 Lesson details
 Transcript
 Instructor
 Erik Olson
 Subjects
 Perspective
 Materials
 Colored Pencil, Kneaded Eraser, Mechanical Pencil, Ruler
 Duration
 2h 29m 33s
 Series
 Perspective for Artists
In this highly anticipated lesson, Erik Olson tackles the challenging subject of Three Point Perspective, elucidating the difference between one, two, and three point perspective. Building upon prior lessons, and with an understanding of vanishing points, measuring points, station points, and centers of vision, you will learn to construct scenes with “bird’s eye” and “worm’s eye” points of view. Erik’s lessons are the best way to develop your threedimensional mind, which is vital to incorporating interesting “multipoint” perspective into your art. He shows you that it doesn’t have to be a daunting or overwhelming subject– with patience, concentration, and practice, three point perspective can be a fun and valuable tool in your artistic repertoire.
This is an advanced lesson, we don’t recommend you start here! CLICK HERE to browse Erik’s other Perspective lessons.
Materials
 454590 Transparent Triangle Ruler
 306090 Transparent Triangle Ruler
 Alvin ProMatic Lead Holder – 2H Lead
 Alvin Rotary Lead Pointer
 TSquare Ruler
 Protractor
 Prismacolor Verithin Colored Pencil – Red/Blue
 Paintbrush
 Kneaded Eraser
 Hard Eraser
 Helix Technical Compass
Discuss this video in the forums!
DiscussOur first section of diagrams here will be the basic introduction,
I’d have to say, to threepoint.
Why is it different than one and twopoint?
You’re taking a threedimensional idea in the real world, and as most all perspective
does, it converts it into a twodimensional illusion.
That becomes a little more tricky in threepoint, but not so much you can’t understand it
within just a few diagrams to introduce it.
We want to marry perspective with your natural drawing practice, meaning how you like to
draw on a sketchbook or in front of the figure, all that stuff.
Instead of making perspective this measured thing that everybody dreads, I guarantee you
if you memorize these steps in the beginning part to the threepoint, you’ll be well
on your way to actually visualizing infinite amount of views, looking up or down and looking
at the world at really strange steep angles and stuff.
It actually becomes fun.
It’ll make your thumbnails, your sketches, and all your drawings much more understandable.
So, I hope you enjoy it.
Try to absorb as much as this as you can so we can onto the little more complicated, little
more applied stuff as we go into the lecture series.
Fear not, we’re going to do it a step at a time and see why threepoint when we’re
looking down or up into or down into the world is different,
but yet the same as one and twopoint.
A lot of people are confused as to why threepoint works, and it’s not obvious.
It’s not something you can figure out past the simple parts and also the distortion issue
with threepoint is much more dramatic than it is in one and twopoint, obviously, because
you have now diminishment to the vertical.
So, let’s review.
We still have all the same things that are ours.
Remember the head gear that we talked about at the beginning of the lecture series and
one and twopoint.
We have headgear with a piece of glass in front of us, and we always have our own eye
level straight in front of our two eyes going horizontally.
Then the center of vision plane is a true vertical straight in the middle of us projecting
out forever.
We have our own station point.
How far away are we from the subject matter?
Then there is a picture plane exactly in front of us, flush with our faces all the time.
Then we have a projected cone of vision which is a basic determinant of distortion or nondistortion.
It’s just basic.
It’s a soft idea.
But, all five of those elements are forever ours like we’re wearing a diving bell from
the 19th century, or if you want to look at it like you’re wearing some virtual reality
mask you’ll always have those elements that are ours.
Everything else—the horizon line, subject matter, mountains, ducks, streams, panthers,
pagodas, it doesn’t matter.
That’s all part of the world.
It’s not ours.
So think about what is mine, and I am the camera.
The camera can move anywhere, and we have an infinite ability to get any angle on the
world we want.
The subject matter can change and spin itself, but we’re not concerned about that right away.
We want to know the difference between what is ours, the eye level, the center of vision.
The station point, it means the distance we are from the subject matter or chose to be.
The picture plane itself, the imaginary piece of glass in front of us that’s straight
in front of us that we’re drawing on.
Paper, a mural, a computer screen, doesn’t matter.
The cone of vision that projects out from the distance we are in real space to figure
out why we see distortion or not.
Again, it’s important to say those are still ours.
Again, the horizon line and all the things in the world are the world’s.
They’re not ours.
Only those five items are.
Just got to repeat that a lot.
What we mentioned earlier is thumbnails and sketching often get dicey in threepoint for
some people because it distorts so fast, or they don’t know how to make their diminishments
consistent to what are now three vanishing points.
You’ve got your left vanishing points like always, right vanishing point on the horizon
line representing the ground plane, but now we have diminishment to the vertical.
When we start looking at the diagram we can say instead of verticals being truly up and
down now in our world—they were before—so we can say in red that’s how the world used to be.
Now these ideas where we used to find our sloped perspective, auxiliary vanishing points
and all that, what we’re really doing is saying oh that’s right.
When I’m looking down into the world in this case, those ideas pinch in and become
triangle walls.
I’m going to start drawing things in slowly and explaining it.
We still have our center of vision plane here like always.
We still have the point where a onepoint vanishing point would meet where the center
of vision crosses the horizon on it just like before with the horizon line, and we have
our left and right vanishing point effectively.
We’ve got our little mountains and our clouds and our sun.
That’s the horizon line.
The important thing is our eye level has now moved down.
We’re not going to draw the eye level right away because I want to clarify why things
behave in threepoint.
It’s just that our eye level has moved somewhat down because even though the horizon line
in the world has stayed the same, you and I are agreeing to the fact that we’re looking
down some.
Our eye level, remember is what we carry with us in the center of our vision horizontally,
always, since we’re babies until we die.
It doesn’t matter.
Every time you open your eyes, it’s right there.
So, we are carrying that down to be able to view us at an angle to the earth.
We’ll look at side diagrams and explain all this.
I just want to do it a step at a time.
Now I’ve decided that my diminishment rate is going to be how this triangle fills out.
And so I’m doing these little light drawings to being with, and I’m going to say, you
know what, I just want to have my triangle this proportion.
Why is it a triangle?
Because there is a relationship to our horizon line.
When we’re looking down our horizon line is here.
This is our left triangle wall, and that’s our right triangle wall.
That’s where basically what used to be straight up and down representing verticals now pinch
in and meet at the center of vision.
That is called a vertical vanishing point.
Right there in bold pencil.
Vertical vanishing point.
Now verticals are not straight up and down like the old world used to be because we’re
looking down in this case.
We’ll also look up but now we’re looking down.
We have some diminishment down to this point on the center of vision.
This triangle will always behave somewhat like this, even if it’s short or long and
different subject matter is in it.
It just depends on how far away the vanishing points are from the center of vision just
like in twopoint and in onepoint—well, particularly in twopoint.
Now we have to do the third consideration of the vertical vanishing point.
No big deal.
So now, this is still my left vanishing point, right vanishing point like in twopoint perspective.
Still have a center of vision.
This is the horizon line.
But now our eye level has moved down a little.
I’m not going to bother with it now because I want to make these diagrams a little simpler
and more clear at first.
But we definitely committed now to a vertical vanishing point.
That’s where we decided the rate of diminishment came down and met at the same place on the
center of vision plane, and we’re going to call that vertical vanishing point.
That’s going to be with us the whole time we do threepoint, just as importantly as
what the right vanishing point and the left vanishing point have been to us and will still
be to us.
Let’s start drawing squares.
We’re not going to worry about the center of vision yet.
We’re going to add that on later.
Don’t want to get confusing.
We’re just going to draw a couple little cubes really simply.
So, right vanishing point, left vanishing point, vertical.
Now I’m going to draw on my verticals the idea of a little cube.
I’ll overdraw, overdraw, and go ahead and do my first plane.
I’m just kind of guessing.
There is no real measuring here.
I believe I guess this is a square so I’m going to do that.
Great.
I have a standing square, basically.
It represents a square in perspective, and I’m going to say, alright,
you know, nothing fancy here.
I’m going to also draw to the vanishing point and then say, okay.
Then if I estimated that to be there and that wall goes to there, what would I estimate
would be the proper stopping to the far right side of that plane standing up?
I’ll just guess and say, alright, I think something like that works.
Then I’m going to close off this shape.
Going back to the left just like you do in twopoint.
Right?
I’ve got my closed off space, and if I want I can even take the back corner
for a transparent cube.
I’ll just do that more lightly.
It’s not as important, but we do want to show that we’re kind of working
with transparency here.
So, we just did our first little cube in threepoint.
It’s a little long on this side because I’m guessing and hurrying along.
It’s not that important.
What we’re trying to not do is be perfect right now.
We’re trying to understand the setup, why threepoint operates.
In this case, bird’s eye.
We’re a bird in the sky.
We’re looking down.
When we do our other diagram we’ll be worm’s eye.
We’re a worm that’s a little low to the ground, and we’re looking up.
That’s what it has been referred to as for well over a hundred years, probably, or more.
So there is my twopoint cube in threepoint really.
I mean it’s really a threepoint cube.
I’m referring back to twopoint perspective because we can make an analogy, what we’re
already comfortable with an associated with from the previous lectures and experience.
We’ve just got the added idea of the vertical vanishing point which is always on the center
of vision somewhere.
Now I’m going to do a onepoint cube in threepoint.
It’s going to go to that vanishing point, and it’s horizontals are going to be truly
horizontal across the plane just like in onepoint perspective.
We don’t have any perspective going across this way, but we will have it to the diminishment
to the vertical, and we will have it plummeting back to that onepoint vanishing point.
Why don’t I go ahead and just put the first face of my cube on and see what I think.
It’s a little one, but it’s okay.
I’m going to draw down to my vertical.
I’m going to draw the other side.
Then I’ve got to see how deep I think I want to make it.
Remember, we’re having foreshortening now because we’re going down to the vertical
vanishing point.
The difference is, this is no longer a true square like in onepoint.
There is a little bit of foreshortening to the face of that plane because we are looking
down at the world, and there is diminishment now to the verticals.
They will have then foreshortening as we get steeper and steeper to them.
So, I shorten that square up a little bit, and then I’m going to project back to my
vanishing point, and then I’m going to decide on the depth of my cube.
I can’t do that until I get my three planes going to it.
We can even make it transparent, but let’s do the three main planes.
Great.
I’m just going to guess at where my depth cuts off here.
I’ll make this aligned with my horizon line.
You guys are welcome to use Tsquares.
Don’t let me mislead you here.
I did a very light draw through with these so I could be very clear about what I’m
doing film, and I’m sitting on a little bit of an odd angle to not be in your way
for the filming.
Therefore, I want you guys, if you feel more comfortable, for your diagrams, use a little
Tsquare or be accurate that these are true horizontals and you’re getting true verticals
when you are doing your center of vision and some of your other framing and stuff.
Remember, you’re using drafting tools or being accurate to a true 90 degrees.
I’m using these because I basically lightly drawn in the ideas, and then I’m expanding
on them for you guys as we walk through them.
So, there is my depth guess of that square.
I’m going to come up them and I’m going to go to my vertical now.
Remember, anytime the world dictates to us that we have what was a vertical usually straight
up and down in one and twopoint, now all verticals in this world have to be going to
the vertical vanishing point.
I don’t want to make the mistake of trying to draw my square and make it straight up
and down because now all these verticals of this object that are real verticals in the
real world now have this diminishment to them because we are at an angle to the world as
a viewer.
You and me with our little 19th century diving bell, you know, head unit, we are looking
down at an angle with our picture plane.
Therefore, we get this distortion and this diminishment to the vertical.
I know it sounds obvious, but this what people are not getting consistently even from the
beginning of why it behaves like this.
So, we’ll finish off our little square.
There it is. We can do the back wall if we wanted to like this.
Do it over and do it back like this, and then come back and do that.
Remember, every vertical goes down to the vertical vanishing point.
There is our little cube.
I know it seems like a cute little insignificant cube, but you’ve just drawn a cube to what
I call onepoint, threepoint, it’s a single VP on the horizon just like onepoint perspective
is and standard perspective, but of course, we actually have the triangulated perspective
of threepoint, and all verticals are going to the vertical vanishing point.
So, I call it a onepoint, threepoint cube.
This is standard threepoint when you’ve got all three.
Obviously, we know what identifying them all means.
Take this into consideration.
It’s very simple.
We’re not dealing with the cone of vision yet.
We’re not even taking and drawing on our eye level.
I want you guys to get used to why the basic differences of the world when these side walls
collapse into the center of vision.
They become the vertical vanishing point.
We could have a much longer triangle with less diminishment,
and we could have a shorter triangle.
We’d even be looking more steeply down on it.
We’re going to get to all that.
Okay, so how do you make a little applied version of this.
I already drew in my frame, so there it is.
I’m saying, okay, I’ve just drawn in my little Tsquare from my frame and my true
triangle, verticals. Here we go. There is my frame.
The idea is how do I get and guesstimate the idea of where these vanishing points are in
this one, but they’re farther away and I’m not going to draw to the vanishing points.
I’m just going to make my diminishment guides like we did many, many times in the onepoint
lecture—one and twopoint I should say, the more traditional stuff back in the earlier
lectures.
I’m going to put in a rate of diminishment after I put in my center of vision.
I choose to have my center of vision in this because I want my cube tilting a little bit.
I’m going to say my center of vision is truly vertical right here.
That is an artistic decision.
It’s not based on some rule or whatever.
I’ll just say the only vertical that will be truly vertical is your center of vision
just like here.
If we had a stripe going down here—why don’t I take my red pencil—and it happened to
coincide being lined up just with the center of vision.
That would be the only vertical in my picture back here that would be truly a real vertical
and not tilting as it diminishes to the vertical vanishing point.
That is true here.
So now the only things that are lined up with this would be truly vertical.
I’m not drawing my cube based on that.
What I’m doing is I’m saying, alright, I’m going to make slow
diminishment this time.
I’m making my diminishment guides first before I draw my cube just to roughly say
I’m going to do this.
This is showing me my diminishment to my vertical.
Even though I’m not drawing to a vanishing point, I know that I can make consistent tilts
going further and further out consistently like this, and if you get good at this, you
don’t need to do all the formal all the time.
You can do perfectly fine guesses.
But those guesses are based on how steep and shallow angles actually behave in the formal.
So, by doing the formal and exercising it and doing the diagrams, you will actually
have a threedimensional idea in your mind, literally why and how it works, and you’ll
have way better guesses, so it goes faster after that.
I’m going to put my diminishments on this way now.
To my left one, I’m going to say, how about that.
Remember, why am I diminishing this way?
Well, my verticals are slowly going somewhere down here.
I’m not thinking about particular parts now because I’m not drawing
in my vanishing points.
My left vanishing point is diminishing to a horizon line that is up there somewhere.
I’m making fairly consistent diminishment to it.
Not too quickly, but not too conservatively either.
I’m just guessing at this.
You’ve got to get used to doing this in your sketchbook.
There are my diminishments that way, and then I can say what I do
diminishments going over here.
When you’ve got to get used to this, these aren’t even objects yet.
These are simply the guides we’re going to put in and then draw much darker for what
we think our cube is, and in future diagrams, what are subject matter is.
These are literally just the diminishments to the vertical vanishing point over to the
left vanishing point way up on the horizon and way up over on the right side.
Let’s say I want to do a cube within them, let’s say I’m going to make the front
end of my cube right here.
I’ll go ahead and just make that real dark.
Okay, then I’m going to splay off both directions longer than I need to be.
Then we’ll cut off that cube where I think it needs to be.
And cubes are easy and good examples because they are as tall as they are wide as they
are high, and they are deep.
So, no surprise if you get good at understanding why a cube and rectangular objects work in
threepoint, it’s much easier to understand why more organic curvaceous things behave too.
I’ll go ahead and draw back to that.
I’m just guestimating the cube based on my diminishment guides.
No magic here.
It’s no big deal.
A lot of you are going, oh, this is so simple.
It’s not about that.
It’s about thinking about why this works.
We haven’t even gotten into officially why it works.
Just the idea of it, can you imagine why things diminish to the left, the right, and down,
and what is your true center of vision.
That’s important, so I’m going to draw that with a little more red and be really
clear about it.
That’s my center of vision which is very important because that allows me to understand
the rate of diminishment I want compositionally and then eventually how the rest of the perspective
behaves because this triangle when it’s done, measured just like in 3D perspective,
has to be a particular configuration, but we’re going to get to that later.
There is our little cube drawn in here for our downshot or bird’s eye.
I’ll just make it a little darker.
Alright, there is that cube.
We just did an applied picture, everybody, even though it’s fairly boring and just a cube.
We actually drew out diminishments that could work for a huge painting that’s really complex.
You could be drawing this whole city in here or vehicles or some train station.
As long as you keep the diminishments going properly, you can draw any amount of space
into this as luxuriously detailed as you want, just like we did when we did the spiral staircase
and all that crazy stuff in the first lectures.
We don’t have to be that complex in threepoint.
I don’t want to get that complex in the threepoint lecture.
We’re only going to be doing simplified and intermediate subject matter so we can
clearly see the layout of the perspective.
If you want to go ahead and do an 18th, 19th century, late 19th century locomotive and
go nuts and spend four days drawing all the parts, be my guest.
That doesn’t mean it’s going to change the perspective any. It's not.
The perspective setup is what we’re after, and then you can draw any amount of complexity
you want. Be my guest, okay.
We’re looking down in bird’s eye here.
Now we’re going to go over—bird’s eye looking down.
Let’s go through here.
How shallow or how steep are we looking down will affect the size of your triangle, or
I should say the proportion of your triangle, not the size.
Where is the vertical vanishing point?
How is the subject turned?
How is my cube turned so that would affect how I slide back and forth with my right and
my left vanishing points just like we do in twopoint perspective?
How is my subject, turns toward us, left vanishing point, right vanishing point.
So, shallow or steep has to do with the vertical vanishing point.
How our subject is spinning or turning on the ground plane has to do with the left and
right vanishing point. Okay?
That’s something you want to keep in mind too if you get confused of why we’re doing
these things.
Now we’re going to be looking up in what’s called worm’s eye.
Now we have our horizon line like before.
We have a light—we’ve already dedicated a left vanishing point, right vanishing point,
horizon line.
We’ve got a little cloud and mountains here, horizon line.
I’m going to find my center of vision which I want here.
I’m going to go ahead and draw that in.
Then I’m going to have a particular portion of triangle, based on how I want my rate of
diminishment.
There is my center of vision right now.
We’ll just call that center of vision.
I’m going to have these rate of diminishment, so I’ve already decided I want the vertical
vanishing point there, which connects the two sides of the triangle, exactly the same
as over here, except now we’re 180 degrees upside down.
The perspective for bird’s eye and worm’s eye works exactly the same way, except they’re
exactly upside down from each other.
Nothing else is different.
We are simply looking up at cubes or objects when we’re in worm’s eye.
We are looking down at stuff at an angle to the earth when we’re in bird’s eye.
That’s all.
There are my triangle edges so I can really get it rehearsed into my mind that’s the
relationship, the three vanishing points, they create a triangle with the horizon line
being the flat top or bottom edge.
The two leaning sides that used to be straight up and down for finding auxiliary sloped vanishing
points and all that stuff we used, now they bend in or tweak in because they’re coming
to the vertical vanishing point.
So, there that is. Alright.
Vertical vanishing point, left, right.
Now I can start drawing my cubes.
I’m not putting in the eye level, and we’re not worrying about the distortion area.
I’m drawing within reason why I know is the distortion area generally.
And then we will explain more and more about how we’re setting it up as we go.
This is the simplest stuff, obviously.
A lot of you are going to say, yeah, duh.
You can get this from most books.
Believe me, you won’t be saying that in a few minutes.
There is going to be added on complexity here, and it’s going to be easy because we’re
doing it a step at a time, but this is the simplest way why threepoint works.
Let me get my diminishment from my cube here.
I’m going to start it here, throw that main line up, and I’m going to draw my right
plane first or my left plane first.
Real simple.
Then I’m going to calculate what do I think is a square in this perspective with some
foreshortening happening.
I’m going to guess at that.
Just a guess.
Then I’m going to go back to my right plane.
I’m overdrawing, and again, I’m going to guess at my right plane.
Or I could guess at my square underneath.
I could do both.
Alright, I’ll just guess it here.
That was my guess.
I could also, if I wanted to, first guess at this one and close it off and say now.
I want a little wider, little less wide.
I was fairly happy with that.
It might be a little tweaked out and stretched here.
See how a little distortion is happening here.
It’s like cockroaches invading the world.
It’s like distortion.
I’m getting near to the count I can tell.
You can already tell where the count is once you see one corner.
This corner is starting to distort.
You’re like, yep, I bet you the cone is real close to that area.
We’ll get into that in a couple diagrams.
But, you know the drill when you start seeing distortion in one and twopoint as well.
You know you’re getting near the edge of the count even if you haven’t put it in.
It’s kind of an automatic process.
So there is my twosided cone with a thing spinning to the ground plane.
Now this is floating like a spaceship, but we’re going to a little onepoint cube again,
going to the single vanishing point here with the horizontals going straight across.
They’re still be diminishment and foreshortening up to the vertical vanishing point like this
object with this little one.
Let’s draw in the front square plane like we did before in the bird’s eye version.
I’m going to draw my verticals up to my vertical VP.
I’ll overextend them, overdraw, and then I’m going to close it off with a guess.
This is a guess.
What is my foreshortening because of my diminishment to the vertical.
Okay?
Now I’m going to take these four corners, go back to my vanishing point like we would
even in standard onepoint, but we’ve got to constantly remember we’re diminishing
to the verticals.
And it’s something I’ve got to repeat like a mantra because people all the time,
my students all the time, and including myself when I was at the stage constantly make the
mistake of drawing verticals back to being straight up and down.
You’ll just go what did I do that for?
But you just have to keep repeating to yourself all the verticals in the world have to behave
to that vertical vanishing point, and it usually gets pretty ingrained in us pretty soon after
starting but it takes a little while.
I’ll draw a really light version of the inside of the cube as well so we can do that
really lightly there.
I’m doing it with these tools just to be precise.
I don’t want to make it unclear by just drawing stuff.
Drawing freehand is great.
It’s wonderful to watch people draw cars and be a big hero.
This isn’t about being a hero.
This is actually about teaching people straightforward perspective and then adding layers of complexity
onto the perspective, not onto the objects.
Again, we’ll be doing simple and intermediate objects for these lessons, but we’re going
to be doing all sorts of crazy stuff with the actual setup for the perspective that
will give the same exact accuracy as the 3D programs, just as fast and just by hand that
people that are long dead invented, a lot of them we don’t know their names because
they were unrecognized, probably.
Who knows?
Man in the Iron Mask?
You tell me.
Who was sitting in a tower inventing all this stuff in like 1480?
You tell me because there are not many records.
There are a few people that get credit for it, but it’s interesting reading, but it’s
pretty obscure subject matter.
Here is my little frame, and we’re going to do the same thing we did here, just looking
up a cube.
Alright, so following this basic logic, how do I start setting my diminishment guides.
I’ve got my frame.
That proportion won’t change whether I’m doing a book cover, a big mural.
You’re doing a big painting on canvas, or you’re going to turn this on its side to
be a horizontal for the proportion of your computer screen for gaming.
It doesn’t matter.
You can still put in diminishment guides.
I’m going to put in my verticals.
There is my true center of vision.
I’ve just decided to put it more on the center of the frame.
Mark that clearly in red.
There is my center of vision.
I’m going to just guess at my diminishment and go up because that’s the rate I want
it to be, kind of similar to the one we just did here in the triangle, and I’m just going
to plow this in real quick.
Diminishment guide is just going up like that.
Another one over here.
I’m trying to get an even rate of diminishment, which I feel, you know, feels even going to
the center of vision being truly horizontal—sorry, vertical—and then boom, boom, boom.
They don’t—this does not represent a grid.
This is not accurate to cubes counted in space.
This stuff is just diminishment guides that help you draw in between at the changing angle
at an even pace so it looks like it’s truly diminishing way out there for our distant
vanishing points.
That’s why we’re doing it.
I’m going to do my right side diminishment now that would be eventually—now remember,
don’t be confused.
We are going down to the left vanishing point now and down to the right vanishing point
because we are looking up into the world in worm’s eye.
Therefore, this is going down to my left.
This diminishment is going down to my right.
Let me draw on the darker lines for you on camera here.
A lot of this is selfexplaining.
As long as you keep kind of the story going about why we’re looking
at the world as we do.
So here, again, let me darken it up.
Here is my frame which will stay consistent even for my large, more formal version if
I was doing a big painting or whatever you’re trying to design all this together.
There is my frame.
There is my diminishment to the right, but I’ve got to do my little guestimate.
Remember, this is guessed diminishment to the left.
Here we go.
I’m not going to make it super dark.
I’m just kind of telling you, these are not grids.
These are diminishment guides.
They’re not actually representing any kind of real counting of space.
They’re just diminishing to our vanishing points or pretending to.
They’re going to be a little off, but it’s going to be close enough if you’re good
at it, and take into consideration the center of vision, again, that middle line here.
Where are we going to go?
Alright, so let’s do a little cube here or whatever we choose to do.
I’ll set maybe the front corner here and here like I did before.
I’ll just try to get that, so that’s the front corner.
I’m going to draw my left plane first like before.
Again, is this about right or a little more tweaked?
Maybe I’ll come out a little from that diminishment guide or pretty much on it.
It looks right.
And I’ll come down and do my other ones and then figure out how long they should be.
Cut off the right plane.
There it is.
I think it’s about that, again, a little bit out from there.
Okay, just guestimating.
Then we come back and we’ll cross over.
Again, very simple stuff before we get a little more complex.
I just want to make sure we see our nice dark floating cube.
This is getting a little bit distorted down here again.
It’s no surprise that we’re getting this little bit of pinch here because we thought
we did it fairly conservatively, but when we really look at the diminishment rate it’s
pretty fast to these vanishing points, so it looks like there is just a little bit of
tweak there.
It’s just, again, we could our diminishment guides even more gently going down to further
away imply vanishing points, and we’d get less distortion.
So, if you don’t like distortion then you want your diminishment rate to be less, slower.
But if you like distortion or you want to play with it, eventually we’ll have the
cone of vision in there.
But even without the center of vision, you will probably want to ride the edge of the
wave and say I’ll try to make my diminishment a little faster than I think I can get away with.
Once you realize you might get fairly gross distortion, you might go, nope, I’ll do
another sketch.
I’ll hold off on that a little bit.
It’ll all about trial and error.
There is no one answer to a perfect formula for doing applied, just fromthegut, handdrawn
threepoint.
These ideas we can get more and more measured with just like the 3D programs.
That’s straightforward stuff.
All the storyboard people used to know this, obviously, for entertainment.
The reason they didn’t teach it to anybody a lot of the time is you had to die to get
into the union.
Actually, they kept it secret.
Sadly, that’s no longer necessary because 3D blew all that out of the water, obviously,
in the business in the 90s.
The real thing is this stuff was taught to a good number of us, obviously, that were
at places in the west coast and people who worked in TV in New York.
The idea, the more formal idea of threepoint has been available for people for a long time.
It’s just not many people had a reason to necessarily want to do it other than people
working in film and television and people that did large representational paintings,
like Thomas Aiken certainly knew it and stuff like that.
He was renowned for teaching measured threepoint and stuff like that and twopoint.
So, we are not measuring yet.
We are just estimating by hand, but I wanted to take time on this one.
Again, what are we asking?
Worm’s eye, looking up.
How shallow or how steep are we looking?
That determines where we put our vertical vanishing point.
How is the subject in the world turned toward us.
That rotation has to do with the placement of am I looking at the onepoint, threepoint
vanishing point, or how far out is the right one coming closer to the left as the cube
rotates.
That all has to do with how we could rotate our subject, but the vertical steepness or
shallowness would stay the same.
Just because these cubes would be rotating would only
change the ground plane vanishing point.
Same with the bird’s eye.
It wouldn’t change our aspect of how steeply we’re looking up or down.
We’re going to do diagrams together like pretending we can see each other from the
side looking up and down.
It’s just I wanted to give you the visual template about how this
actually works compared to one and twopoint perspective by just doing these little runthroughs.
Okay?
We will go on to the next one momentarily.
looking down into the world like a bird.
One is going to be more shallow over here, and one is going to be more steep.
Just to show you the difference of where the subject matter appears and the nature of the
design of the triangle.
The triangle is important because it’s your memory of why that convergence of the two
walls becomes the vertical vanishing point.
Again, the rule would be the longer the triangle or the further down the vertical vanishing
point is from the horizon would be, the more shallow the view is.
It’s getting closer and closer to going all the way back for being traditional one
and twopoint again.
Why would that be?
If the distance down to the vertical became so long it was no longer perceptible, that
it was actually diminishing, then you’d be way, way—if it was way down it would
eventually become perpendicular, and then it would be truly vertical again, and you
would not have the diminishment to it.
So, we’ll talk about that as we go into different shapes of triangles more later,
but really this is a relatively shallow view.
Then we’ll do a setup for a steeper one.
So, here we go.
We’ve got our horizon line, which is not our eye level.
Our eye level would be separate to that, somewhere in this area in the center, but we won’t
worry about that yet.
We’ve got our left vanishing point.
We’ve got our horizon line.
Our clouds, our sun, little mountains in the horizon.
We’ve got a right vanishing point.
And then the rate of diminishment could decide where you wanted it.
That also will decide your distortion range.
In this case, I have a triangle like this, and I’m just saying that my diminishment
rate is something like this for that first corner of the cube.
That ends it down here for the vertical vanishing point.
It’s a little sloppy.
So VVP, vertical vanishing point, and then I’ll put my triangle walls in for good practice,
just to show why and what we can do with those later, what they mean.
Okay, so now we’ve got our center of vision plane.
That’s obvious.
We have our left and right triangle walls, and we most certainly have
our vertical vanishing point.
We’ll just draw these out again, being a relatively shallow view.
It’s obvious it’s threepoint because you clearly will have diminishment, but not
a huge amount.
Again, we’ll overdraw to our vanishing points here and just overdraw our extended planes
and then decide where we want to cut them off.
Okay.
Go down to my vertical vanishing point and say that looks good about there if I estimate it.
Again, we’re always using—well, I always like to use the transparent triangles because
you can see all your work underneath it, and then the edge of your triangle just becomes
another line that you can estimate diminishment or endings or starting and object with.
It just becomes much more helpful than an opaque straight edge, which would make you
blind to those edges and those additions.
Okay, there is our little, simple cube.
There we go.
Now we can put in again, we can put in the interior stuff if you want.
It’s really about where objects are simply behaving too.
That’s all.
We’re just trying to—there we go.
That’s a basic cube.
It’s a little short, so I’m going to go ahead and extend it and say, I don’t think
it’ll be quite that much foreshortening.
Maybe it’d be that, something like that.
Anyway, there is that cube.
Then we’re going to do two more that are behaving again to the onepoint, threepoint
vanishing point, which I call it in the middle as just the single vanishing point, and we’ll
draw straight across horizontally again.
And then I’m going to try two planes going down, overdraw.
Then I’m just taking my best guess at the foreshortening of the onepoint, which I think
would be right around there, slightly foreshortened square because we are looking down in space,
so there would be some foreshortening to it.
Extend that to my single vanishing point on the corners,
and then I have to guess at my depth.
I’ll just do that by lining it up at the old horizon line and saying okay, there is
my guess for depth.
Strike there at the corner, come back down.
There we go.
We can actually draw the interior if we want.
We don’t have to do that with all of them.
We’ll just do a guestimation of what that looks like, kind of like that.
Draw right up here, back up at the vertical.
Boom.
Okay, so there is our other little cube.
Make sure that has dark enough walls to see on camera.
Should be pretty good.
We’re in 4K so it’s pretty darn clear.
Okay, one more here.
This actually goes across our eye level.
You can still show subject matter and more shallow, more shallow bird’s eye or perspective
in general.
You can show a little bit of action above the horizon line, and then very quickly you’ll
get kind of unrealistic, warped distortion, but with certain angles you can cheat it a
little bit, too.
Even with measured threepoint, if you set up a shallow enough angle with your cone of
vision and your triangle configuration, you can actually draw subject matter.
Let’s do this again.
I’m going to draw what I think is the top plane here about that far up.
The bottom one is going to be about down here.
Then we’re going to shoot down to our vertical vanishing point.
This is going to look a little strange, but this is what a wide angle camera
can do a little bit.
Then we shoot our diminishments back to our onepoint vanishing point.
We’ll even put in a little bit of the interior ones real quick.
Then we’ll just guess.
I’m just going to guess.
Oh, that’s my depth.
I’m going to guess that with a mark, but officially come down to a good diminishment
to my vertical vanishing point like that.
There we go.
It’s just behaving and warping a little bit now because we still have that diminishment.
Typically, this corner would be probably getting out of the cone around here just getting pulled
a little bit.
Again, these are fairly close vanishing points because we wanted to show the whole triangle,
no surprise.
But in reality, you’re not compelled to have to have really tight vanishing points
to your image.
In fact, if you want no distortion, you would put them intentionally further away than you
think you need them, and then you will get no distortion most of the time.
That’s how we see anyway.
Our cone of vision for how we actually see is about half that of the 60 degree cone.
Our real cone for our peripheral is very limited if we’re the same distance.
The 60degree cone, remember, is for twodimensional drawings that were
taken from threedimensional ideas.
But, our real cone of vision, our peripheral is so limited, it’s really less than 30
degrees total.
But will talk about that later about why people complain about distortion and perspective
and actually are just using too much of the cone.
If you actually use a much smaller amount of the cone near the center of it, then you
pretty much can view things as we do with our eyes all the time.
We’ll discuss that later.
What do we need?
We need our frame, and we’re going to do little diminishment guides again, but we’re
going to do it real fast.
I’ve picked this for my center of vision again, kind of near the center of the picture,
so I’ll just run that through.
That’s our only true vertical, the center of vision.
We’ll do some diminishment guides as we go out, or I think I want my cube.
This is pretty relaxed now, pretty shallow.
I’m not going to do it too quick.
You know, I’m just going to guess at it coming out like that.
Ten I’m going to say, alright, what do I like for my average left line of my cube.
I’m going to say that’s my first one.
Again, it’s going to diminish fairly kind of quick because this is
faster than way down here.
On these shallow view, remember, that means shallow for bird’s eye, means that the vertical
vanishing point is further down in proportion to the width of the triangle where the left
and right vanishing point are.
So it makes sense when I’m doing my handdrawn version that I have faster diminishment to
my left and right vanishing points than I do to my vertical that will make sense.
Then the opposite is going to be true when you do a steep review.
You’re going to have faster diminishment oftentimes to your vertical on a steeper view,
which we’ll do over here, and more subtle diminishment or slower diminishment to your
ground plane vanishing points or your right and left vanishing points.
So it reverses.
Then we have an average halfway down shot somewhere in here, you get about the same
rate of diminishment.
We’re going to go all through that because we’re going to do many, many examples.
Okay, so here are the diminishment guides to my left.
I’m going to do the quick ones, cross into what I believe are correct, and we’ll go
deeper into a little check system about just guestimating these angles
as you get more experience.
Okay.
And we’ve got a couple more up here.
You can pretty much draw a square wherever you want.
Add a little light one down here.
I can see the corner is that to that.
I’ll just do it darker.
No big deal.
I’ll just fit it right in here.
We can do a bigger one, smaller one.
The whole point is you’ve got your diminishment guides, so you are following them no matter
what size the square is until you feel like you’re getting some distortion probably
near the edges.
We’re going to have a little bit, but not much.
Not acceptable.
But again, later we can do stuff where we really get more conservative diminishment
if you want it.
If you like distortion then you can play with that too.
I’m coming down again to my vertical just a little like this.
This is just all guestimated from following those diminishment guides.
Just to make it clear that I’m not forgetting to make all of my verticals diminish way down
here somewhere.
That’s what we’re doing.
There is that square there.
Again, it’s just a lesson.
This could be filled with subject matter that’s way more complex than this, but it wouldn’t
change the diminishments.
Those would remain the same no matter how crazy you got in here and how many hours you
spent drawing and measuring and getting scale, being careful about all the little things
in a very, very difficult vehicle or something.
It doesn’t matter.
It’s your setup that matters.
As your original diminishment compared to your frame and the amount of distortion you
want, predictable in the way you want it by the time you commit to that finished version.
That is the deal.
Now we’re going to do a steeper view.
We have our horizon line here with our left and right vanishing point, and our center
of vision basically established.
Now we can say, alright, what if I want steeper diminishment like that?
That would be looking down probably about 60 degrees, something like that.
It turns out it hits it about here.
That’s where we’re going to put our vertical vanishing point.
Then we’re going to connect our triangle sides again just for understanding the relationship
of all the planes, which will be important later.
We’ll definitely be getting a little distortion with this one because it’s so far down getting
out of the cone.
Remember, our eye level is way down here now.
It used to be up here at the horizon line because that’s where we were looking in
traditional one and twopoint with straight verticals.
But once we’ve looked down into the world further and further, the eye level comes down
further and further away from the horizon line and is crossing somewhere in the middle
around here.
We’ll get more precise with that in the next couple diagrams.
Let’s just draw out some cubes behaving a little more steeply now.
I’m going to draw back to my, here is my original cube, so I’ll draw that to my left
and right vanishing points real quick just to kind of get a feeling for what they look
like, overdraw those planes.
I can make a guess from the top this time if I want, so if my guess was up here, cross
over from here.
You can do it any way you want.
That would make those sides there.
You can draw the inside if you want.
See how accurate we were.
Remember, these were all guestimated.
See if our insides end up kind of where we want them here.
Yep, there.
Boom.
I’m a little off there right in the middle so that would be the back end of it there.
A little bit like here.
Then we’re going to do another one that’s further down on the ground down here,
so we’ll just kind of draw the planes out for this one.
It’s going to be pretty foreshortened on the sides.
We’ll see some more distortion come into this one, but I just wanted to give you a feel.
If I started one that was like that, and I said foreshortening was about this high, it
should come down about there.
I’m just guessing at these planes.
How do we know?
I’m feeling like I’m looking that steeply down on a cube, I feel the foreshortening
to what was an actual flat facing square.
It would be about that much based on that angle.
It’s a guess.
It’s never going to be perfect, but we’re doing more guestimates now and we’re not
measuring them.
Just to get familiar why it behaves.
I’d much rather have everybody just do this and play around with these ideas in getting
a feeling of why these things are coming close to being cubes because drawing cubes is the
way you can really check yourself if you believe you’re getting the same amount of distance
and depth as in width and height.
I can’t stress how important that is if you’re trying to understand movement in
general perspective.
It is frustrating in threepoint because you do tend to get more distortion, so you want
to have even a more clear checkpoint.
Here is another one.
We’ll do a little onepoint cube going to this vanishing point again just because we
always want to include its little baby brother, the onepoint thing, because that is here
for us the same as it is in traditional onepoint.
There is the top.
I’m guestimating that it foreshortens about here.
Then I’m going to go down to the vertical vanishing point and I’ll guess at my foreshortening
again out there.
Work it back to the single vanishing point then close off the vertical for that.
I can draw a little bit of the anterior.
Alright, so we’ve got these three cubes.
This one is behaving to the single vanishing point on the center of vision crossing the
horizon line.
Our eye level has been brought down around here, which we’ll start putting in very soon.
We just go three cubes, basically.
Two of them behaving to the left and right vanishing point in the vertical and then one
of them to the single vanishing point, which is what I call onepoint, threepoint, and
also the vertical vanishing point too.
Again, now we’ll draw maybe a steep review of this just by hand.
I have a cube kind of thought out in here about the front plane being about that long.
I’m going to start with a center of vision here, which is random.
That’s just means I feel I want my diminishment coming down a little off this way and this way.
If that’s my true vertical, where do I want my diminishments for a little steeper view.
So, a steeper view I’m going to make faster diminishment to the vertical, which I’m
doing with these diminishment guides, trying to do it fairly evenly.
Now I’m going to go to my left, my right, but I’m going to slow down and not have
as fast a diminishment as here to the left and the right because we’re looking down
more steeply.
The vertical diminishment would become faster, but the diminishment rate of the guides going
back to the left and right vanishing point would actually slow down and become a little
less severe.
I’m going to try to make that consistent.
These I’m going to slow down quite a bit and just make kind of subtle.
I’m just trying to figure out a swing that looks consistent, then I’ll come back with
what I think is my proper diminishment to my right vanishing point.
Then, again, fairly slow diminishment, not super fast.
Yeah, that’s fairly slow.
I can draw a cube in here if I want.
Overdraw it, just try to visualize it.
It can be bigger, smaller, but I base my original diminishments on that kind of vertical, right
and left.
So again, these are just really fast little exercises that you can do on your sketchbook,
just do I understand cube.
Let me get the interior of this again.
Something like this.
There is the interior.
It’s a steeper shot than that.
It’s not super severe.
We’re going to get into really severe after we’ve talked about real angles on a protractor,
basically real degrees of angles.
We’ll get very severe downshots and very shallow, very, very shallow downshots, only
15 degrees down and as much as 75 or 80 degrees down, which would be extremely, almost looking
straight down into the ground.
But, right now we’re kind of dealing with just simpler to understand differences.
There is bird’s eye in a couple of different ways again.
We’ve got a more shallow view here playing around, steeper.
We’ve done our little applied versions.
We’re just trying to get a feel for why is he guessing at making the diminishment
guides like this?
I’ve based it off of my guesses from here, and the rules would be, of course, if the
diminishment to the vertical were more shallow here or slower than the diminishment to the
side VP would be a little faster and vice versa for the steeper version.
Faster diminishment to the verticals, a little slower to the left and the right.
We’re just trying to get used to these ideas slowly, like they’re part of a story.
That’s the best way I learned, and certainly it’s not overwhelming.
You can just do it a step at a time.
You’ll remember the stuff as you’re drawing.
You’ll adjust.
Perspective is about taking a kneaded eraser and a pencil and adjusting three or four times
until you get it right.
It’s not about being perfect or slamming on yourself because you didn’t get it right
exactly.
It’s not a good way to learn because you’re going to make mistakes.
That’s going to happen to all of us.
Okay, alright.
We’ll continue all the fun here with threepoint and get a little more into the formal or why
it actually works in the triangulated version here as we go on.
we just looked at bird’s eye.
We’re going to have a more shallow view and then a good deal steeper view.
Then we’ll be able to move onto why the mechanics works as far as how we’re really
looking up or down into space, particularly down in bird’s eye.
We’ll be working with bird’s eye a little more than worm’s eye because
you can actually look down to a kitchen floor or a grid on the ground in a city.
When you’re looking in the sky, you almost have to invent a tile like ceiling structure
because there is really nothing up there.
We always know there is going to be something in the ground where we can make a grid from it.
It’s a little easier to deal with bird’s eye looking down.
We are going to jump right into worm’s eye too, just the way it behaves and why it’s
just 180degree difference turned upside down and then bird’s eye.
Now we’re doing worm’s eye.
We have our little horizon line here, left and right vanishing point.
What’s my rate of diminishment?
Fairly slow.
Not super slow but fairly slow.
That means that that vertical vanishing point is a way up.
If I look at the diminishment I set for this one—we’ll just kind of draw it in like
that, that means it’s way up here so I already have a set position.
That’s where I wanted my vertical vanishing point.
There it is.
I will draw in my triangle walls just for good form and understanding of the relationship
between the three planes eventually will become important, not so much now.
Horizon line?
Now, remember, our eye level only went up a little here, but now because we’re looking
up our eye level separates from the horizon line.
The horizon line is part of the world, remember.
Our kit or our headgear includes the eye level and center of vision, this SP, the picture
plane, and the cone.
We’re not doing all those elements right now.
But, we are thinking, yeah, you’re right.
My eye level does separate, and it’s somewhere in the middle here in the shallow view.
We’re not going to quite draw it in yet until we get past some other explanations.
I’ll go ahead and I’ll draw in the two planes.
I’ve kind of made my mark here going up to the vertical.
I’ll make that a little more obvious with this cube here that I’m going to draw.
Then I’m going to quickly put in my diminishment to the right and the left or the left and
the right.
I’ll overdraw a little bit.
That doesn’t mean you have to.
Of course, your drawings will be very light if you’re trying to figure out the proportions
of stuff before you committed to them.
Again, I’m doing them darker and filling in these light drawings with dark pencil so
we can see it clearly and go over it with each other on film here.
Then I’m going to close off the square with my best guesses and say, okay, I think that
would be about right for the shallow view.
I could even draw and close off the bottom of the square.
It’s the square on the bottom plane, but it’s a cube overall, obviously.
There we go.
I can even draw in my little bit of my interior items quickly.
Get my hand out of your way here.
Okay, so yep, there is my first floating cube again.
Pretty shallow, right?
It’s coming really, really close to the horizon line.
Now I’m going to put in a little onepoint cube again, which is floating and going to
this vanishing point.
I’m just going to guess at how it behaves and diminishes up to here.
Same vertical vanishing point as the other one.
Both share the same one.
They just share different ground plane vanishing points so that’s important to remember.
That’s my guess at my foreshortened cube for its front face as it diminishes to the
single vanishing point on the horizon line.
Then I’ve got to guess at my depth, which I’m guessing right here.
Close it off.
I will also run that back over horizontally following my horizon line.
There is my cutoff. There is my little onepoint cube.
It might be a little long, a little foreshortened, but either way.
Now we’re going to have this behave right on and you know just below the horizon line,
see how much distortion we get there.
We can actually draw a little bit into our horizon and below it in worm’s eye as long
as we don’t have too fast a diminishment to our vertical.
We’ll see if we’re pushing it here and how it looks just playing around.
I’m putting it back to the onepoint there.
I’ll go back through here.
This is going to be kind of inside the cube, so I’m going to put this corner back in.
And then where is my cutoff point?
Pretty fast foreshortening there for that little edge.
There it is.
That’s that little cube down there, and that goes straight up like that.
Again, that cube is just now below the horizon line so that could actually be resting on
the ground in front of the horizon line, unlike the other two cubes, which are floating because,
of course, the ground plane we’re implying is the only place that a cube could be resting.
This could still be floating and the ground plane could be lower, or this could very well
be just resting on the ground plane with the other two cubes floating above it.
Again, we’ll do a real fast version of our frame, always following up with this little
applied—there is my true vertical, the center of vision.
Let’s go ahead and put in—the rate of diminishment is pretty shallow so I’m going
to kind of say, alright, that’s pretty slow.
Again, like that.
That’s a pretty slow rate.
Here’s my center of vision, the true straight one here.
Do that in red if you want.
And then since I have a slow rate of diminishment up to my vertical vanishing point, I’ll
have a little faster diminishment rate down to my ground plane vanishing point.
The left is down here.
Right is down there according to the logic of this.
I’ll go ahead and draw what I think is reasonably fast diminishment.
Not too super fast down to there.
We could even see part of the horizon here if we wish.
That would actually be the horizon line.
Let’s put that in and say, okay.
Just like here we can actually see our horizon a little bit above our original frame.
I’m going to draw the frame in darker just to not be confused.
That is the actual bottom of the frame.
There we go.
Alright, so we have our diminishment, and now we’re going to get our left, and then
we’re draw our little cube in again just as an exercise.
It’s a good one to see why the diminishments works.
Again, slower diminishment going up to the vertical vanishing point because we agreed
we’d have a shallower view with slower diminishment to the vertical, and that means that we would
have a little faster for our ground plane if you did that because of the
way the perspective works.
We can see how it behaves in that triangle.
So, there we go.
Now we’re just drawing our cube.
Alright, let’s do average cube in here.
Front corner.
Where do I feel I go back.
Fairly shallow cube.
We’ll go back here.
Darken it in, real simple.
Cut it off where we believe it cuts off, probably about right there.
Draw into our diminishments.
Remember, we’re not measuring anything here.
We’re just drawing to quick diminishments that we feel are proper.
So, let me do that.
There is the floating cube.
Again, if this takes up even a huge painting, as long as you feel like your diminishment
guides work within the context of that proportion of frame, then that’s all you need because
you’re not going to distant vanishing points.
You’re only implying the diminishments to them.
If you can work within those diminishments, you can draw something extremely complicated
in here.
And we get the bonuses showing our little horizon line there.
So it may be mountains in the sky there like this going across our picture.
That little place is the ground plane just like in this area.
Here is our ground plane right below our horizon line here.
There is our floating cube there.
We’ll do a steep version now in worm’s eye.
Again, I’ve got my center of vision in here and my horizon line with my left vanishing point.
My right vanishing point for my horizon line.
Get a little cloud, mountains and a sun.
I’ve got some amount of steepness I want, so I’ll start with that corner and just
describe to myself—I want it to do that diminishment rate, which lands my vertical
vanishing point right there.
Close off my triangle once again.
Alrighty.
There it is.
Let’s start drawing this main cube again.
This is more steeply looking up than before because shallow, more steep.
Not the steepest, though.
We’ll do that later when we get a little more control of how to set up the perspective
a little more officially and use the cone of vision and understand distortion
a little better. Then we can get into some real
steep and shallow angles that are just so steep that you almost
think you’re looking straight down into the earth.
And so when you’re looking up you almost think you’re looking straight into the sky,
that kind of thing.
That’s the difference.
As promised, you’ll be able to create infinite views in threepoint perspective as long as
you understand how to set them up.
You can draw any subject you want, but without a good setup to diminishments and understanding
the angles, most people actually don’t even attempt them.
It just depends on what kind of work you do.
Okay, so there is my little cube floating.
I’ll go and draw a little bit of the interior in.
Bring that corner up to the VVP.
There is a floating cube.
We’re kind of getting a little distortion down here.
That’ll be a little bit of a pull.
Either way.
Again, we’re working a larger part of the cone of vision.
You might be looking at these going, well, they seem kind of pulled anyway.
I don’t want mine to look like that.
If you don’t want any distortion.
Then just, again, use a much bigger triangle compared to the size of your subject matter.
That’s all you’ve got to do, or use a smaller subject matter inside your frame with
more conservative diminishments to farther implied vanishing points.
Either way, you’re going to get less distortion.
And then I’m going to have two little cubes behaving to the single vanishing point here.
This cube is obviously behaving to the left and right vanishing point.
Now we’re going to go to the single vanishing point with these little cubes tilting up.
There is the front plane.
We’re looking way up underneath this cube, underneath its underside.
I’ll guess that it’s foreshortened to being about that as it tips back and travels
with the vertical vanishing point.
Remember, I’ll overdraw it so I make it obvious.
That’s behaving to the vertical.
This is coming back down and behaving to the single vanishing point on the horizon line.
Again, I’m just guessing at my foreshortening which is relatively the same as the vertical.
Then I’ve got to close off my shape a little bit by drawing back to that, drawing back
up to there because that’s very foreshortened side on the cube.
I can draw the interior of the cube in a little bit as we go.
Okay, so that one is behaving.
We’re pretty far into that one.
Remember, this side is going truly vertical up, and this plane is parallel to the ground.
Remember, this is flush or parallel to the ground, flush and parallel with the ground,
flush to the ground, flush to the ground.
Vertical, vertical, vertical.
Just get used to what is each plane doing and how is it affected by this setup?
The last little cube will do a same thing.
We’ll do a square face behaving to the single vanishing point.
Do our verticals, going to our vertical vanishing point.
And we’ll close it off.
I guess I’ve got my foreshortening of my cube.
Draw back the corners to our single
vanishing point and then guess at our foreshortening again.
Again, before we get into the formal, more mechanical perspective, which we’re not
going to do all the time, we’re always going to go back to applied examples.
Before we get into that, I want to make sure everybody had a fair run through of why this
behaves without getting too technical.
All we’re doing is representing the three vanishing points in the center of vision plane.
Big deal.
Why these behave to just guesstimating foreshortening.
That’s the best, more natural way to start.
In the previous diagram we did two in bird’s eye looking down more shallow and more steeply.
Now we’re looking up more shallow and more steeply in worm’s eye.
We’re hitting it all together.
There is no difference between bird’s eye and worm’s eye except worm’s eye is turned
180 degrees upside down with the vertical vanishing point being way above the picture,
and the vertical vanishing point being way below the picture or somewhat below the picture
in bird’s eye.
That’s the difference.
Alright, so now we’re going to go into a little more analyzation of why and how we’re
looking down and considering looking up at different angles.
We’ll be doing it mostly in bird’s eye at first to understand the relationship to
how much we’re actually looking down.
We’ve got one more little one to do here and my steep one.
Here is my center of vision.
Don’t want to forget about my little applied version here.
That’s our center of vision right there.
I’ve got my frame, but now I’ve got much faster diminishment up here.
I’m going to get crazy a little bit and do this diminishment at about this rate as
I planned it out here.
Alright, a little faster like this.
That’s definitely faster than how before.
Look at how conservative that is, much faster.
So now, again, the trick is this diminishment to the vertical up here was much more conservative.
I got faster and a little faster diminishment to my ground plane vanishing points for this one.
This one we just need a little bit the opposite again.
I’m getting much faster diminishment to my vertical.
I’m going to hold off how fast the travel and the diminishment to my ground plane vanishing
points is a little bit.
I’ll go to my right side one, a little slower now, a little slower, a little slower, and
a little bit slower.
I’ve got my left side too.
Not particularly fast diminishment to those.
Then I’m going to draw in my cubes about here.
I’ll draw a nice dark line there.
Extend the planes down toward the left according to my diminishment guides.
To the right.
Then guesstimation here on, this will be a little bit out so I’m going to make that
a hair out from the diminishment guide.
There we go.
And I’m going to make this one about right there.
Okay, so there are the edges I want for my cube.
Come back.
Follow my diminishments and come back to there.
Again, I’m constantly diminishing down to the left, diminishing down to the right.
It gets confusing.
Otherwise, you’re going to go the opposite way, and you’re going to go that looks wrong.
You’ve got to remember, if I’m making this last move here, I’m going down to the
right so it diminishes smaller and smaller as it goes this way.
Let me slow down on that and show you.
There is my diminishment this way a little bit.
Get that right plane at the bottom.
I’ll make them nice and dark here.
Alright, so we’ll get into some more analyzation of why we’re looking up and down.
There is a steeper view looking up at the cube and a more shallow view, obviously.
It’s all about the diminishment guides here.
We’re not drawn to any vanishing points.
It’s just the idea of what this does or this does or what I know about threepoint,
got to be logical.
If I’m looking shallow, I’ve got more diminishment to the ground plane vanishing
points and shallow diminishment too.
The vertical in the opposite here, steep view.
Fast but diminishment to the vertical vanishing point, slower diminishment to the ground plane
vanishing points down here.
Alright, we will move onto different angles looking down in threepoint and how we can
figure out from a 90degree angle on a corner of a cube how we would do our diminishment
guides just on totally straightforward freehand drawing with the assistance of a triangle
and stuff on the next one.
Take a little bit of time to analyze that.
down compared to straightforward and traditional one and two point.
As you know, if we look over here in the diagram, in one and twopoint perspective, in general
traditionally, we’re looking straight into the horizon which would be zero degrees down,
and that would be generally what we’re doing most of the time in the entire lecture series
we just did.
Now we’re looking as shallow as 15 degrees down, 30 degrees down, 45 degrees down with
a little man standing on a pedestal.
45 would be exactly looking halfway down compared to looking straight out or straight down;
45 would be in the middle.
Then 60 degrees down is a little more steep than that, then 75 degrees would be about
as steep as you can go without looking like you’re doing what Superman is doing.
Superman is here flying over the city looking straight down onto the ground.
That’s no longer threepoint perspective.
That is actually onepoint perspective with onepoint vanishing point being actually where
the core of the earth is.
So, if you were looking straight down into the earth, the very center of the earth would
be exactly where your eye level crosses and had that one traditional onepoint vanishing
point crossing.
But we’re not doing that.
What we’re doing is we want to either be looking 75 degrees down; very, very steeply
down in perspective, 60 degrees is still steep, 45 about in the middle,
30 a little more shallow, 15 very shallow.
If you’re going to do any less than 15 degrees down, you’re going to get so little diminishment
to your vertical vanishing point, you might as well just do traditional one and twopoint.
It visually won’t make that much difference.
We’re going to use the idea of 15, 30, 45, 60, 75 degrees down angles.
You’ll get enough of a difference in each shift in those to be satisfying visually without
being so tedious to have to think of every angle between one degrees and 89 degrees,
which is a pain to think about.
We’re going to do every 15 degrees, and that’s good enough to change the compositional
feeling enough without changing it so much you have to get ridiculous with it.
So let’s look at 90 degrees down.
We’re doing a cube now that actually has real 90 degree corners because we’re looking
straight down.
I’m going to draw out the idea of this lightly drawn cube, and we’re looking straight down.
We don’t have any perspective to the plane that is parallel to the ground, the top and
the bottom of the cube.
It’s straightforward.
Okay, so there we go.
And how do we prove it?
We say that’s a real 90 right there.
If we know we’re looking at a real 90 degree corner in traditional perspective in twopoint,
we know we must be looking at it straight.
It’s not in threepoint.
In fact, either the object itself is tipped, we haven’t put the right diminishment because
this whole thing here is a true 90 degrees.
That means there is no perspective.
Now when I draw I’m still going to have a vertical vanishing point, but it’s really
still the traditional one point vanishing point like this.
Notice there is no diminishment to the sides of this cube because there wouldn’t be.
We’re looking straight down, and there is no perspective to that plane or those planes
top and bottom.
But, we still definitely have severe diminishment to the onepoint vanishing point, which is
traditionally straight ahead.
Because we’re like Superman looking in the ground this onepoint vanishing point diminishes
around here somewhere if I were to draw it in, but I’m not going to interfere with
the second cube.
It works just like looking steeply down, but the difference is there is no actual diminishment
as you go to the side.
There is true 90 to this, and that won’t be the same even when we’re looking down
75 degrees.
So there is truly looking straight down at a cube with our one point vanishing point
being about here.
Remember, when you’re looking straight down into the earth, that onepoint vanishing point
represents really the exact core of the earth way underneath.
So there is 90 degrees.
Let me put my little arrows in.
Next we’re going to do a 75 degree down angle.
I know that I’m going to have very fast diminishment still, just kind of like this.
But now I’m not going to have quite 90 degrees on that corner.
Let’s do the thing we’re looking for here.
I’m going to draw this projection first out to here, and that would be going to my
right vanishing point, which is, you know, the steep view would be way, way up at a horizon
line way out there.
It wouldn’t be much diminishment.
What I would be doing is I’m going to do very little diminishment.
These are closing in on each other just a tiny bit now in this really steep view, just
enough to eventually meet up there at the horizon line, way the heck up there because
it’s so fast.
But, the deal is, we can’t have a 90 degree, so here’s a real 90.
Let me draw that in.
That would be a true 90 degrees from this line.
We can’t do that like before because we’re actually looking 75 degrees down, so we’re
not looking straight down anymore, but it’s close.
I’m going to take a guess and say that’s the amount of diminishment,
that much of a difference.
I know it doesn’t seem like much, but when you put in your initial crossing of what you’re
going to eventually turn into your diminishment guides or even a grid, even if you’re just
guessing freehand, that’s the difference in a really steep 75 degrees.
It’s just off a little bit and a little wider than it would be.
That would be 90 degrees, but this would be what it would be.
It would be a little wider than that.
It’s not quite 90, and that gives us a little breathing room.
Also, I’m going to have really slow diminishment here.
This will be diminishing very slowly way up there to the right.
That would be the to the left vanishing point.
I’ll go ahead and put that in.
Okay, then I’m going to put really, really fast diminishment down, kind of like we did
for looking straight down because it’s almost indiscernible.
Not quite as fast, but pretty fast.
With 75 you can have your vanishing point right near your object or very close to it.
And so now when I put the bottom edge of the cube that I’m guessing in, it will have
a slight diminishment again, eventually ending up at a vanishing point way up to the left.
I’m putting in a slight diminishment to this plane even though it seems fairly subtle.
That’s what you need to do.
I’ll do that with this plane too.
That’s when you can start gauging just correct, freehand drawing.
We’re looking way down at this cube.
It’s very, very steep.
Very foreshortened side walls, but those side walls, the top and bottom planes still have
a little bit of diminishment going to that distant horizon line up there.
We have very fast diminishment for our vanishing point, which is down.
That’s pretty much just approximating a drawing of a cube that takes up a decent amount
of space in a composition of a 75 degree downangle.
It’s just a little bit off a true 90.
Let’s do a 60 now.
It’s a little more shallow than that.
We’re going to start with our projected plane off to the left again.
Then I’m going to say, okay, there is a little more diminishment, a little faster
between this one and this one.
Remember, truly looking straight down there was no diminishment to these planes.
They were exactly parallel.
Now we have a little bit more, so I’m going to have a little bit more than I had in 75
degrees for 60 degrees.
These diminish a little faster than these did going this way.
But now, I’ll draw in a true 90 degrees picture again here and draw it in in red,
but now because I’m 60 degrees down, I’m a little more shallow than I was at 75 degrees.
I’m going to allow a little more room to get away from that red line that represents
90 and come out to here.
Now the difference is a little more than it was before up here, and that’s just a guesstimation.
Now, if that’s going up to my right vanishing point.
I want a little bit diminishment kicking in so they eventually meet way up there to the right.
That’s what my guess is to this side.
Again, we’re taking just kind of handdrawn with a straightedge assist guesses with what
we’re trying to think of as a 60degree down angle.
Then we’ll do a 45, a 30, or whatever.
It’s just we have not quite so fast as diminishment down.
We have still a good deal, but it’s not quite as fast as the 75.
You’re just kind of gauging all these things in comparison with each other.
Then we have some diminishment, a little more fast than here for 60.
We can see more of the side of the cube.
All we’re doing is kind of estimating our thoughts about how threepoint is working
even on a single object if we’re not going to use any official triangle
or a lot of formal setup.
We can still think of how it behaves through these simple ideas.
We know this can’t be a 90 degree corner if it’s a cube because we’re looking down
at a shallower angle than we would be if we were looking straight down.
We’re going to keep knocking this angle more and more out from the 90 degree.
It’s going to splay open.
A 90 was doing this, and it’s going to start splaying more and more open like that as we
get down to shallower and shallower angles.
We’ll also be able to see more and more of the side of the cube because we’re not
so steep on it.
We’re getting more shallow on the top, more shallower on the vertical.
Anyway, that’s about 60 degrees down.
I’ll start the other one, again, at 45.
Here we go.
That’s just the beginning lead again.
That’s going to our left vanishing point somewhere out there.
I’m getting a little faster diminishment now because, as before, I had no diminishment
looking straight down, a little bit with 75, a little bit more with 60, but now at 45 we’re
about halfway down.
So, the diminishment up to our average ground plane vanishing points, if they’re relatively
evenly spread out, would be a little faster and fairly even to that of the diminishment
for the vertical.
It’d be about the same because we’re looking about the same foreshortening down.
Now, if this was spun, if this cube was spun and it had a much longer left vanishing point,
let’s say, and a closer right vanishing point to the center of vision, then there
would be a diminishment difference, and you’d have to consider that.
In this case, if they were generally splayed out equally, what we’re going to do is we’re
going to have a little more diminishment now to our left vanishing point.
We’re going to draw at a true 90 degree angle, again, in red to our beginning left
spread there.
That, surprisingly, would be right there.
And so we’ve got a lot more room that we want to draw over until we get to our much
more obvious diminishment here.
So there is even more room than we had here.
We’re getting around 45.
This also has more diminishment change, so I’ll go ahead and draw that in.
Then I’ll go ahead and draw a more subtle vertical diminishment because we’re really
steep here with very fast diminishment to the verticals, still very fast diminishment
to the vertical for 75 degrees down.
Sixty, we’re tapering off a little, a little more subtle diminishment, even a little more
subtle diminishment for a 45.
I’ll just go ahead and do that, and then I’ll guess what the foreshortening might
be on the bottom of my cube.
Again, I’m going to have more obvious foreshortening to my left vanishing point here at the bottom
and also tape it in a little like this.
Alright, so that’s a roughly 45degree view.
It’s just the idea of this true 90 coming off your lead projection.
What’s a real 90 in red compared to how much you splay open that box.
Now we’re going to 30 degrees, so that will be even more.
So, here we go.
Even more diminishment coming together closer for that left diminishment.
There we go.
Now we’re going to draw on that 90degree square again, and we’re going to really
see how much our right vanishing point plane can come away from that.
So, there is that.
That much difference now, which is quite a bit.
I’ll go ahead and have a faster rate of diminishment going to the ground plane vanishing
point because we are getting a slower and slower rate going down.
A really fast rate going down vertically here, but now the vertical is slowing down quite
a bit and will be even slower for 15.
These are approximations only, but it’s just kind of good sound exercise to get used
to the idea of how fast the diminishment might be compared to the diminishment here to the
sides like this.
There you go.
Extending out there.
Again, 30 degrees looking down.
A little less severe on the top.
More foreshortened on the top, less diminishment going to the vertical for 30 degrees.
Now 15 degrees is very subtle.
We’ll go ahead and draw our first lead to the left.
We’ll have faster diminishment to the ground vanishing point, which might be a little way
over here.
But now, when we put in our 90 now it’s very severe.
There is the 90 cropping up, and there is the actual real 90degree relationship to
that left plane here.
Quite a ways, so we’ll put the arrow over here.
Now we’re traveling all the way to there to make my guess for my 15degree down angle.
Then we’re going to use more severe diminishment right here.
I think that’s about right, then much less diminishment for the vertical again or somewhat
less, so it’s pretty subtle at this point.
There is not a lot of diminishment to the vertical.
We’ll try to square in our boxes here.
Again, always reminding ourselves where those planes are going.
They’re going to the left vanishing point up there on the horizon, which isn’t that
far away now because we have such a shallow view.
We’re not in the center of vision.
The center of vision would be somewhere here.
This is a little past vertical going to the right, so our center of vision is probably
around here with this one.
This is tilting more, something around there.
I want to put it in in blue.
You can gauge all that stuff.
We could have cubes that are leaning over to the right or the left more because they’re
not quite lined up with the center of vision.
They don’t have to be.
The center of vision is not something that anything has to be lined up with.
It’s just the center of our view as the viewer, the plane that comes directly from
our face, off vertically forever.
Of course, the eye level as we’ll get to now very soon here, is where we’re looking
straight into as we’re looking below the horizon or above the horizon, depending if
we’re in bird’s eye or worm’s eye perspective.
There is 15 degrees again.
We’re looking straight down, very steeply down at 75, a little less steeply at 60 degrees,
about halfway down between the horizon and the earth at 45.
Then we’re looking more shallow at 30 and fairly shallow just to the point if we used
less, even more shallowness, we wouldn’t really notice the diminishment to the vertical
that much.
It wouldn’t be that visually appealing probably.
Again, I’m usually sticking right around
15 degrees down if I’m going to bother using threepoint.
Otherwise, it would probably be more continuity just to go ahead and be looking straightforward
with traditional one and twopoint perspective then.
There are the basic ways we look at the world.
That’s little representations of us, zero degrees being the traditional horizon, 90
degrees always looking straight down at the earth, and all the ideas in between it.
You can take this exact idea with these exact people and have them look up like their heads
are tilting up, and the exact same rules would apply looking up at all these cubes.
There is no need to really repeat it.
It would be the exact same lesson looking up.
In worm’s eye, if you were simply looking above the horizon degree at 15 degrees,
30 degrees, 45 degrees, 60 degrees, 75 degrees, it would be the same lesson.
It would just be that we’re looking up and not down.
Same logic.
Alright, and now we’re going to go onto the actual reason why we know how to set the
triangle up.
There are some rules about the triangle we’ve been using in the earlier diagrams with threepoint
just previously.
Now we’re going to work on the four things that we really need to understand from that
triangulated diagram in order to do officially measured and/or formal threepoint perspective.
So that’s what we’ll be onto next.
about with the triangle that’s created by the three vanishing points, the left vanishing
point, the right vanishing point, and the vertical vanishing point,
but there is a missing element.
The 4th critical element in threepoint would be the three we just mentioned plus the center
of vision point.
The center of vision point as you know from one and twopoint perspective is where the
eye level crosses the center of vision plane, making not only the onepoint vanishing point
in one and twopoint perspective, but the very center of where the cone’s radius is
projected from, and that’s the very center of your view that you’re looking at as the
viewer in the center of our distortion range with the barrier of distortion
going out from there.
So, we’re going to do it right here, and it should be pretty obvious what’s going
on because, remember, our eye level switches.
Let’s just do this one slowly.
So, three of four of these things can be random, and we’re going to talk about that.
So, in the first case we randomly set the left vanishing point, the right vanishing
point, and the vertical vanishing point.
This is our horizon line.
Now we’re going to start having to deal with our eye level as well, but that’s after
we understand how we place the center of vision point.
The center of vision point is how we know that we have our eye level properly in the
center of our view so we know we can gauge distortion.
So, left vanishing point, vertical vanishing point, right vanishing point.
The only thing missing in this particular number one, we’ll just call it version number
one of the triangle, is how do we determine our center of vision point, which is equally
as important as the other three items.
All you do is you strike at a 90 degree angle from this wall here back across to this vanishing
point, in this case, or vice versa.
So, what does that mean.
If I take a 90 degree angle back from this side wall and draw it.
I’ll draw it in red here, and I draw it back to here.
That gives me the center of vision point, because where it crosses the center of vision
plane, this is the center of vision plane.
I just at a 90degree angle from this triangle wall projected back through to the RVP, the
right vanishing point.
Conversely, I could do it again, the same angle here.
It’s going to be crossing at a 90degree angle here as well.
The first one was critical because I said, yeah, I want to go from the left vanishing
point or the left triangle wall through to the right vanishing point.
This is how you always find the center of vision point when you’re dealing with a
triangle. In fact, sometimes we’re going to find our center of vision point first and work backwards
to the triangle.
We’re going to do all different things, and it’ll actually seem pretty simple when
we get there.
So, the first one, though, the thing we were missing is the LVP was random, correct?
We had it when we began.
The RVP, the right vanishing point was random.
We had it when we began.
The vertical vanishing point was random.
We had it when we began here.
We also had our center of vision plane.
The thing, the critical element missing from the four important things was the center of
vision point.
I’ll just put in the CV point.
That is equally important as the right, left, and vertical vanishing point.
That’s the thing we’re missing in this one.
It’s a given.
Because these were allowed to be random, only three of the four important elements can be
random. The three only. The fourth only is only a given.
In this case, random, random, random triangle.
Horizon line, we had it all drawn out.
This strike across here from 90 degrees where it crossed the center of vision plane became
our center of vision point, and that’s going to be critical when we create our vertical
station point and cone to understand where the barrier of distortion is in the threepoint
setup, okay? This is the beginning of that idea.
So, number one we got out of the way.
It was the center of vision point that was missing.
All four are equally important.
Again, only three of the four of these items can be random.
The fourth item must be or is a given.
The four important items are vertical vanishing point, left vanishing point, right vanishing
point, and the center of vision point.
Let’s do item number two right here.
In this case, we have our left vanishing point.
We have already decided where our center of vision point, and we already have our vertical
vanishing point.
We are doing this method, not as an applied method to start drawing threepoint, we’re
doing it to rehearse why the relationship between these four ideas and four points are
so important.
You won’t understand how we setup the rest of threepoint when we do it.
And it’s really fast and easy once you understand the memorization of these relationships.
We have left vanishing point, center of vision point, and the vertical vanishing point.
Those are three random items, and the fourth must be a given.
If we already have this point here what we can do is we can take this point here, and
again at a 90degree angle we can say at what point is my triangle going through the center
of vision point at a true 90 degrees to that left side wall.
It turns out right there.
That gives us our last item.
Since we had our center of vision point, or left vanishing point, and our vertical vanishing
point, if we came straight out at a 90 from this left wall going through the center of
vision point, that gives us our right vanishing point.
Then we can close the triangle off after that.
I’ll put a little arrow going this way.
So, we went through here first.
Came back down.
That closes it.
Of course, after you have the center of vision point and your vanishing point, you can come
down and say the other crossing would be like that.
That’s the standard routine you’ll do for an official setup in threepoint.
The three vanishing points, the center of vision point and the crossing hitting each
opposite wall at 90 degrees.
That’s going to be standard no matter what official or formal threepoint setup you do.
That’s going to be the way it is.
In this one we did not have our right vanishing point.
We had our left vanishing point—it was random—vertical vanishing point was random, center of vision
point was random, but we had to find, and the position was given or automatic to where
our right vanishing point was by shooting through from 90 degrees through the center
of vision point to create our RVP in that case.
In this case, we had to create our CV point.
In this case, we had to use the information we had from these three items to get the fourth.
Let’s go on to number three.
Now we’re saying how do I figure out where my vertical vanishing point would be if I
already know randomly where my LVP, my left vanishing point, my center of vision point
and my RVP is?
Well, what you can do is we can draw across from the RVP, let’s say, through the center
of vision point like this.
Keep going.
Where the projection from the left vanishing point then crosses this at a true 90 degrees,
if you want to get official about it.
You’d line this up like this and say true 90 degrees.
You’d continue down and that’s how we’d get our vertical vanishing point.
We basically had to come from our cross right vanishing point going through the center of
vision point and past where we perceived the wall should be.
Then the true crossing of this projection is at 90 degrees.
That gives us our vertical vanishing point.
So, in each one of these cases, we’re missing one element, and there is simply a constructive
way to find where the other missing point is, and so I just want you to get used to that.
Then this comes up to here.
This is going to be confusing at first.
You’ve got to memorize it.
You’ve got to play the tape a few times, this particular version over and over again
until you go, oh yeah, that’s how I knew that was there.
I’ve got to go here or go there, and through there gives me the fourth element that’s
missing.
Only three of them can be random.
The fourth is a given, but if it’s missing, that’s how you know where that last point
is put in.
In this case, number four, we have our RVP, our center of vision point, and our VVP.
Again, it’s a pretty easy idea.
Simply come through from our right vanishing point coming through to here.
Again, we should be able to figure out at a true 90 degree crossing there, leading
to our vertical vanishing point we should get our answer to where our left vanishing
point is now.
So you would keep going like this and then past that item.
Keep going.
Right there would be our left vanishing point because that is also that 90 degree relationship.
As long as we had these three we could shoot through here and then come at a 90 crossing
that, that gave us how far out the left vanishing point would be.
We had our RVP random, our VVP was random, and our COV point was random, but the left
vanishing point had to be a given by finding the strike across here crossing this line
at 90, this line at 90 and keep going up to the horizon line, and that gives us our left
vanishing point.
It's a horizon line here.
I just want to make that obvious.
That’s always a horizon line.
Now, the big surprise is we’re not drawing it in yet.
Just wait, we will.
No surprise, the center of vision point that we’ve been getting here is, in fact, the
very point where truly horizontally every time our eye level, the place both of our
eyes are actually affixed to and we’re looking down because we’re no longer looking at
the horizon.
We’re looking somewhat down from the horizon depending on the configuration of the triangle
or the steepness or shallowness of how we’re looking down.
Our eye level now goes through here.
But first, I wanted you to memorize this.
Just know that our eye level in a horizontal manner goes all the way across the diagram
after you add it on here.
If you want, we can add it on in blue quickly here.
But, don’t be confusing this with the rest, but that’s how we know where our eye level is.
I’ll just kind of put that in quickly.
We’ll do the cone next.
Don’t want to confuse everybody too much.
It’s just we have to find where is our center of vision point?
It’s got to be in our center of vision plane somewhere below the horizon, above the VVP,
but this is how we determine it.
There is a 90degree angle configuration that goes across the center of vision point that
hits opposite triangle walls at 90.
That’s how you always know where your crossing is, where your eye level will be met.
That’s going to be true no matter what you do in worm’s eye or bird’s eye.
There in blue, again, is the eye level.
Blue is the eye level, and once again, eye level.
That’s important because we’re adding another step.
Now we have an official way to understand not only where a horizon line is and our three
vanishing points and the center of vision point, all the elements we need, we also need
to know where our eye level is because we eventually need to find our vertical station
point, which is critical just like the standard station point is critical for measuring one
and twopoint or even being formal with them.
Again, to review real quickly, we’re missing the CV point here and found it.
In this one we were missing the vertical vanishing point and found it.
Please go back and review this three or four times so you’ll understand the different
ways we’ve memorized whatever the missing issue is or the missing point.
We can easily find it.
Close up the triangle and realize a real threepoint view once we learn how to apply the cone of
vision, which we will be next.
Again, this one, we had the RVP was missing.
We had to put that one in.
Then in the final one for number four it was our left vanishing point that was missing
and we had to triangulate this cross in the proper way to find it.
It’s not random.
You can’t have three of these items random and then have the fourth random.
No matter what the fourth item is, it must be a given or automatic.
Otherwise, you’re not dealing with how we see into space as human beings in perspective.
The geometry has proved it a long time again, and this triangulation has to happen this
way or else you’re not having the proper relationship with the vanishing point and
the center of vision point.
That’s the reason we’re memorizing this stuff.
Not to say you can’t draw a threepoint, we just got done having fun doing simpler
stuff, but if you want to know how it works officially and lead into that in tandem to
how we’re going to do the more applied versions, you’ve got to know this stuff.
This is the hard memorization I was talking about, the triangulated relationship along
with the center of vision point.
Alright?
So, it’s the triangle of the left vanishing point, right vanishing point.
VVP, vertical vanishing point in conjunction with the center of vision plane, and we’ve
got to have that center of vision point in order to move on to actually get real views
and measured threepoint.
projected cone of vision so we know where our distortion space is and, of course, how
our view is centered.
We’re going to keep running with those memorized ideas over and over again.
It’s pretty simple.
We have all these triangulated setups looking down in threepoint in bird’s eye and then
we have things looking up in worm’s eye in the thing.
We’re just taking these random shapes of triangles that have already been worked out
for everything that’s important to find.
We just have to add the eye level.
Then we have to find the method for how do we know where our SP is.
And so in this method we’re going to use the method where we have to come at a 90degree
angle to find it.
Let’s put our eye levels again in blue like we did before.
We’ll do that real quick on all of them.
Actually, we’ll do one at a time.
Here is my eye level for this one.
It’s truly horizontal.
Right through the center of vision point.
A nice big eye level there.
Now the method to find where the SP is, we have to use a 90 degree angle
like on my triangle here.
What we’re doing is we’re taking the single vanishing point at the crossing of the horizon
line and the center of vision plane.
We’re also aligning the edge of the triangle on the other side
to the vertical vanishing point.
Where those two are lined up together and meet at the corner of the triangle right on
the eye level, that is always the location of the vertical station point.
So, it’s a 90degree idea.
The line coming down here represents being parallel with the horizon, and the line projecting
down to the vertical vanishing point represents truly looking down to the core of the earth,
which we’ll explain later again as we keep going.
So, I’m aligning my tip of my thing, my pencil to the vertical vanishing point.
I’m also finding how it leads in right here, and I’m going to draw that idea in.
Where it meets at 90 degrees is, in fact, the vertical station point.
That’s how we know how to project back and get our cone from the side now.
Unlike when we were at the bottom and were in traditional one and twopoint, because
this has to do with verticality.
This has to be off to the side.
Let me be clear.
This is the actual distance from this center point here out to the VSP is the real distance
you and me would be looking at this.
We’ve have to swing it up like this.
This is the hinge point.
This distance straight out in front of us is the distance we’d actually be looking
at this diagram, and it would look this most real.
That is the distance of our station point brought up to be a real threedimensional
idea, like you and I are actually standing into the picture.
We’ve just flattened it so we can work with angles on paper because you can’t work with
threedimensional ideas sticking out of a piece of paper.
It has to be flattened like we explained how one and twopoint is.
Okay, so there is our vertical SP.
Now I’ve got—just like the cone of vision traditionally in one and twopoint, I’m
projecting back at 30 degrees and 30 degrees to get my cone.
I’m also going to show that in blue, and I’m going to get my 30degree triangle now,
which is this one.
You can see it reflecting in the light.
It’s fairly invisible.
I’m going to simply, really quickly get those 30degree angles projecting down from
the SP like this, and then like this.
This is how for any configuration of triangle the same process is going to look a little
different in each one, but the same process finds your vertical SP and eventually your cone.
There is where the cone crosses here, and then I’ll get my compass.
I’ll simply set it up real quick to the distance of there.
Is that about right?
Let’s see.
Yeah, about there.
Something like that.
That’s where my cone is.
I’ll open it up a little more.
And so there is the cone for this particular triangle setup.
SO now we have a complete formal idea of why threepoint works.
I know it seems like oh my God, look at all this.
Do I have to do this every time?
No, you do not.
The idea is you have to look at this sometimes to understand why formal perspective works
in threepoint, so you can take better guesses for your applied perspective setups that we’ve
been talking about too, and we’ll certainly do more of.
So, let’s go over it again.
That’s 30 degrees and 30 degrees equals 60 degrees for that.
And that equals a total of 60 degrees for the entire cone.
There is the cone.
I’m just doing it in pencil.
There is where it touches the four points.
That’s our traditional cone of vision.
There is our center of vision point.
Now we can look at the left side vanishing point, the right side vanishing point, the
horizon line, the center of vision plane, the center of vision point, and the vertical
vanishing point all triangulated, and this relationship is how we can draw full threepoint
in and know that we’re in the distortion.
By the way, we have to talk about this.
The degree of distortion that happens near the edge of the 60degree cone is more severe
in threepoint, and you’re probably going to want to work well inside of it if you’re
not a big fan of getting stretched out, basically results.
You’re going to be having your vanishing points even further away from your framed
area if you wish to have no distortion.
But for now, we’ll work with the traditional 60degree cone so that we can understand why
it relates to one and two point and what we did so often.
Remember now, the vertical SP is taken off to the side of the diagram because it’s
representing verticality.
This actual distance is our SP out here that’s been taken as a flap and put down to the side.
Here is the edge of the flap that’s flexible.
Here is the point.
It’s standing up usually, and it’s collapsed down.
It’s either standing up when we’re really out here in space.
It’s collapsed down as a flat flap.
That’s why we know how to draw it in twodimensional terms accurately still.
There it is.
So, let’s do this one real quick.
We now are going to take the same idea.
We know our eye level runs straight through this one.
It’s a different configuration but same process.
Just do it again for the second time.
There is my eye level.
How do I take my 90degree triangle edge—again, line it up to my vertical vanishing point here.
Let me draw that in so it’s not a mystery there.
You’ve got your horizon line.
What we do, again, is the same thing we did before.
I line up my vertical vanishing point and my single vanishing point at the horizon line,
meaning the center of vision plane.
Then I take the tip of the triangle.
It has to be meeting right there on the eye level.
Then we get this idea.
Same here.
We have that really clear idea of 90 degrees.
No surprise.
That’s 90 degrees, 90 degrees.
That’s an important point.
The verticality we’ve checked between this representing the horizon or the horizontals
and this representing the verticals, and you have a true 90degree relationship, just like
real verticals meeting real horizontals.
So, the same idea.
Here is my VSP for this one.
Now I can project back at 30 and 30 to get my cone again, so I take my 30degree angle
from my triangle.
Go ahead and use my blue again.
I’ll go ahead and draw that in quickly.
Project.
That crosses down.
Where it crosses here would be where my cone would be.
Also, use my 30 again.
Project up from the VSP.
Crossing there.
There it is.
If I take my compass I can then draw from the center of vision point because that’s
the center of our actual vision now when we’re sitting in front of our own diagram really
looking in.
This center of vision point is obviously the place that’s the center of our view.
There is the cone of vision with the 30 degrees, 30 degrees total of 60.
There it is.
There is our cone.
That’s the area.
You wouldn’t have much distortion in about half of the cone, the 30degree cone as you
work further and further out the barrier of the 60degree cone.
You’re going to get some pull from objects in threepoint, even if you’re thinking
that it won’t look that distorted.
It’ll start pulling.
We’ll work on a method to kind of always be inside the traditional cone a little bit
if you don’t want distortion.
We found our VSP again, same method.
Project to the cone, got the cone.
This is the real distance of my station point.
Remember, this is called the vertical station point.
Until it comes up and meets the actual distance away from the diagram.
That would be the single SP because it’s a real threedimensional idea.
Other flaps are going to come up and meet that same distance we’re going to get to
in a few diagrams so we finally understand why this stuff is triangulated.
Again, that’s our real distance from the diagram, and that’s why real angles project
from the actual SP just like they do when it’s flattened.
Okay, so let’s go on to the next one.
Again, we’re just doing this as practice.
We’re going to put an eye level in this one again and practice the same thing.
Same routine for all three.
Different configurations of triangles.
Different look to them, different sizes of cone, but the process is exactly the same
to derive the vertical SP in the cone.
Okay, so we’re going to put our eye level in again.
At this time, it’s down here because the crossing of the center of vision point is
way down here.
This is a pretty steep view.
This was a shallow view.
This is kind of an intermediate view.
This is a very steep view looking down in bird’s eye.
There is my eye level crossing.
Put my eye level signature in.
Then I’ve got to take that same 90degree corner idea, and I’ve got to lead it from
here, the single point where the center of vision plane crosses the horizon line and
my vertical vanishing point.
Then I’ve got to make these corners come right up here.
That’s where the corner of the triangle is.
That’s how I find my vertical station point again.
Project back at 30 degrees and 30 degrees real fast.
Get the hang of it here, it doesn’t take that long.
We’re not doing this every time.
We’re talking about this being formally the reason why measured perspective works
in threepoint.
And so we will be talking more about that, and we’ll also be doing more applied versions,
which have nothing to do with measuring.
They’re just good guesstimations.
We’re doing both.
Get my cone here through my compass.
Again, if I twist this around a little I get the same cone.
This one is a little smaller, again, because of the severity of the down angle.
There it is.
Right in my 30 degrees plus 30 degrees equals 60 degrees for the cone of vision.
That’s the center of vision point right there, of course.
We put in our eye level.
So that’s all that material.
Let’s do a faster version now.
We’re looking up.
We’re looking for the same thing.
Now, we’ve reversed it a 180degree turn, but it’s the same process.
Let’s not get confused.
We still need to strike an eye level through our center of vision point right here.
I’m still going to find a 90degree relationship here in my triangle between this single point
again, the vertical vanishing point, and the tip of the triangle, the corner coming to
the eye level.
Good.
There it is.
Projection we’re going to need.
That is my vertical station point to project back at 30 and 30.
We’ll get our cone in the same way.
Let’s do that fast.
Also, come up at 30.
Again, this is just a routine 30 degrees and 30 degrees, total of 60.
The 60degree cone is agreed up to be the barrier of distortion of one and twopoint,
but again, you’re going to get more severe distortion because of the diminishment to
verticals, and you’re probably going to want to pull in the amount and tighten in
on a smaller cone of vision most likely.
We’ll still use the full cone so we can get fairly big diagrams.
Once we start doing single diagrams with some of the points off the board, we’ll be getting
clear larger drawings too.
These are just from memorization.
Remember, the last diagram and this diagram purely from memorization of the step process
and the relationship between all these different elements.
Just watch these over and over again so you can understand this triangulated relationship
of what we’ve been adding on since the first diagram in threepoint.
You’re going to easily be able to create scenes, guesstimate where things should be
better on your more applied scenes with your diminishment guides.
It’s just all additive.
We’re going to get the cone again with the compass real quick, and then we’ll do the
next couple and move on.
I just wanted to make sure we all have this applied practice on setting up the cone with
the VSP and the other elements of the triangle being present like we’ve been building over
the last few diagrams.
So there is the cone, 30 degrees, 30 degrees.
There it is, 30, 30, a total of 60.
There it is.
There is your cone of vision within the triangle on that one.
We’ll do this one.
Add the eye level real quick.
Again, using my corner of my triangle.
I’ll use the long side.
I’m connecting the VP up with the single vanishing point and meeting that corner of
the triangle on my eye level; it gives me the SP.
We’ll find a couple of other ways to find the SP later.
More importantly, we’re trying to memorize the elements and why the relationships are
all important in the flat geometry before we start doing threedimensional imagery in
perspective.
There is the VSP.
Oops, that’s toasted.
Then we’ve got to project in for cone again for blue from the VSP real quick.
There we go.
Okay, and 30 degrees again down here.
Almost right at my horizon line there.
Okay, there it is.
Again, compass, cooking along here.
Here we go.
There is the cone for that one.
There is the center of vision point, our cone, center view in there.
That would be our barrier of distortion.
It would get fairly, you know, pulling pretty strongly there.
Put my 30 and 30 in; 30 degrees, 30 degrees, again, a total of 60.
One more time.
Quickly.
Right here, this is a more shallow view.
This is worm’s eye.
This is a steep view in worm’s eye.
Intermediate, shallow.
Why do we know it’s shallow?
The eye level is just a little bit above the horizon line, so it’s going to be pretty
slow moving vertical diminishment, faster moving to the ground plane vanishing points.
Eye level.
Take the corner of our triangle again with our red.
Single vanishing point connecting to the vertical vanishing point and the corner of the triangle
at 90 degrees meeting out here.
Let me keep making sure that I put in this as 90 degrees, which I should have done earlier,
but the same idea.
This is definitely 90.
It’s important leading to there, to there, and that’s how you get your vertical SP
that allows you to project in for your cone and understand your true distance.
Up is the true distance from us viewing the diagram in real space.
That’s why the SP is important, actually.
It engages all the proper projections into space that you’d actually see in front of you.
And that’s why the 3D programs work.
Same stuff.
A total of 60.
There we go.
Let’s put it in with a compass.
There it is.
Our cone of vision one more time on this little pass here.
Okay.
Again, six different setups.
Three looking down in bird’s eye.
Shallow bird’s eye, intermediate, steep bird’s eye.
Steep worm’s eye looking up, intermediate, shallow worm’s eye looking up.
All these things we’ve applied cones to.
We’ve found the VSP for everything.
Same process no matter what we’ve been doing.
It’s a memorization game, so please, the last couple of diagrams on this one, just
memorize, memorize, memorize, and you’ll understand how this relates to the perspective
you already know because you’re already familiar with the cone and the idea of why
an SP works.
We just have to point out why this is different in threepoint.
But, you have the fundamental building blocks if you understand one
and twopoint pretty easily.
This is the memorize setup for threepoint, and we’ll keep having a discussion now about
how we actually look through a picture plane when we’re looking down for the next diagram.
There is a little more kind of explanation and narrative going on.
Well, it is about a guy looking through a table into a real scene.
What I’ve done is draw a twopoint scene involving a guy actually looking down in threepoint.
Here is our horizon line for our twopoint scene.
This is the actual horizon.
Ten we are up this high looking down at this dude looking through the drawing table drawing
the cube that happens to be in the position.
I’ve put diminishment guides on here for the basic perspective of the twopoint scene,
but actually he is looking down in threepoint.
But this diagram explains what we just did in a way, how it looks in real space if someone
is looking and actually drawing a cube dutifully in observational threepoint.
It would be the same idea is that we just did this.
Here is the most critical thing.
This is his center of vision going through the table and hitting a real place on the
ground.
When we drop down and line it up directly with his actual line of sight from his body,
this plane, it cuts right through the cube at this point, and it has a real location
on the ground.
There is a direct translation in relationship between the actual space the man is taking
up, his view projecting through the table as if it’s made of glass, and the subject
matter that’s beyond him in this environment.
It’s all tied together due to the same type of perspective view.
In our case, that point right there that he is looking at in his drawing on his drawing
table is also right there in real space in front of him on the ground, assuming he can
see through the table because it’s made of glass.
Also, his real SP is up here in real space at this distance, but as I was just mentioning
on the last diagram we did, or is should say diagram series on the six setups, this space
is the flattened version.
This red space I’ve actually toned out in red right here.
Actually is a flap that moves down with these arrows and rests, and that’s where our VSP is.
It’s the same thing as the real SP right in front of this person’s eye or eyes, I
should say, looking down at the table.
That same distance to his picture is the flattened version of how we set up our VSP on the flat
diagrams.
Real space, real person in 3D space, flattened version, twodimensional space.
Same thing.
We can project our cone right from there if we wish, or we can project our cone right
from the man’s eyes.
We would get the exact same result on the diagram on the table.
By the way, we’ll get the same results projecting real angles through the table to the real
scene, or in some cases the flattened VSP measured geometry.
Same results.
That’s why measured perspective works and the 3D programs work.
Euclidian Geometry.
It’s been going on for centuries.
It’s just an explanation.
There are our vanishing points out.
There is our vertical vanishing point.
See the man’s eyes.
The real vertical in the world are twodimensional, or twopoint perspective diagram, the verticals
are going really vertical because we’re not seeing him in threepoint.
Straight down from his eyes, through the table to the little point on the ground is where
that vertical drops and then forever into space from his eyes through the horizon line
center of vision point going on forever would be to the horizon where that point would connect
up in the real world.
It’s all related between the real scene in the real world and those points hitting
vanishing points that are marked on a table on a diagram on a twodimensional drawing.
We’re just trying to see threedimensionally why threepoint works.
We’re looking down at this down angle at this cube.
He is discovering how to draw that going to the real vanishing points of the triangulated
setup with the center of vision point and the crossings and everything we’ve learned so far.
So, this diagram in real space on this table in front of us in this twopoint scene is
working just like and explaining hopefully a little more why what we just did works and
has to be set up this way so we can actually replicate and measure perspective kind of
like it’s in the real world with real space just like we did in real point.
I just want to kind of slow down and explain why that worked.
Here I’ve got the cube in real twopoint perspective, but he’s actually viewing it
and experiencing it in threepoint through the glass table.
Here is the deal with how he’s actually looking down at this approximate angle from
the side.
This is not unlike the ones we just did the diagrams looking down at the various cubes
a few diagrams ago.
This is the cone of vision projected from the man’s head and the true vertical dropping
down here, true horizontal going on forever into space, but it actually connects with
the drawing right here on those vanishing points on the paper.
Remember, the vanishing points are created by projected lines of sight going straight
from the man’s actual SP standing here through the board and ever into space.
They only look like tubes to him with ends because looking directly at the ends of the
tube would create something like a vanishing point.
Only we can see the projected lines because we’re the third person.
He’s the first person.
Just like when we’re in front of our own picture drawing it, we’re the first person
in the picture looking through the illusion of the picture plane.
We’re actually the third person in the book looking at somebody looking into space so
we can analyze how he’s seeing everything as lines.
All these intersecting lines with his eyeballs coming and going from these vanishing points
are actually like little rods that are facing straight toward him.
He only sees them as points again.
It’s a weird thing to think about, but once you start understanding why this works from
our actual angle in front of picture compared to being able to observe and abstract it as
human beings do.
We’re not dogs.
We could have little paws drawing, but dogs can’t abstract like this.
We figured out how because we can think about it as real life or the illusion of real life
on a twodimensional surface.
No 3D rendering is actually 3D. It’s actually many, many, many frames on a twodimensional
computer screen.
No different than this.
They can render them so much faster with thousands of frames.
No difference.
The perspective works the same.
I just wanted to mention that.
Now we’re going to do a little perspective drawing realization of what’s happening
here and part of the explanation here.
What I’ll do is I’ll draw in a little horizon line again, and we’ll kind of get
going on this.
This is kind of a prethoughtout idea to kind of explain this better.
What we’re going to do is we’re going to start in the center of vision point here.
I’m going to get my center of vision plane going through here.
I’m going to reverse the idea here.
I kind of have my horizon line here.
I’ve got my center of vision plane so we’ll just put that in here.
This is my center of vision point.
I wanted to draw on the little man’s head from behind like this with his ears sticking
out and his little neck and his shoulders because that’s us sitting in front of the
picture actually staring at the picture from this particular distance out, which I’ll
showcase next.
Let’s do the cone next.
We’re going to work in a way here that is now much more applied.
We have nothing down here except an idea where I might want my horizon line.
I’ve got my center of vision plane.
Let’s start with the cone first and say, okay, how big do I want my diagram.
Let’s not worry about the other stuff.
I’ll start out here.
I’m going to draw on my cone in.
What can I deduce from where the cone is?
Easy.
How do I work backwards to my SP?
If we did all that exercise before with the 30degree and 30degree for a total of 60
projection from the SP, now we can go back and reverse and find our SP.
Let’s do that.
We can do that in blue like we did before.
Now I’m going to take those same angles and I’m going to reverse it now from here
on the cone in here and go back toward the eye level.
Let me get my eye level in.
Eye level.
I’m going to reverse that same angle and go okay.
From this point, where does that go down from having this lined up where this edge of the
cone of vision is going straight down to the eye level.
That gives me where my VSP is, so I don’t have to do it the way we set up in the last
diagrams.
This is more of an applied method.
Ignore the fact that I did the horizon line.
The important thing actually is that I did the cone first, worked backwards with these
same degrees.
This would be 30 and this would be 30, a total of 60.
We just did the same.
That’s a 90.
That’s a 60degree angle there.
The important thing is you can work backwards and find your vertical station point.
There it is.
So, in red there is the vertical station point.
I’m going to have the man’s face here.
In red there is the vertical station point.
I’m going to have the man’s face here.
His little nose, mouth, ear, top of head, neck, collar.
There he is staring into the picture.
This is the distance of our SP.
This person is actually this far out.
If I take this distance and raise this rod like this, that’s how far out that person
is, the actual SP length out there.
That’s why the perspective works.
Anyway, we have this.
Now we need a 90degree relationship between the horizon line and the vertical
vanishing point.
In this case, let’s say I wanted to start with this verticality.
We’ll work backwards here.
I’m going to say in my cube I want this kind of vertical right here.
I’ll just add it on the front cube like we’ve done before.
That comes back down and lands about here.
Okay, so that I decided completely randomly let’s say in a viewing, I didn’t have
to have the vertical vanishing point here.
All I had was my cone and working back to my VSP, which I have to write in here.
Vertical station point.
The next choice was completely aesthetic.
I could say, yeah, I want that rate of diminishment, and I know I want my center of vision here.
Okay, that’s what I just did and I arrived at that vertical vanishing point.
Well, then I have to go up to from my vertical vanishing point up to my VSP and turn 90 degrees,
and that gives my horizon line in.
If I come right up here like this, here we go.
A true 90 degrees, and I go my horizon line, which I already put in early, but honestly
I should have started with a VVP.
It doesn’t matter.
You can start with a horizon line, come down, turn 90 and get your VVP.
I’d prefer to get the VVP first because that’s the thing that’s the exception
about threepoint is the verticality.
Now that I’ve got this relationship, now what do I do next?
I have all my verticality.
I have my cone of vision.
I understand where my VSP is.
I’ve done the relationship between the amount I’m looking down and my vertical vanishing
point.
I also have come back to the VSP and come straight up at 90 to get my horizon line.
I can also list my horizon line.
Now I’m going to take my cube and say, okay.
I’m going to do my right plane first.
I’m going to draw over here, and that creates my right vanishing point.
I’m going to go ahead and lead all the way to the horizon line and say, yeah, that randomly
creates the RVP because I just decided to do so.
Now, I already know I have my vertical vanishing point so I could guess at the side of the
cube if it wanted to and say, okay, there is a standing square, but I don’t know what
the proper relationship would be where the left vanishing point is.
It can’t be random anymore.
We have already gotten our center of vision point right here where the little man’s
head is.
We have already gotten our VVP.
That’s the second item that was random, and I randomly assigned the RVP on the horizon
because I wanted my plane facing this way and behaving that way.
That’s three.
I only get three out of four.
The missing element is the left vanishing point somewhere over here, but I have to use
that mechanical means again.
Well, that’s easy.
If I take my RVP through my center of vision point just like we did in our memorized triangular
setup, I come through, and then at 90 degrees from that line a projection from the VVP should
come up and cross that line at 90 degrees.
If I wanted to show what 90 really was, I would do this.
Line it up with the RVP at that point through the vertical vanishing point and extend it.
The result I get is this direction directly up at 90 degrees to this projection through
the RVP through the center of vision point striking through here.
Then at 90 degrees to that I get up and I find my left vanishing point.
Now I have everything I need.
What was random again?
SV, center of vision point based on where I wanted to start my cone.
The other thing that was random was the RVP and the VVP.
Even though I set the cone of vision and the VSP, the fact is I randomly chose how steep
I wanted the view and where that right vanishing point was.
Again, these three elements were already chosen.
This has to be a given because it’s out there.
According to the geometry, the correct geometry, that’s where the left vanishing point has
to be to be correct to view it like we see it with our eyes.
We’re still in the cone.
We’re going to get a little distortion getting near the edge of the cone.
Now, let’s draw on the left vanishing points, or, I should say, the left plane.
Take my guess at what that square is because we’re not measuring anything yet.
I’m just taking a guess.
Then I’m going to shore it up and finish it out.
There it is so I can do a little bit of the interior again if we want to be through and
transparent with our perspective, as they say.
Okay, right.
So, there it is.
Another stunning cube in threepoint, but the idea is we’re learning why the same
activity we were just doing in a more guesstimated perspective and learning threepoint, we can
now actually put more officially and get the correct answer every time about what the relationship
would be between the center of vision point, the vertical vanishing point, the cone of
vision, the VSP, and the two ground plane vanishing points.
This is correct perspective.
We haven’t measured yet to get true standing 45’s to prove that we have squares.
But all the vanishing points set up along with the center of vision point and our SP,
the position of us in front of the picture is all correct.
We’ve just done the first applied instant, or instance I should say.
We’ve done the first applied instance of actually doing a real applied working backwards
normally applied perspective setup.
We started with our image area first.
We could have just as easily had a frame in there.
We then automatically got our center of vision point crossing the center of vision line and
got our eye level.
We then made the cone, worked backwards to find our VSP.
Then we decided our vertical vanishing point or rate of diminishment for our verticals,
which set us a point, which we connected to the VSP.
Come back at 90, creates the horizon line.
Once we had the horizon line we know our vertical diminishment.
We then randomly chose our right diminishment by creating the planes leading to the RVP
which was random.
But then our left vanishing point could not be random because we’d already chosen our
three items out of four that could only be random.
We came across on the right vanishing point to strike this line at 90 degrees compared
to that projection.
When you have this line coming back and moving past you have to set a triangle up to go through
the vertical vanishing point at 90 and continue back up to the horizon line.
That gives you your left vanishing point.
It seems like a lot of work.
This stuff like a clutch car after two days will seem fairly automatic.
You just have to remember, if you want correct perspective that actually is how we see, except
we see in a smaller cone of vision.
We would be in about a 30degree cone instead of 60.
There wouldn’t seem to be any distortion whatsoever.
It would look just like we just see it, basically.
We’re going to work with a larger cone at first, just to bend it around and get a little
larger image areas and stuff.
So, we just did our first applied setup in threepoint.
We got our CV first and our eye level, everything we needed at our CV plane.
We got our cone.
We worked back to our VSP.
We set our VVP, vertical vanishing point.
That was able to project up the VSP and get a horizon line.
Then we randomly chose our RVP and then as a given we had to have an automatic setting
for the left vanishing point.
Okay, anyway, enough of that.
Try to look it over and, again, run this through as many times as you need to to try to visualize
why we’re looking at him creating threepoint.
Why does this flap work when it creates this flat area here?
This flap here is what comes up and is this to him.
To us, this distance comes up and is right up here.
Same thing that is happening to the viewer we can see.
Try to relate why these two or three ideas relate to each other, and you’ll start getting
why it’s so fast and easy to set up good threepoint even if you don’t want to measure
exact cubes.
You still have all the vanishing points and the center of vision correct in the VSP.
Okay?
Alright.
We’ll move on and kind of get a little more involved on doing a slightly applied version.
We’re going to do another applied version of some simple cubes, but we’re going to
start with a process that is a little more in the order you’d want if you were doing
a frame, or more important, kind of starting the area the cone wanted to be in.
Then we’ve got this idea again of we’re going to be looking down at a cube at this
basic 50degree angle.
This is our little person.
That’s true horizon.
That’s the vertical.
This is our drawing table or our piece of paper looking through to the cube.
It’s just the idea of getting used to what the side view with no perspective looks like
compared to what we’re doing here.
The more you can do that, in having the little threedimensional, threequarter angle version.
We had the old man looking through the table before.
You should start getting an idea of what we’re doing here when we’re looking down and we’re
looking up.
What I’m going to do is I’m going to start with my eye level and I’m going to start
with my crossing of my center of vision plane, which would marcate the area.
At least I knew I was going to do my thing.
We could start with a frame, but I’m going to hold off a frame.
I’m just going to deal with a cone.
We’ll get into framing and then the cone right around the frame.
One more time I just wanted to show some distortion and what distortion does within the cone.
I start with my eye level.
I’m going to label that.
I’m going to just intentionally put the center of vision plane right here.
Those are the most important things you can get going because that tells you where your
center of vision point is, obviously, where that is crossing.
What’s the size of the cone I want?
In my case, I want it about this big.
All I need is one mark to say I want my cone about that big centered around the center
of vision point.
I’ve got my eye level already, my center of vision plane, even my center of vision point.
Again, so I’ll work backwards in a little bit light blue.
That’s a 30degree angle of this triangle.
I’ll lay it flush against the eye level, the backside, and I’ll just line it up like that.
Coming back from here I’ll do it in blue.
It gives me my SP right there.
I’ll put in a little red VSP, and that’s our vertical station point.
Now I’m going to set my rate of distortion.
I’ll get my cone in first, but I forgot.
We only need one mark for the cone.
Just pick up our compass.
Mark that distance right there for the cone.
I’ll just start drawing around.
Here it is.
Cone is around here.
There is our cone.
I’ll set up the verticality.
If I set up the top corner of this cube tower I’m going to make or something, I’ll just—this
is you randomly deciding, okay, I think I like that vertical diminishment.
You could come outside with diminishment guides.
One way or another, you’re committing this.
I think that’s about the verticality I want.
I’m not concerned with the exact downangle.
I’m just kind of guesstimating.
It’s still pretty organic here.
But anyway, that first guess does come back and create the vertical vanishing point.
Now I’ve got that for sure.
I’ve already had my VSP, so of course I just run up a straight line to that.
Remember, and turn a 90degree corner.
If I turn a 90degree corner with my triangle from there, that mark with that 90degree
turn gives me my horizon line.
I’ve got to draw out my horizon line now.
I’ll just make one lone lineup here across there vertically.
You do this with a Tsquare.
I’ve kind of matched what I’ve done before, but however you get accurate 90degree relationships.
This also is, obviously, a 90degree relationship.
So, this is my horizon line, obviously.
Let me label that.
Look at it as having mountains and a little bit of sun or whatever.
We haven’t set our ground vanishing point directions.
We haven’t done that.
We’ve got all our verticality.
We understand the proper relationship of our eye level sunken below the horizon line.
All this setup is going fine.
Do I want to choose my right or my left diminishment?
Either way, maybe I’ll do my left first this time.
I’ll think about this original square I’m going to create.
Maybe I’ll do the left diminishment going out like this.
This is just kind of a random decision in your case.
I already have a plan, but in your case, you could be saying, nope.
There it is.
That makes our left vanishing point.
Now I’ve got to connect my vertical vanishing point to my left wall to make my wall.
There is my left wall.
Remember, the rule would be to get my right vanishing point.
I have to take a 90degree angle directly from my left wall, in this case, through the
center of vision point right here in order to properly determine where that random, I’m
sorry, given vanishing point is.
We’ve done our center of vision point, our vertical VP.
We’ve done the cone and the VSP, and we also randomly chose the direction we wanted
to lead to for our left vanishing point.
The right one is not an option.
We have to get correct perspective.
Go at a 90degree angle from the wall through the vertical vanishing point up to our right
vanishing point.
So now, because of that 90degree relationship, we have our right vanishing point.
Then I will make a triangulated close out here.
There we go.
That’s pretty much how we’re doing it formally.
I know it’s a pain, but you just keep memorizing the same routine.
Again, you can do tiny little ones on your own.
Don’t just wait around for me to do it.
You should be doing lots of little ones on your own.
Now I’m going to create a square, still guesstimated squares on the ground here, so
let’s do that.
I think my original square I want right here.
As I recall, I’ll create a square to my right vanishing point, left vanishing point.
This is just an estimated square on my part for my first square.
Then I’m going to project and do some diminishment guides back like this.
Then I’m going to cross my square this way from my left plane as well.
Then we can start building a square tower here.
Here is the distance I had from my bottom corner, my top corner, so I’m going to go
ahead and draw those out as well.
Again, you’re just estimating your first square within here for
your proper vanishing points.
Now I’m gauging what is my first square.
I’m going to guesstimate through my square wall here, and I can do a little wall above
or below that.
Then I’m going to close out the other one here as my guesstimation.
I’ll have a little bit of a wall go above it.
There is my first square.
I’ll close the top of that out like that.
Now, if I want to add another square tower on, another tower cube, I want to X off this
and go through the middle like we would with traditional X’ng and doubling and X’ng
and quartering, so I’ll go ahead and put an Xmarksthespot middle part.
I’ll probably do that in red.
Okay, so now we’re going to start getting into the stuff we were just doing in the last
series in one and twopoint perspective.
We’re going to find the middle, and that gives us a reference point on the bottom and
the top we can use.
So now I simply go through the kitty corner, through the middle spot, and that gives me—that’s
how fast the cone of vision stretches this puppy.
Here is our second correct square based on my first.
My first might have been a little tall or short, but also you’re clearly seeing the
effect of the distortion if you’re using the entire cone.
Most likely you’ll want to use an inset frame well inside the cone if you want no
distortion, certainly the way I would do illustrations and stuff if I wanted.
But, if some people really want it kind of inyourface and starting to do that, you
can use the cone as much as you want or even a little outside the cone.
It’s all up to you, but a lot of people get a little mystified by the fact that, yeah,
why does it not look like a cube anymore?
It’s because it’s being pulled out past us in distortion.
Also, I’ll go from this top corner through this reference point again to get the distance
from the bottom cube.
Remember, we’re just doing the same old stuff we were in the lecture series before.
There is that.
So now that makes perfect sense.
Look at how foreshortened that is.
So there is that cube getting really foreshortened, shorter and shorter
according to that X’ng method.
I’ll close off the other square, come up to the wall.
So now we can also repeat squares forward and back if we want from this middle square,
so we’ll do that.
I’m just doing this drawing repetition here, so I’m going to take this plane out in front.
Let’s use our same X we did before.
Find the middle.
We can just X off and double and triple stuff if we wish.
Probably a little bit higher than that.
We’ll just start doubling the bottom corner up to here.
That would be the next one.
Double that.
Same methods we use in the last one.
Still coming up.
Double over in that.
You’re seeing where that is.
Right over there.
You’re starting to see how distortion affects everything.
There is the last thing, according to that.
How narrow those get, and let’s see how long these get going out toward the cone here.
Let me get the bottom corner here.
I’m going through to meet this plane here.
That’s kind of frightening.
All it does is get way long.
Basically, there is the next vertical vanishing point.
That’s the answer we get from the next box actually here.
It seems kind of unbelievable.
Here is our initial square cube here, and just by X’ng, putting a double line through,
through horizontally and vertical; doubling, doubling, doubling; we get back, and we get
these narrower and narrower.
Squeeze here once we get out of the cone.
Already just our second cube, excuse me, or square side is that.
We finish that cube off as well going to the left.
You can still work outside the cone, but it’s going to look fairly clown like.
There it is.
I’ll go ahead and finish off all the other ones, too, remember, that we just found.
There is the back of that, like a train car kind of idea going across.
There they are.
Then we can finish off our top square, which is also in distortion, but I’ll go ahead
and figure that out or finish that off.
There we go.
Again, you do it at your own pace, but you’re doubling over these just like we would in
the X’ng and doubling method, and you can also be halving and quartering the square
at the same time.
Look at how much pull this gets when it’s just outside near the cone.
It gets very distorted when it’s outside the cone.
But, even by the time you get out here it starts to pull, pull more, pull more.
Essentially, again, if you want fairly conservative perspective, you’re pretty much putting
your fame within almost half of the cone, traditionally, instead of going all the way
out here.
It would be almost just in half.
If you have traditional frames you can float them around in a much smaller area within
the cone or in vice versa.
The vanishing points are much further away.
You’ll get a lot less distortion.
This is a good idea, how it distorts.
This is the first square, second square and tower put on top of that.
It gets that tall and that pulled that fast.
Then the third one starts getting squashed, and we could go through and do even one more
like that going through.
That would be that last square in the bottom there if we wanted to show a real foreshortened
version there.
That’s the idea.
We’re actively showing why distortion, how distortion affects it so you’re basically—if
you’re saying, yeah, I like it up to about that point.
There is a little bit of sauce or spice in this, but this gets ridiculous.
Make sure you work your framing a good deal within the cone of vision.
That’s the traditional cone of vision.
Or, you can just give yourself half of that cone that would be a 30degree cone projected
out at 15 degrees and 15 degrees.
This still is a traditional cone.
Let me mark sure I mark those and label those properly.
That’s 30 degrees, 30 degrees just like we’ve been memorizing for a total of 60.
The downangle is also this 50degree downangle we can actually measure like that, because
that’s the actual amount of angle from this plane down to the eye level.
That’s how you determine that.
We’ll do more of that and measure the degree of that as we get into subsequent diagrams.
That way you get in an exact amount of down or up angle based on this, basically a protractor,
which is right here.
We’ll be actually measuring the degree of angle in some cases from the VSP of the actual
down or up angle of the bird’s eye and worm’s eye.
So, there we go.
Again, this is more of applied idea of how to work from the cone of vision out to get
the VSP.
We’ve got our rate of diminishment for the verticals.
We came back, found our horizon line.
It shows the left vanishing point first.
Then we worked the, pushed through the 90 back to here and was able to find the right
one by making the 90degree turn on this wall.
So, just memorize what we did here.
It’s listed right there.
Yeah, again, these are the critical ones.
If you work them you’ll understand basically if you can set up the triangle and understand
how the perspective gets weird, we’ll move on and try to get some 45degree reference
points to get out, to be able to measure squares more accurately and fairly quickly.
We’ll still keep doing this kind of activity for a little bit.
Alright, so a quick review of what we did.
We covered threepoint as far as why is it different than one and threepoint, and we
kind of memorized the triangulation and why what used to be straight vertically has now
crimped down and came down toward the center of vision plane
and become the vertical vanishing point.
Also, that works when we’re looking up in bird’s eye.
Then we just are memorizing why the operation of the triangle and the foremost important
elements work together.
Again, those elements are the left vanishing point, the right vanishing point, the vertical
vanishing point, and the center of vision point.
Those four items are critical as to why we actually see the way we do in threepoint
when we look down or up into the world.
And so, memorizing how to set those properly in relation to each other in the triangle
is what we have to do in order to do the more applied version where we start with the frame
and the cone of vision, work backwards to the VSP, the vertical station point, and then
randomly we can choose our vertical vanishing point and our horizon.
After that we get one choice of either our right ground plane or our left ground plane.
After that, the last choice is a given.
It has to be where it is in order to be in correct perspective.
Our main emphasis of the entire scene is really about that.
Okay, so keep memorizing it.
Keep playing these back over and over until you think you’ve memorized the process.
You’ll find the following material even easier to understand, both applied and formal.
Okay?
Hang in here.
Do the work, and we’ll see you in the next diagrams.
Okay, now that you’ve been through the basic introduction to threepoint, obviously we
want to have practiced why, just in a basic manner, looking down and looking up works.
How did the two side walls that used to be above and below the twopoint vanishing points
converge to become the vertical vanishing point on the center of vision?
That’s the clearest difference in threepoint when we look down or up and our picture plane
is at a tilt.
After that, we started practicing many versions of how do we memorize the crossing relationships
of 90 degrees that the two ground plane vanishing points have with
the two side walls on their opposites.
All these things are critical to understanding the geometry that happens when we look in
threepoint perspective through a picture plane.
You should memorize those ideas where you’re particularly learning why the threepoint
triangle has all these correct relationships.
Only three of the four elements we want to find can be random.
The fourth has to be a given.
The four items, as you know, are the left vanishing point, right vanishing point, the
vertical vanishing point, and the center of vision point, where the cone is centered and
our view is centered.
Only three of those can be found randomly.
The fourth element of any of those elements can only be a given or an automatic.
After that, we’re adding the cone of vision, which is even more important for distortion.
How do we add the proper vertical station point and get through to understand where
the cone is so we can control our distortion.
That’s also critical learning that we should have gotten through and you should memorize.
So, hopefully, you’re all set with that stuff, and you can move on to do more scenes
now with some intermediate perspective.
Okay, so let’s get on it.
Free to try
Watch the whole lesson with a subscription

29m 25s
2. Introduction to 3Point Perspective and How it Differs from 1 and 2 Point 
18m 11s
3. Cubes in 3Point: Shallow and Steep Bird's Eye Views 
16m 57s
4. Cubes in 3Point: Shallow and Steep Worm's Eye Views 
16m 23s
5. Looking at the Top of a Building from Various of AnglesofView 
13m 36s
6. Critical Elements: Left, Right, and Vertical Vanishing Point + Center of Vision Point 
17m 12s
7. Plotting the Vertical Station Point for an Understanding of Distortion 
17m 30s
8. Man at Drafting Table: Conceptualizing the Elements of 3Point Perspective 
19m 0s
9. Applied 3Point Perspective Demonstration and Review
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