lot, looking at the world around you with your
eyes and walking around environments, why things look the way they do. In this case,
the camera was being held just slightly downward. It will have a tiny bit of an implication
near the edges. The verticals tip in a little bit. Not that important, but it’s just so
that we’re aware of what we’re dealing with when we actually X off and find the true
center. So here’s the true center of the camera frame: It’s the pink, but the real
one we’re looking for, horizon line/eye level that we’re concerned with, which leads
to the vanishing points and the SP at the center of vision point, which we’ll look
for next, is all based off the white line horizon line eye level in that setup. Okay?
Just wanted to point out the difference there. That’s the difference in the pink there.
So we’ll go back and we won’t concern ourselves with that. We’ll go back now and
find the SP, which we’re going to do by—the idea would be we’re going to work down from
our vanishing point left and then our vanishing point right coming down toward the center
of vision as usual. And at 90 degrees we find that station point.
We come down in this case—because we’ve already
established vanishing point left and right from the diminishments in the
photograph itself; therefore, nothing could be easier than working toward the center of
vision. You’re simply coming down, and that point at which that meets at 90 degrees becomes
our station point. That’s where we really are. Remember, that station point represents
this actual distance from here straight down to here. That’s how far we would actually
be right here straight in front of the photograph. This same distance is how far from this point
we’re standing straight in front of this picture plane looking in. But since we can’t
represent that in a 2-dimensional presentation, we have to represent it as flattened out.
So this is the flattened or collapsed station point. Our real station point would be that
same distance out here in front of the photo as you remember with all these same angles
and projections striking the exact same way.
Okay, next what we’re going to need to determine our auxiliary is we’re going to determine
a measuring point for vanishing point left. Remember how we do that? Here we go. We’ll
turn that on and off. Remember the distance from vanishing point left coming down to the
station point, that same distance replicated on the horizon line becomes our measuring
point left. In this case the arrows show you that it’s been projected up. That same distance
between vanishing point left and the station point is simply brought up to our projected
out from to be the same distance. That makes the measuring point left. That allows us,
the measuring point left now, that allows us to project up to the real angle. We already
know our auxiliary vanishing point left was established from casting back the real angles
from the boat. Knowing that this is it because next we have to find out what would the verticals
of the tilted boat be doing if there was an actual mast sticking out of here straight
up. Well, we know that, but if we come down at the true angle here to the measuring point
from that auxiliary, if you take the horizon line right here as a straight line and take
our angle of our auxiliary, those two make a real angle. That would be the real measured
angle from the point of the measuring point like we just discussed in auxiliary vanishing
point and slopes back in the lectures. That real angle here is the real angle of the slope
or the tilt of the boat. So the degree that boat is actually tilted to its side is what
this really is on a protractor. A real angle.
Since we now have our measuring point, we can take a real 90-degree angle and find out
what the vanishing point is for tilted verticals, like a mask. They would all actually diminish
to one point. That one point is going to be way below the vanishing point left down here.
Let’s do that. We’ll out it first at this. There’s that 90 degrees projected down from
here, and that’s going to way, way down until it finally meets way down here. That’s
quite a ways down. So what I’ll do is I’ll come out a couple more times here. Let’s
see if we can put that—there we go. So that’s what that looks like. There’s that 90-degree
projection down from the measuring point once we have our auxiliary angle coming for that
real angle we can measure off the horizon line, and the tilt of that real angle will
give us the real tilt angle of the boat, as you remember from, again, auxiliary perspective,
or I should say sloped perspective.
We have the real 90-degree projection down here. What is this giving us? It’s giving
us next the real projections back up through the boat that would be true verticals. If
we had a mass standing in the middle of the boat that was truly perpendicular or it was
straight up from the boat because the boat is tilted, that would be the vanishing point
that all those true verticals standing in the boat would meet. Even if a person was
truly stranding vertically this would be that point. That’s important because you’re
estimating it.
Even if you don’t have the space to go all the way down here, if you can estimate from
your auxiliary angle originally from the boat, and you understand the basic cone of vision
setup or where your vanishing points are, you can estimate very closely by casting way
down here the idea of being way below the vanishing point left where that point would
be where all those vertical projections would be coming through at what angle and then eventually
diminishing down to this exact point down here.
It’s the idea of it that’s really important. Even if you can’t draw in the vanishing
point itself, drawing to it and imagining the space and why it works is the important
thing. As long as you know formally why perspective works, you can informally draw it very well
if you can just think and concentrate a bit.
Okay, so now we have that so I’ll go ahead and zoom in a bit here. Alright, so next we’ve
got—I’ll just flash those on and off a little bit again. Those are those verticals.
So now we know we have in yellow our projections up to the auxiliary above the vanishing point
left. We have our ground projections to vanishing point left, which made that originally. We
have our diminishments to vanishing point right. Now we have our diminishments that
go through the picture going way down to the a tilted vertical vanishing point, auxiliary
vanishing point for the boat’s tilted verticals.
Now we can make a diminishment guide. We’re going to do the cone of vision first because
I want to show why that’s important to understand what millimeter of lens we think this photo
was shot with, so you can always to try to match the perspective or understand how it’s
working. Tracing back from it is helpful. Especially if you’re grabbing reference
and wanting to change it. Let’s say you have a photographic reference of this of a
boat. But if you draw the boat just as it is in the perspective given to you from the
photo and the rest of you’re perspective setup for your drawing that you’ve already
done or plan on doing is not the same perspective. You have to change one of them. For consistency
you’d say, oh yeah, I’m not going to use such a wide angle lens. Understanding how
to determine how wide angle something is or why film in the picture plane works as it
does in film cameras and photographic cameras, it’s important and it just gives you a better
knowledge base of why the perspective is behaving as it does. So let’s do that for a second.
We’ll back off here again and let’s see if we can get that cone in just like that.
So here we go. So that looks like a whole mess of stuff. All that is really doing again
as we well know is—let me zoom in just one time here—all we’re doing is from the
SP we’re projecting up 30 degrees and 30 degrees. Center of vision in the middle for
a total of 60 degrees. That collides with or hits the eye level horizon line. We then
take the center right here where the eye level crosses the center of vision, and we take
and draw a circle all around that. That gives us our cone of vision that demarcates the
basic beginning of distortion in one and 2-point. That’s what we’re working in here is some
2-point with an auxiliary vanishing point.
Okay, from there I also put some framing in. So what is this millimeter framing I’ve
done? As you remember—let me come in a little closer. Within the cone here, as you remember—back
to our diagram on how film frames work—if we take a 3 x 4 frame that this is right here,
the smaller one inside, and it just centered on the center of vision crossing the eye level,
if those corners of a 3 x 4 frame just touch the cone of vision that is equivalent to an
approximate 50 mm lens. Now, we know our frame that the camera took the boat in is not 3
x 4. It’s longer than that. But, the important thing is the width and the idea of where the
center of it basically is. So if we take the width of it and extend that to the idea of
a larger 3 x 4 frame we come up and we know that the thing was shot in approximately 38
to 40 mm, according to how the basic gauges of how millimeters work in proportion and
context to the cone of vision. We discussed that idea of film frames and how to the gauge
the millimeter of lens approximately. You can get pretty good steps from that to approximate
it.
Just for information, this is where the cone is in relationship to this particular picture.
The perspective we’ve gleaned and projected back to from the picture. We also are kind
of paralleling our little diagram here. Don’t forget about that. So 38 to 40 mm is how I
figured this was shot. Again, this is all formal. I know it looks like a big mess, basically.
Remember the pink line here was the centering frame for the picture plane of the camera
itself. We’re more concerned with since that is so close with the perspective working
from the photograph, we’re not that concerned. I’ll back up from this one more time to
show everything. There it is. Even more time. It’s crazy to see how small this is to show
the whole setup. I know it’s really small but that’s the entire setup we have just
from the simple tilted boat and a simple 2-point environment. The idea is if you know the formal
you can keep working back to these things if needed to approximate other things. But,
because we set up the first vanishing points here be aware that we were able to get to
this real auxiliary vanishing point by using the measuring point from the true vertical
tilt here in measuring the actual angle.
If we come up again it’s interesting to find that all this actually works out pretty
easily if you’re doing the formal. Again, the cone works out and shows you the proportion.
There is the whole setup including the station point. That’s why we were able to derive
the measuring point. Remember the distance from vanishing point left to the station point
gives us the measuring point on the horizon line. We’re then able to gauge the real
angle of this, the tilt of the boat because the widths of the boat go to this auxiliary
above the vanishing point left. We already have the projections to vanishing point right
so we got our SP. We’re able to project a cone from that. All these things we’ve
done before. We can take and understand the flat information from the basic diagram of
what a boat would be like of this type from above and the side. We’re really thinking
about the formal setup of perspective.
Beyond that, now we’re going to move on to moving in close up to the picture again.
We’re going to create diminishment guides based on this because of that. Because of
these vanishing points now we’ve actually found, or we could become very close in projecting
just beyond off our canvas and be close with, I’ve created diminishment guides based on
them in pink again. So here they are. Now I’m going to get really close up, and then
we’re going to zoom back in on all this. Let’s do that. Go up to 100%. Here we go.
I’ll bring the picture down and center it for you.
Now this seems like an insane mess, of course. I want to show you this because it’s all
the thinking involved. I know it’s crazy and it’s all these colored lines. If you
were to draw them to set them up for a drawing they’d all be very lightly put in. You wouldn’t
even need to use them. This is just formal drafting, formal perspective. But it’s why
and how it works, again, to remind you. It’s a nightmare of webbing here because we had
to make it clear enough to be able to see when you’re on your computer screen. Obviously,
we’re going to remove all this. But remember, all this is just based on what we originally
quickly projected out from the actual just incidental photo that we liked and wanted
to start analyzing how to either add subject matter to this exact angle of photo, or to
be able to take this photo or this item in the photo of the boat and slightly change
it or do what we want with it, all from understanding why it’s working in perspective. It’s
just analyzing.
Let’s remove these layers now and get back to some of the basics. I’m going to leave
layer two in there so we can now see—let’s take the diminishment guides away. We’re
back to the original simple horizon line we had eye level in the middle of the picture.
That line I’ve drawn from the bow straight back to the stern leading to the right vanishing
point way off there to the right. And from all those vanishing points I got from that
whole formal setup now we have our diminishment guides. Of course, I’ve added them too.
If you notice when I do that they also change on the diagram to show you we’re just simply
dealing with the length and the width of the boat along with the true vertical standing
up in the boat. Since the boat is tilted, though, they’re not truly straight up and
down like the buildings would be or the rest of the environment. Those have to diminish
way down to the left below the left vanishing point if it was already discussed for that
auxiliary vanishing point for the tilted boat verticals. These true verticals in the boat
represented on the little diagram here are actually these tilted coming from our vanishing
point, which we plotted from the original auxiliary slope coming back to the measuring
point at 90 degrees way, way down to that line. There they are. So those are the diminishment
guides from that. Of course, these diminishment guides here are up to all our actual auxiliary
angle above the left vanishing point. Then we have, of course, these projected back to
the true right side vanishing point on the horizon line.
So those are the three diminishment directions you see here to help us draw when we do our
sections, which we’re going to be doing now. All we need, basically, is an idea of
where our horizon line is just to remember. We’re going to start with this important
line drawn back to the right vanishing point again from the bow to the stern straight back
through the boat. We’re going to make a sanding plane basically for the middle of
the boat. How I based that was simply by following the bow down through the bottom of the boat
and then connecting up considering the thickness of the wood going a little below these planks
and just following the actual center of the boat to the back where I see this seam coming
down here in shadow. Then I go back right up now on the rudder board back here, where
the rudder is right against the back transom there. That’s basically what? So I’ve
made an entire shape there which is important to start my sectioning.
I’m going to start the sectioning either on the front half of the back half as I see
fit. We can do either. In this case we’ll be doing mostly the back half first. But in
the very back of the boat I will be doing one here where I can see it. Next, what we
have to do is to say, okay, what ribs would I be following my sections like we did again
in archways, curved objects, and intersecting planes? We rehearsed that a lot. Now we’ll
just build some. Here we come into those. Here are the sections. I’m going to flash
them in and out. I’ve taken them off various ribs at points.
So let’s just explain how I derived this logic. It’s simple. We’ll start with this
middle one, let’s say. I started with this rib here at the edge of the boat and the back
half and said, well, that’s easy to follow back down here through the floorboards through
the center. Now I considered the rib compared to the thickness of the boat. There’s a
little bit of a gap space here between that boat plane. That’s fine. My section is derived
from the top of the rib back to the center. Then I project straight up vertically, which
would be the boat’s verticals because it’s tilted. I’m simply using my diminishment
guide so I have to gauge how my projections in between those diminishment guides would
work as well as being very close to them. I’ve gauged how this actual diminishment
goes from up to down. It gets larger as it goes up, and the diminishments get smaller
as they go down toward the vanishing point way down below the left hand vanishing point.
There’s my first section I derived from the first rib drawing straight across width
wise. I know that from my diminishment guides that are going across the boat from the auxiliary
vanishing point above vanishing point left. That’s how I have that height. So I meet
this plane by going down the rib to the center, the true vertical coming out of the boat going
to that auxiliary way down to the left. Also, my tipped auxiliary to the right is where
I meet up with it. There’s that plane. What the red mark is is the remaining space that
has to reach the true height of the very top of the part bow going to the stern. We know
that the boat dips because this particular section we’ve been looking at is right at
almost the center of the boat. There’s the very center between this filled wood space
here between these two planks. I just went with the one back here. If I project all the
way across past the little section on the other side and just leave it like that we’ll
catch up. We’ll do our X’ng and boxing and doubling over to find the second part
of the section as we did with the drawings. But first I created all of them on the backside,
except the back here for which I created this section because it’s easier to see the seam.

The same idea, though. Once I can catch this I can double it over from the other side.
Remember, all these red spaces here are simply with all these sections after we figured out
the center coming from the bottom seam and from the side meeting and intersecting here.
But we know now from perspective that gives us the answers from the X, Y, Z that this
is the remaining space to this true height line or vertical line—Sorry, I should say
length line going all the way through the boat to the right vanishing point here. That
would be the higher line up here on a diagram. Then we can see that these edges as they go
toward the middle or the center of the boat, the main beam crossing are at the lowest point.
We can say this basically is the lowest point here and here. But we really haven’t drawn
over here yet. We’re just going to stick to the back half of the boat right now. Same
with this section. Same thing. Same thing. Did the same thing. Follow the ribs down to
the natural conclusion where they hit just above the center there taking into consideration
the thickness of the wood. We came straight up according to our diminishment guides that
are verticals for the tilted boat. Then we also came straight through the width we’d
go to the auxiliary vanishing point. Matching up with that we’ve got a section. Then there’s
the remaining vertical until it hits the height of that main length idea of the top plane.
Remember, that’s the top of that plane we created originally for the center of the boat.
Same here. There’s just a little bit of space from this section right here. Again,
this is based on the half of the boat at this point going down. This line here is the back
half of the boat. Obviously, all these ribs that we’re following here on the back half,
except for this last section. Again, start it from where I believe the floor is. The
top at this point straight across width wise to the edge of the boat, and then I follow
that seam. I can actually see through the shadows to approximate that seam. The idea
is when you’re drawing it from scratch you can make the seams anything you want based
on your design on the boat. That would have to do with what you’re following from your
imagination or from possibly a plan in an elevation or plans in general. Either way.
It can be a number of things, or it just purely be from imagination. You want to create sections
after your general sketch to make it really consistent from side to side.
Again, side to side symmetrical sectioning. Now we’ve got all these positive sections
in. Then we’ll do some of the X’ng and doubling work on the first section here. We’ll
go back to that. I’m sorry. It’s this section here. What we’ve done is we’ve
taken and we’ve boxed the first section here, as you can see. There’s the section.
The first box we put around it. We’ve X’d it. We’ve found the center and driven it
to this reference point in the center, and then we’ve taken the bottom corner coming
through. We’ve found striking the top line where the end of that is, right on the edge
of the boat coming down. Now we’ve got the two section boxes.
We’re going to create our next section, the one that is opposite, the mirror reflection
of the first section coming over. We’ve also noticed we’ve made this reference point
on this line where that actual section strikes here. So if we come over here we make this
second line going from the top middle down to the bottom just like here. It’s mirror
image. If we come across with this that makes an equal reference on the other side. So when
we bring our section through we know we have to run through it. The opposite angle this
is coming through here on our way up to the top corner. We should find on accurate representation
of the second part of that. That’s what I’ve done here. There’s the other part
of the section there. As you notice, that section is basically the rib following the
contour of the boat right inside. You have to take into consideration the slight thickness
of the planks, but that’s the other side of this rib right here riding up this all
the way up. So we’ve done that with all of them. If that logic works for how to X
this off, find the center, double the square over or the rectangle over like we did with
many of the sectioning of objects we did back in the lectures, it’s the same process.
We just want to keep it clear. There’s that remaining height left between the height of
the section compared to the true height of the top part, the higher part of the bow here
and the stern here. Bow, stern over there.
Okay, so let’s show you the rest of the boxes. That’s how the rest of them work.
So now I’ve applied that same doubling theory and that same yellow reference point on the
back side once we’ve made the equivalent cast diagonal from the top middle to the bottom
front corner. We cast that forward and then that reference point helps with all the sections
after that. Here are the added sections. Now we’ve taken various ribs in the boat and
made sections of them just like we were creating it from scratch or whatever. I haven’t done
them evenly in exact step order. I’m just picking the ones that are visually the easiest
to see, and they don’t get in each other’s way. I had to just make it clear visually
as demonstration as a diagram rather than necessarily picking all the exact ones I might
do if I was drawing one up. It’s to me much more important you understand the concept
and the execution of the concept so that you can apply it to anything you want to draw.
The first ones will go more slowly as you know, but as you get better at this the logic
of your mind snapping into why these sections work and all the little reference pointing,
you know, X’ng, halving, doubling space, finding equal reference points on one side
doubling over in the mirror image to the other.
That’s basically what this practice would be that you’d be doing with difference
objects as we did in the lecture demonstrations when we’re drawing.
So here we go. To work back again let’s just go backwards, I guess. So we’ll go
back to the original sections. Again, we have that middle section here.
We now know the middle plane section of the boat. We then added all those sections based on following
the ribs down to the center plank basically, projecting them up to the true verticals,
all using our diminishment guides. As those sections grow we understand that they’re
not reaching the full height of this original length plane at the top because the boat sags
and sinks a little bit and then comes back up for the bow and the stern. Also, it actually
is growing wider to the main beam and then coming back on itself again. Again, this diagram
or this top view and side view don’t represent this exact boat. It’s just the idea of what
it’s doing in the space involved.
We have that tapering and then coming back up. So that represents the space. Finally,
when we come to the front and the back they meet right at that same height. We’ll explain
a little more of that in a bit. We added the work for that one section to double it over.
We find that. In the same manner we create all the sections and also find all the forward
sections. So now we have all the sections we wanted to do of the boat. That can get
a little bit confusing. We’re going to also add the idea of extruding something out of
a big block and coming into the curves next. I just wanted to run over that again. What
I’m going to do is I’m going to get rid of the box shapes most likely like this so
that now all we’re left with is the sections. Now we’re left with the standing middle
section of the boat in the middle plane of the boat and then the sections we drew both
the back ones first and then came forward. I’ve just gotten rid of some of the other
ideas there. I want to keep the diminishment guides in though. We could still remove those,
wherever those are. Let me remember—I think those are it. Yep, so if we want to make it
clearer there are sections without the interference of the guides. That’s according to the perspective
that we laid out from the photo itself and then applied the logic of what we understand
about the station point, the measuring point, the cone of vision, all that stuff.
That's one part of it.
The applied part is, yeah, but when are we going to get to draw an object and blow everybody
away with that. Let’s great. But as long as you understand how and why the perspective
works, you can set up and entire scene of complex perspective. Then you can go about
sectioning all the objects anywhere in that scene you want all day long because you know
that the perspective is correct rather than, you know, trying to individually draw things
and eventually think they might compose themselves together with the perspective of everything
in the picture. That’s just doing it backwards. It’s putting the cart before the horse.
We need to always discuss the larger reason the perspective of an entire composition works
first if you have to consider it before you go ahead and draw individual objects.
Obviously, if you’re not composing pictures but you’re just designing objects or designing
objects as an endeavor, then all you’re doing is showing the one view of that object
or two view of them in separate perspective. You don’t need to basically
congeal the entire composition together.
Alright, so there are the diminishment guides. Those will also help us, those diminishment
guides, in drawing our next thing, which is a big block. I forgot to mention that I just
drew this kind of thing to remember. Anything directly outside of these curved sections
is water if the boat was in the water. I’ve just drawn the idea in if we had these sections
back here. That’s where the water would be. I know it’s obvious, but we tend to
think of, oh, since we can see the boat sections we’re not really thinking that right outside
this space for the remainder of the rectangle is in fact or would be in water. That’s
important because that’s outside of it. You’re just constantly thinking even though
I’m looking at an opaque photograph I’m thinking very transparently about what’s
happening around this form. That can help quite a bit. There’s that idea.
Alright, so let’s take this one off and this one off. Let’s draw the rest of this
thing in. Here’s another weird one. I’m going to get rid of the diminishment guides
which are confusing pretty soon here. This is assuming we take a block. I’ve also drawn
it in on the plan. This block would simply on the side view go all the way from the very
top bar in white that we had originally going all the way back here. And assuming the depth
of the lowest point of the lowest part here—that would be right here—and just made a width
of the thing. So it’s almost from here to the lowest part here and made a block of it.
It’s just to understand the idea of how we can take the curves. If you actually look
at the varying heights of this same center line, and then you actually take the height
of the sections and we were to carry that true height of the sections all the way out
to this block and also take the true height all the way up the top line of the bow and
stern out, you would actually eventually get this idea as a section curve.
So if we had a block just covering of Plexiglas the entire top of the boat with the very top
of the block touching the very top of the bow and stern here, you would have this curved
in this red line. That is the curve in more of kind of a flat side plane of what the actual
boat does here from our side view. All I’m attempting to do is create this block section
right there on this diagram of the boat above and create that kind of curve that kind of
goes like this in red. That’s what this curve is here in red. It’s just showing
what is the actual curve that was scribed or designed into the boat. Also, on the backside
we have this same curve. Well, if you take all the elements, what we’re doing is taking
an actual curved shape on a block, and then we’re pushing it in intersecting planes
until it touches the side of the actual boat, which tapers in also as the next dimension.
It also tapers in. That’s a complex idea.
So the boat is not only going back in space, but it is tapering down and getting wider
and then tapering in and getting higher again. So if you were to take a block of the complete
maximum width of the boat at its widest point, the widest point of the beam right here and
you were to take a block and surround the entire boat from its highest point at the
top down to lowest point of the lowest part of the rim you would actually see this block,
and then you could actually see the designed curve on the flat face of the block on the
very outside of the boat. It’s just not necessary to this all the time. It’s an
idea of how we can look at what’s happening with intersecting planes a little more interesting.
Each of these sections represent the bottom of the actual sections we made from the ribs
of the boat coming up to meet the highest point as a section and then continuing out
to go to the widest point. We’re working with ultimately the height, the width, and
the length as depth of the entire thing. That’s how we know this curve if it was carved into
a flat piece of soap or something as a bar. That curve is really represented by the entire
curve of the length of the boat, except the boat also gets narrower and then wider and
wider and narrower again.
How we deal with that issue as kind of like almost like a railing on top of the boat is
that if we want we can also add the idea of that, idea of the height too. This is meeting
the actual height. So in another sense we can add that on, which I remove the other
part first. Now, we can reach all the parts at the top of the boat that go to the section.
Now we can see that kind of shape that’s created by the very top of the boat going
straight across in this middle section as we’ve been talking through about the diagram.
We can also see the sag of the boat or the tapering of the outside lip of the boat and
then it coming up again. You can see it here. Here is where it would be straight on that
top plane if this was just a flat board that represented the very highest point of the
bow and the stern, and it was the entire shape of the boat. Here it is represented in green
so let’s look up at the diagram here. Essentially, we’re still representing all these dimensions.
Okay, there it is.
There’s the very outside taper of the boat. So it’s the deepest right about there in
the middle of the boat, and then it comes back up and meets itself as a flat plane at
the top. It’s just two different ways to think about intersecting planes. These planes
and the actual sections of the boat and why and how the tapering affects the rest of the
idea of the true height of the top of bow and the middle of the stern, and then why
these taper down and get wider. It’s a simple idea but you can think about it in different
ways. It’s not that you have to think about regimented in this exact way. It’s just
different ways of playing with the idea of how you could draw a boat out of a block really
if you wanted to and then think about it not only tapering as it goes toward its own center.
But then it gets thinner and thicker.
All those happening at once can be a complex idea to draw.
As we learned in the sectioning of lectures 14, 15, and 16, if you think relatively simply
about things being blocked first and then moving into that block like you’ve put a
Plexiglas box or a solid block of clear lacquer or Plexiglas around something and how you’d
carve that shape out of it. That’s the kind of thinking we’d need to do this when we
talk about the side of it being a curve. The red line is an actual curve in a block for
the side view for the elevation and then again this curve here. So it’s kind of a long
walk to just section a boat, but it turns out that we can use everything to talk about
why we’re doing this. Again, this could be applied to a very complex object. Obviously,
this is just an intermediate object. It’s not big deal. But, if you went into something
very complicated like a boat with many, many things, like a whole floor section or a battleship
or anything that gets complex you have to keep thinking in terms of the nature of the
boat itself in the water and then what part stacks on top of that and then what relates
to the different heights.
So these sections and references continue and continue and continue if you want to do
them really accurately in perspective. Even if you’re just sketching with them you’re
still using the basic parameters of this sectioning in your mind if you’re not really representing
it even in a hand sketch. It’s still there, though.
That’s the kind of thinking we’re doing.
Again, we’ll go through the whole thing from scratch here. I’ll turn these layers
off and we’ll go back to the beginning.
Here we are with just our boat. What we did
is we said let’s extract all the logic of all those planes that go off and make our
vanishing points. That’s what we did.
That led us to our official setup, let’s say.
That led us to actually label everything and say there’s our real horizon line eye level,
our center of vision, our vanishing points, our auxiliary vanishing point.
We can see our auxiliary vanishing point left. All that is set up. We glean from what we need to set
up and understand. Even if we’re not drawing all the way out to an official vanishing point
outside our frame we’re very clear on where they’d be resting and why they’re there
even if we’re just drawing them in our imagination or
kind of making ghost movements to when we draw.

Next, we found the true center of the picture frame again. So if we come in on that a little
closer it’s just the idea of being aware of what the true center of the picture frame
is of the camera as opposed to the environment we were in knowing that the camera in this
case was being held just a little bit lower a hair below the horizon line. No big deal,
though. Very close. As we mentioned in the earlier digital draw overs earlier in the
lectures it’s very hard to know when you’re actually outside on the street shooting reference
without a tripod or a level if you’re actually flush to the picture plan, you know, going
straight with the horizon in the middle or not. As long as you’re pretty accurate and
close, it becomes close enough to draw from. You’re drawings as an artist will always
bring things back into form of a one and 2-point if you want. What’s the point of copying
a photograph exactly that’s a little off from being in one and 2-point. When you draw
it you can just tighten those, snap those things into actual one and 2-point, kind of
like what we’ve done here.
Next the idea of the station point. What we’ll do we’ll go down a little bit here and then
remind ourselves. We added the station point coming down from the vanishing points which
were already established. Remember if you already have your vanishing point left and
right in the horizon line in the center of vision and all that you just come down and
meet at the center of vision at 90 degrees. You’ve got your SP. We created a measuring
point as you remember. That measuring point was to be able to get this in here.
That measuring point was to be able to gauge the actual angle, which is going up our auxiliary vanishing
point for the tilted boat. If you take the actual horizon line and that real angle to
the auxiliary that real measured angle and a protractor again is the real angle that
the boat is tilted to from being perpendicular and parallel with the ground. It’s been
tilted. That’s the actual angle from right here to that measured. That measuring point
also allows us to then come back at 90 degrees and go way, way down.
Way down here to where this meets down here.
Quite a way. For tilted boat verticals auxiliary vanishing point.
And so what we can do is see the whole thing now. We’ll go way down in size. We want
to go tiny. There it is. That’s our whole setup. Obviously, if we come back in now.
Next we actually drew in our verticals, and we could see that the verticals matched up
with what we actually saw in our picture. So let’s draw those in a bit. Actually,
I should say flash them in and out. There are those verticals. We can see that they
come extremely close to matching up exactly with what the verticals would do in this boat.
We’re just trying to show ourselves that we know that the formal can lead to exactly
what’s happening in a photo or reference or an imagined scene or vice versa. If we
just draw something we really love we can see how close it comes to the formal and decide
if we want to change it or not. If we love it as it is, and it’s just a little bit
off or somewhat off in the formal and it looks convincing enough, you leave it. You’re
drawing it. It’s not trying to be an exact computer generated perfect virtual space image,
but it can be if you use the measuring and the perspective in a formal way. It can be
either. You can use this perspective any way you want. We’re just showing in length of
why formal perspective works. You can use it as you need it depending on how much you
want to go into it. Again, those are those verticals coming in and out.
Next we did the cone. Again, if we come back from here the cone is just projected.
Remember we did the framing. We put in our cones like we did many times, but remember we reminded
ourselves this time of why our framing—if we take a 3 x 4 fame and actually touch it
to its very corner centered in the cone of vision that’s basically a 50 mm lens in
3 x 4 format. Our format is a little bit wider than that so I took the width of its center
and then also brought it up and down to being a 3 x 4 format, which is a little longer than
the format of the picture frame. Either way, because I can gauge it from doing so, I realize
that looking at my diagram I’ve made for myself and we did earlier in the lecture series
with you guys, the different millimeter of lens is approximated on basically
these movements in and out of a cone.
I’ve estimated that this is a 38 to 40 mm lens setting when this shot was taken.
We know from doing this that is, you know, it has a bit of wide-angle lens effects, and
we have to be careful if we’re trying to fit that into something that has very conservative
perspective. So when you draw your boat or think about the idea of your environment you’d
have to want to basically have continuity between that so everything moves properly.
The problem is that if you’re not thinking about how perspective works or you don’t
care, oftentimes you get a very wide-angle boat in a very conservative 2-point perspective
because you’ve combined the two or juxtaposed them together, and it can look awkward.
Okay, next. From all that we added diminishment guides just to make it more crazy, but then
we’ll remove all the other information so I’ll get up to full size here.
Zoom this down to right there.
So now our diminishment guide, as we can see, come in and were based on those three major
vanishing points on the yellow projections from them. Now, we’ll get rid of everything
else we don’t need, and we’re just left with the basic horizon line and that original
true horizon that’s projecting from the bow to the stern of the boat along with the
all the diminishment guides. As we reminded you, that’s the true vertical of the tilted
boat now, the true of the boat here, and then goes all the way back to the traditional horizon
line right side vanishing point here. Then we started adding in sections. We’re making
these steps, of course, as the diagram continues on the boat. I didn’t want to forget that
on the diagram up there. There’s the idea of the three dimensions we’re looking at
in the boat from the diagram in pink. We already have the ones in yellow in for 3-dimensions.
That was also helpful to just look at what we’re trying to deliberate from an actual
top and side view of a boat. But again, that boat is not the same boat; it’s just the idea of it.
Alright, there's that middle section we created in the boat, remember, following that
horizontal all the way back from the bow to the stern coming down, following it around,
so basically that’s where we’re going to base all our sections. We created a whole
bunch of sections in the back and the forward one of the back one because I could see that
seam in the back here. Created all the rest of them and then also made it very clear that
how far these came short in height to reaching that top height of where we
know the bow and the stern end up being.
We know now that there is a tapering to the outside as it gets thicker and as it comes
back in it also gets higher again just like in this basic diagram.
We then added our first section just to play with the idea of the section.
Again, what we did is we made a rectangle.
We X‘d if off, found the center, drove it for the reference point
in the middle. Took it diagonal from the bottom back corner through the reference point to
get our front of our square squared off here.
Then we can follow the same diagonal, come back down and opposite to find that
reference point where the section actually this that.
That’s an easy way to get a reference point to know. We have to that same reference point
on her section on the way back, as in this case. Then we went ahead and drew all the
rest of our boxes same way and using the same reference point and methods we get all of
our sections together. Then we remind ourselves that everything outside those sections that
is just through the thickness of the ribs of the boat, of course, would be water outside.
So it’s just a reminder of the fat that what we’re thinking about when we’re doing
the boat even though boat is opaque in the photograph we have to think very transparently
to find our sections and the idea of what is inside the boat compared to outside the
boat. That seems obvious but we have to keep that in mind. Then if we want to take away
the idea of the sections here we can take our idea of our block that we talked about.
We can remove the idea of actually even the diminishment guides because we don’t need
them anymore. Then this block following the diminishment guide shows us what the outside
design from a side view would be on that tapering all the way to the lowest section back up.
If we extended the entire boat’s shape to being a block from the very top of the boat
on this top plan and to the lowest point touching the lip. So basically here on the diagram
up there on the boat to here, and we’re putting these sections through it to understand
how these intersecting planes behave. If I want that curve on something that’s this
wide as a block, I can then cut into that to find the boat inside of it.
We didn’t make the block the entire depth of the boat, but just enough to find the highest
point of the bow and the stern compared to the lowest point of the boat at the lip of
the boat. Its width, maximum width is right around here. That’s what that kind of helps
us do with these different sections. It takes the sections above until it hits the very
top, flush part of the block, but also the lowest point. It just drives all those out
and find our curve on the back part of our slab as well. It’s just a way of thinking
about how we can deliberate the fact that this fairly complex shape is tapering out
and getting fatter but also getting lower. As it tapers back in toward the sternum then
gets higher again. That is easy to think about when we look at boats, but it’s harder to
draw it. So if we’re fairly logical about how we could make kind of rectangular blocked
sections around it and then draw into meet different reference points and sections, as
we draw it following the contour of the ribs and the height of things. It becomes easier
to understand in perspective as we’ve done here. Of course we can add on the other side
of it as actually following the rim of the boat and what that flushed top section would
be compared to the lower ones. That would be how that would look if we moved that and
even removed the idea of the sections. That’s pretty much how it would look. If we wanted
an idea of the flush top from the highest point of the bow and the stern following the
contour of the top rim of the boat, how would the deepest point or the lowest point look
for the highest point? We also did that with the middle sections here.
It’s just another way of looking at intersecting planes and the idea of how we can visualize
the missing part of the boat like the carved part of the boat that goes lower and tapers
down and gets wider at the same time. So both that and this shape can help that idea. So
both is true. Then if we put them all together it becomes an incredible nightmare of work.
We can do it for fun because it will make us kind of freaked out here. Let’s take
all them away and discuss really quickly what we did in total. It’s kind of frightening
when we put these in. These, these, the idea of some of the measuring points.
More and more the cone of vision then the diminishment guides basic middle section,
back sections, other work. All this stuff added together gets kind of insane. Obviously, if you presented
someone with this people would throw up basically and say, oh my God, and run away forever.
But if we build them and are able to take them in different layers or different sections
when we do drawn diagrams on white bond paper and use lighter lines and toned sections and
explain things with notes, ABC-123, what things are, then they become easy to understand.
But yeah, altogether they seem crazy. The good news is that most of the time you can
get rid of a lot of this stuff, and it still makes sense. There’s the basic sectioning
of the boat minus that little weird blue water thing. Then if we get rid of these two things
we’re just left basically with the sections with their outlines. But then if we get rid
of those we’re left with the sections there.
So that’s about it. Again, the idea is how do you do—obviously transportation designers,
ID people, industrial designers, product designers in the past did very complex, very interesting,
very beautifully delicately referenced and planed drawings with lots of sections and
stuff. Illustrators and commercial people do this quite a bit. As an artist it can really
help if you’re getting into more complex buildings and drawings to not get those problems
with things converging too quickly or not understanding how things double over if they’re
man made. Often the left side is the same as the right side as we discussed a lot in
lectures 14, 15, and 16. So the idea is just keep sectioning things and thinking in these terms.
Again, this is a pretty basic demonstration, but this is really just meant to get in your
mind about how to think about flat space. We’re looking at this diagram with the top
view and the side view. How do we think in these terms on this boat that’s in perspective
in a fixed photograph and then determine where are those vanishing point? Why does it behave
like it does with those vanishing points that we found way, way outside this picture frame?
All of that is important if you want to claim to understand why and how perspective works.
It doesn’t mean you always have to use it each time you draw. It’s the idea of knowing