Alright, so let's take
everything that we have been doing up to this point and put it all
together. So in front of us we have a number of geometric
objects, all of which we have worked from individually
but now they're in a contained, singular environment.

Let's see how all of the principles that we have
been talking about apply
when these objects interact.
Okay.
So what we need to do is
begin in a way that we haven't
really experimented with up to this point.
We need to establish the general composition,
the placement, of all of these objects on the page.
And the important thing here is that we're also including the
surface that they're on as an important
element of the general
composition. So
kind of just try
to get the general placement of the outer edges of everything.
So you want to use as much of the page as
possible without making the objects look enormous.
So,
this will obviously
keep moving and changing as we get more and more
precise. So
and as you start to place these objects, begin to think about
not just the proportions -
proportions within
each geometric form. We're beginning to get a general placement.
Not everything is right
but it's heading in the right direction. As you see I'm not
using my knitting needles, I'm not -
I'm going to be using them to make certain corrections
later. See so I'm just laying everything out.
Where I can see a - where I can see,
sort of begin to get the structure in like this close edge
of the cube I do it. In the case of the
nonagon, the nonagonal prism,
it's at the moment simply rectangular in order to just find its placement
and its proportions. Okay
so I now think it's time to make a few -
take some proportional measurements, some angles,
to just establish where things are. So I'm going to go
from the back of our cylinder to
the top left corner of the
nonagon and see what that angle is. Am I close?
I transfer.
That seems good. I
am looking at what I drew. I'm a little skeptical
about
the amount of space I have here in relation to the ellipse, to the opening
of the ellipse. So, if you're skeptical, then
all you need to do is take a measurement. So here I'm doing a proportional one. I'm
going - I can show you on the page. I'm gonna go from here and see the amount of times
it moves - it fits into the side as I move over.
It's -
it should hit
that mark. And it does.
Okay. Not so bad
for a start. So the important thing is also
to see the relationship of the
corners. Like where does the ellipse end? You can see the
cylinder is I think in
relation to the sphere is good but you can see that
you actually still see a little bit of the top plane
before the edge of the cube. So this is important. This is important
for placement. And then
so this allows
me to get this angle off of that. I think that
angle is closer to what is actually happening.
Just by
eye, I think that this side of the cube, I've opened it up a bit too much. It's too
long. So I'm gonna bring it in and then I'm gonna take a measurement. And this time
I'll take this measurement with my pencil.
I'm going from here to here and then I'm moving it over and seeing how many times it fits into
that side.
It should hit to about that point.
We go from there. Hm.
So I think
that this can be smaller in order to get this
into there. Okay, so -
but at the same time, the relationship
of this edge to
our cylinder as well as our sphere
seems correct.
So this
actually becomes even smaller. So you go
(drawing)
from one part of an object to another part of an object but you can also
take one object and compare it to another one. So for example right now,
I would like to take the measurement of the sphere
on our page currently just a circle and
I'm gonna take it and compare it to the height. So the width of the sphere, or the height,
in terms of the sphere it doesn't matter - and I'm gonna compare it to the height
of this closest edge.
And as you see, I started by - oh it's exactly the same.
It's exactly the same. So we go from here
to here. Excellent.
So I just have to establish which
one is correct. So the size of the
sphere in relation to the cylinder but
in my case, this edge seems a little bit small. So I'm
actually going to take the height of the ellipse and see the amount of times
it fits into this nearest edge of the
cube. And it seems
like it's going in one and a quarter times. That's one
and it's a little less than a quarter I think. So let's bring
this down. If we bring it down then it actually evens out
with what the height of our sphere is. So
as you see, I move within an object and then I move out
to compare one object to another.
And I'm not starting
out by taking any measurements, I am
using them to correct
my
sort of observational skills. And that's the only
way that
they improve. Okay so
here I just place that line in relation to the upper one.
The upper edge, according to the principles that we
discussed that these lines, have to
converge into a vanishing point
along the horizon. What we have here is
that we have to follow that line all the way
to the other side so that we don't confuse the edge of
this upper edge of the cube with the angle of our cylinder.
Because they are oriented in space differently.
There we have
that. Now we can get a little
more clarity on our sphere.
And
remember to
always take the axis of the ellipse. Seems
alright. That is the axis of the ellipse. If you
want to be even more precise then you can of course construct
a rectangular prism around
the ellipse and find
how it is angled in relation to
everything else. In relation to our cube
primarily. But I'm going to
go with what I have.
(drawing)
Here I'm going to look for the angle -
I'm going to use my pencil and my needle. My needle's the constant,
the pencil is the angle of the top of the
cylinder. The side of the
cylinder that's to the top. And make sure that this line is correct, it was.
And here we go. And then here,
before we move on we need to continue with the top plane
of the cube and lock it in place.
And see it all the way through.
(drawing)
Alright. It's coming to life.
So here's what we - we have this, we can
wrap this up a little bit to get these cylinders
or the back to read properly. Move this
lower edge that we can really see what's
happening there. They have to slightly converge
but not too much, we don't want to have any strong exaggerations
of our perspective. There are times when we do need them, or you just simply want them.
And we will talk about
them when we encounter them.
Okay so now, the group of objects here I think is
alright. It's in place, proportions of each
object to itself are fine. The relationship
of one object to the other is fine. And now
we need to start
on the nonagon. And
here you're actually going to be taking a proportional
measurement of the nonagon
and the empty
space between the
nonagon and the sphere as well as between
the nonagon and the cube. So I'm
just gonna start with that empty, also known as negative
space, and I'm gonna compare it to the entire
width of the nonagon. And I'm just gonna
to look for a measurement that's easy to use.
I'm kind of seeing that the space
between the outer most point of the cube and the nonagon is exactly
half the
diameter of our cube. And if you recall,
that's the same distance as this edge. So half of this edge also.
Alright. So this line.
is the correct one. Now if I recall correctly, I think
the nonagon, along with some of the cylinders
we were using,
the proportion of its width to its height is about one and a half.
That seems to be a recurring measurement in our
shapes.
So it's one and a half to the
closest
part of the top plane.
So we could take
a measurement there but we could also take some angles. So for example, we could go from -
we can go from the
bottom, the base if you can call it that, of our
sphere and see where the closest
point of the nonagon is. I'll use my pencil as a
constant, it's just in my hand.
(measuring)
And that's
right. That's about right. And now that we have that point
it's the half - it seems to be exactly half way
into the shape. Our shape,
not our form yet. And then we take the width
and it is exactly one and a half to the closest
part of the top plane.
So we have some experience with the nonagon
so let's begin by
seeing where that closest edge is in relation to the two
sides. I see it as
a little bit closer to the right side
so it's not exactly in the middle. So have your center
line, have your axis,
and it'll be - it's not
enough to really worry about something too precise of a measurement
but it's gonna be slighty to the right of your center
axis. We could, of course,
get a central axis for our
cylinder as well for the sake of consistency.
So here we are with this edge.
So I'm going to just place this edge and begin - and we know
that this is the closest point.
And so we can begin
by structuring some of the planes.
We've already - we already have some experience with this.
These are the planes that we can see. Of course if you
have any
questions just consult your
tools that we use for correcting
our measurements, for establishing our measurements, for taking our angles.
(drawing)
Okay.
So now we go up from here.
I would also
(drawing)
just get these facets
because they'll help us a lot, as we remember, in establishing
that there are in fact nine sides to the shape.
(drawing)
So the other thing I do want to talk about and I will keep talking about it is that
in my experience as a
an instructor, I often see
students
in classrooms
be rather hesitant in placing a line. So I see a number
of things. There's this kind of
line that I've seen, I've seen
that kind of line - and this goes on for
forever. So the one right here, that's kind of a hairy line.
I would avoid it
at all costs. I don't think it's helpful.
The kind of approximation of a line where you start with a line but then you keep going
over it, this helps at times to get a clean
curve, can be useful
in order to establish that clean curve, to get a general angle
and as you can see I've used that in some place myself. But what I recommend
more than anything else is to look at a line,
think about it, and then put that line
in place. Because the problem
with one of these is that you're still gonna have to go back and see
is that the line that I was intending, is that the line, is it somewhere inside,
is it on the other edge of it?
And obviously you can cut into this and
at times you don't need to be as
precise as that. But if you can see, when you just have a single
line and then you look, compare,
you transfer an angle, think about it, it's so much easier
to correct. Because a single line is there, that's all you
see. So for example, I know that that line is
wrong, it has to be like that. So then, all you do
is - so it's easier to correct a single line than it is to correct
a million of them. So
that was an aside
but I just wanted to touch on that.
(drawing)
And there's -
I went from point to point to just compare them. I'm gonna go
from point to point here a little bit too and just see where that is.
Then from here
to about right here is that plane
and then we connect the remaining ones that we have.
So, in order to make sure this is a nonagon,
a nine-sided
prism.
(drawing)
One, two, three, four, five, six, seven, eight, nine. We're good.
Okay, so now let's
get a little bit more clarity on our ellipses.
On our cylinder.
The front and the back.
(drawing)
And have it wrap, right, and have it wrap. And if you
even have it continue all the way into the form
as if it's completely
transparent. Now you're able to do the same thing with a
nonagon actually because now that we have all of our corners
you're able to do the exact same
thing over there if you were interested in making everything look as transparent
as possible.You can just
take this line all the way here
And remember that that line and the one that - and this
line right here have to converge into a vanishing point
at some point along the horizon.
And what we have, at least from my angle, the horizon - actually
it's not going to be about right here. We're not going to
be structuring anything off of the horizon in this exercise.
(drawing)
And then we get
a little more definition on
our
sphere. At this point it's still a circle.
(drawing)
Okay. So here we have
the general placement
of our objects. So you see that I've started with some of the
construction lines here, thinking of these objects as if they were
essentially made of glass. As if they were
completely transparent. So let's just continue
with all of that
for the sake of consistency. Okay so
we have - we've placed the
plane here and so let's just do
the same with all of the planes, all of the facets
of the nonagon. And just take them
all the way, look at
the angle that you have here. Remember that one's
pretty much parallel but slightly converging upwards because if you recall
the upper
planes are always
flatter because they're closer to our horizon line.
So then we can continue with that plane right
there. Here - and also
remember when a plane is practically horizontal,
you're not going to see as much conversion
into point. And then we're going to take this one
right here
Take it all the way down. We have this one right here
and we have that one.
That's one corner.
(drawing)
And then everything else is already connected for you, you already have the points.
Okay, so
now we have a transparent nonagon, we can see all of its facets.
But just going to accentuate
the ones that are actually in front, the ones that we can see, to differentiate
it between the ones that we invented - the ones that we
have invented based on our understanding of the form
and the ones that are clearly
in front of us.
(drawing)
And the left edge.
(drawing)
And we're gonna do a similar thing with the top. And for this
I glance a little bit at the actual
nonagon to keep comparing things to what
we actually have in front of us.
Okay.
And since we already have
our cylinder -
since we already have our cylinder
transparent, let's just complete this
by figuring out where the other side of our cube is.
The edge across from this one.
And here
just take it all the way into
our sphere and take this
and just cut into our cylinder.
We have this line, we have that line. This actually might need to go up
slightly more from this edge. You take it all the way.
And then you have everything you need. That line, this line,
slightly converging, not too much, and you connect
these points. So from this point you can just extend
upwards
and then make your connection with
that plane and that plane.
(drawing)
We don't need to do - I mean we don't need to - there aren't any edges
or corners in -
we've gone from shapes on a page
to three dimensional structures on a page without the use
of shadows or tone. Now it's time to move onto that.

So now that we have some forms in place on our page, let's
apply what we have learned about shadows.
So, always begin
with the object that's closest to your source of light.
In our case, it can be
located as the cube.
Remember that the terminator is the edge,
so let's begin by just finding all
of the terminator.
And
after it's in place,
just find the outline of the cast
shadow.
And
you have a number of options. You can, of course, begin to tone this away
into a shadow in order
to help you see where it is, but I'm just going
to establish our terminators here. Now
if you recall, because this is a
much more continuous curvature, I
spoke to you about
placing a terminator with
a bit of a tone to begin with in order to establish
the like particular quality and amplitude
of the curvature of a form. As you
place these shadows
you can begin to remove some of those
construction lines
at the -
after you place these shadows you can
begin to remove some of those construction
lines that
we placed in order to better understand our forms.
(drawing)
So now we have a little bit of a terminator here
and
we don't see any cast shadows.
The cast shadow is actually going to be
on this part of the cube, but it will
combine with the core shadow on the cube
and you do see a little bit of -
you see a line for the cast
shadow from this entire group of objects
on the surface of our table. Now
before we continue, we need to
actually find the line for our table and just take it - and here's
one of the places where you can actually see it - and take it all the way across.
(drawing)
And at this point
I would ignore the actual -
like the size of
our table. So from my view
I see a smaller amount here and I will
just place a few lines to
evenly place all the objects on top of our
surface. I wouldn't worry
too much about where the closest edge of the table is, you can just hint at it
for clarity. Okay.
So let's move on to the terminator on
our sphere. You can -
you can take the proportional
measurement to see the amount of space it takes up along
the perpendicular axis of
that terminator. So for this, hold one of the needles up
at around the angle of the terminator and place the other
at a 90 degree angle
so that you can get a perpendicular -
a line that's perpendicular to our terminator, which will
give you the axis
here that we can use to take a
proportional measurement.
And
I had it wrong, it's actually a little more horizontal.
(drawing)
And then once that's in place
all you have to do
is take an angle and see where it is.
But also after placing it,
I would take a proportional
measurement along that axis and I'm seeing that it's
along that line, just slightly
to the left
of the halfway point.
But as we spoke about earlier,
I would almost right away begin placing
that terminator with a hatch or a flat
area of tone to
immediately begin to signify that this is
a curved surface.
And
by doing so, you are anticipating
the
soft turn out from the terminator into our core shadow and
a soft turn out into our dark half tones.
And here
let's establish that cast shadow.
(drawing)
If you recall you can't actually connect your terminator
on a sphere with the cast shadow on the surface
that it's on because of the angle of
our light. So
because of that angle,
the cast shadow is
going to be -
the cast shadow is going to be projected
onto the surface of the table
because the
only tangent with the table -
the only tangent the sphere has with the table is at a single point
at the very bottom. So here
we have a situation that's slightly more confusing. And the reason for this
is is that only place you actually see a terminator
is up top here because
the - almost the entirety of the nonagon
is being hit by a cast shadow
from this group of objects. So in this case,
it's particularly important to get that line of the
cast shadow and see how it - the angles on it are changing
depending on what the
surface that they're on.
And this'll be extremely important because you'll be able to use
cast shadows in order to describe
the structure of a form.
(drawing)
Okay.
So now that
everything's in place, let's begin with our
shading. So, once again, we will begin
with the closest object
and
at the moment I wouldn't worry about any
variations within the shadow. I would -
all you need to do is find a flat -
a flat area
of tone that'll be pretty much even all the way across.
The whole point here is to not exactly
copy all of the things that are happening
on the object, but to
make sure it looks convincing enough. And the only way that'll happen
is if we apply or understand
of shadows. So here I'm going to -
I'm pushing the
marks I made into
the texture of the paper a little bit to get
a smoother
tone.
See so I'm
only - I'm working only on
the surface of the cube
right now.
(drawing)
So after we place a tone
you can go back over
in order to
get a more even placement.
And then, remember that our cast shadows
have to be a darker value than our core shadows. Now, in front of us
that's very obvious. But a part of that comes from the fact that
the objects are on a black piece of cloth. So the color
is affecting
the tone. And for our purposes
we're going to ignore this.
(drawing)
As long as that is clear,
use the eraser to get a sharper edge.
Okay
so that's in place currently. Now let's move on
to our cylinder.
And let's just
extend out from that terminator -
extend out into our at first our core shadow
occupying
this area on top and our area of reflected light
which is at the bottom. At the moment, as we did
before, we don't want too much variation
between the two, we just need
to start with the tone in place.
(drawing)
Integrate it a little more with the paper
(drawing)
and clean up your edges.
And the -
once that's in place
keep in mind of course that this edge here
is also a terminator but a sharp line,
a clear, sharp line because of the sharpness of the edge. And then here
underneath the cylinder we're going to have a
cast shadow that falls from our cylinder
onto the top plane of our cube.
(drawing)
So we
have an area for the terminator that you can see is a little bit
darker than the rest of our shadow and we could expand on that
as we
sort of come down our core shadow a little bit.
And you see that if you get a tone over the
entirety of the area of shadow and then just -
and then
tone down your
core shadow then
this whole area begins to read like reflected light.
Because it's a lighter value.
Okay. Let's move on to our sphere.
So the same thing, I will begin with -
I will begin with
the core shadow coming off of the terminator.
(drawing)
And you can see I'm not doing anything in the half tones at the moment
except
with the hatch I'm slightly - I'm, in a sense
I'm planning ahead for the half tones to come. But we're not concerned with them just
yet.
And all of our shadows
are going to be
pretty much the same value.
Remember that you have to think of your shadows
as within - as all within the
serve a singular tonal range in relation to our lights.
(drawing)
Integrate it with the paper a little more so that we don't have
such clear, obvious marks. And then go back over it, but now
you can push the
terminator a little bit and the
cast shadows that follow.
I'm sorry, the core
shadow coming off of it.
(drawing)
And I'm not - I'm gonna just add a little bit to the
general curve of that terminator
and then go back over it. See in here in order to get
a clear hatch, all you have to do is
sort of is tilt up the angle of your pencil.
(drawing)
And now I'm going to hatch the other way a little bit.
(drawing)
Okay, so here's what we have at this point.
(drawing)
I'm going to clean up
some of these edges, make them a little more obvious. The outer edges of our
forms.
Our geometric solids.
And now it's time to
place our cast shadow, which is going to be
a darker tone in order to lock in
our reflected light.
And
remember that you really only have to push
the tone of the shadow
as it's right up against the object in order to
really lock in that reflected light
in between your terminator, core shadow, and -
core shadow and cast shadow.
Even here you might not need to be
as dark as you are here at the very
base, the very -
of the
sphere.
And then just
extend this outwards.
And as you move out, the edge will become softer.
(drawing)
And
I would just - in here. And so
because we have understood
this entire part of the nonagon is
in a cast shadow
then just continue the cast shadow that you have on the
surface of the table into
(drawing)
the nonagon without
worrying too much about
differentiating between the different
tonality as
the planes change, which is kind of
one even
tone.
So when we were working on this
before individually, we were
analyzing each individual plane.
But right now, we're just
thinking of the shadow as a group. So even here
this is our plane of the core shadow
let's just get a tone that's a nice, flat
even tone and disregard
(drawing)
the variations within the shadow right away.
(drawing)
And here
this is all in a cast shadow so we can - just
as long as you can still see your lines,
we're good.
(drawing)
And then kind of even it out a little bit.
(drawing)
Okay. So now
it's time
to begin to differentiate within the shadows. But keep in mind
that this will of course keep changing once we get
to the half tones. Because if you
recall the more that you add,
the more you will have to step back and reevaluate the entire
tonal
situation.
Okay so
let's go to the
cylinder. And let's make sure that the terminator
and our core shadow read clearly
separate
from our reflected light.
So
a lot of what we're doing now
is based on our understanding of shadows
and the practice that we've had with them.
And we're going to have a slighty
darker area coming off of this edge also.
So our area
of reflected light is primarily here.
(drawing)
Get that
edge and keep in mind that you can always go back in and make corrections.
(drawing)
Now here you have your reflected light
but if you recall on the
soccer ball, on the planes that were
turned all the way away from
our light, turned towards our -
the surface of our table, there was something that I mentioned
in brief known as an occlusion shadow,
a place where the smallest amount of light hits.
I also said that we're going to ignore it.
Now you do want to use it in some instances and we are
going to work with some of the
occlusion shadows
(drawing)
but we're not going to concern ourselves with them at this point,
in this part of our -
in this part
of our drawing.
Right now it's important to
establish our terminators, our core shadows, and our cast shadows.
(drawing)
Okay so that's beginning to happen.
So here is another instance
of - here we'll actually have to observe what's happening with
our - so actually
speaking of occlusion shadows, we're actually going
to have to use a few when we get to our -
that surface of the cube. And
you can see that there's a large area of
reflected light because it's reflecting off of
the surface of our sphere. And then
as we get - as we turn back around
our sphere, there isn't
as much light being reflected in. So
the darkness that you see here in relation to our reflected light here
would be part of that occlusion shadow.
So we'll go with.
(drawing)
So
what you need a lot of the time is to get your reflected light
to read as reflected light is not to
erase out of your shadows to establish that
tonal differentiation but to actually just simply
tone down around them. So here we have
the darker area coming off of this edge.
So we're going to keep the initial
tone as our tone of the reflected light.
And then here we have our major areas of reflection
and here they are not as strong
towards the bottom.
(drawing)
You see so it's beginning -
this areas beginning to read like reflected light. And we don't want to
emphasize our reflected lights. It just has to be slightly lighter than
the areas around it.
(drawing)
And then make sure your cast shadow reads darker.
And possibly a little bit
sharper as it nears the
terminator. Now, in a sense you want to keep your terminator the darkest
point because it's also the closest point.
(drawing)
And I'm just gonna go over this and
as we go you might wanna
get a little bit of clarity on the
sphere itself using the shadows around it
to get a clear, clean edge.
(drawing)
Here we have an area of
reflected light that's also coming off of the surface
of our sphere. So we're going to get
that to work by making the area around it darker.
(drawing)
Get a clean, sharp
edge to it, either with a line or by
erasing a nice, clear, clean edge.
So as you see we are sort of taking relative
values. We're not transferring the exact
values that we see in front of us.
The idea here is to be in control
of our light.
And not the other way around. Here
even for the purpose for effect - and that's sort of happening -
we can tone down this shadow
to
bring up closer to us this
edge of the ellipse of the open surface
of the cylinder that we see. Here
(drawing)
and here once again, I'm just going to
sort of work off of that edge
our terminator and
this right now is clearly reading
like a reflected light. And yet it's still part
of our shadows. Now I
am not aware if we're going to have to go back and tone down
our reflected light once we place our half tones
but that is a possibility and happens more often than
not. But
we'll get there.
Okay so here we have
a little more clarity and a little more variation within the shadows
in our
cube and our cylinder. Let's
move on and do a little bit more of that with our sphere.
And
we'll, as always, begin working from your terminators
and establish that soft
gradation into
your
core shadow and
reflected light.
And then -
and then simply by comparing to
the reflected light that we already have established in our other objects,
I have a feeling that what we have on the sphere is going to be a little too light.
(drawing)
And also
you have to keep thinking about which object is closest
to you. And emphasizing that. So even
if we don't really see ,
though I would say that's there, that the terminator
on the sphere is
a darker value than this edge, it makes
a sense to push that tonal
difference just a bit just to make it appear
a little closer. Just to emphasize it a little more.
And we're going to be talking a lot more about
that sort of emphasis of objects -
about parts of objects that are closer
to the viewer than those that are farther away
during the entire course.
(drawing)
So what we need to hear - we have a little bit of that
occlusion that I was talking about so we're not going to worry about it too much here
but we need, more than anything else,
is to make it clear that what we have right here
is our
cast shadow. And it's a darker value
and what we have right here is our reflected light.
Because of the occlusion it's not going to be as bright as, say, some of the reflected light
that we have here. So we need to
start worry about that right now. And then
here you can see that there's this entire area of reflected light
and essentially we're just going to need to
show it as much as possible
with
our core shadow and the cast shadow behind it.
So we can extend our core shadow. It's obviously
already catching a little more reflected light and so it's not going to be
as dark as the immediate core shadows coming off of
our terminator.
And always
keep, you know, keep stepping away to kind of
view all the relationships at once.
And then get back to it.
And now we're gonna need some of this,
some of the tones around this, just to push that cast shadow
a little bit. And as you see, we're beginning to
pull out without actually working on them, our reflected
lights.
(drawing)
Just gotta clean this up a little bit.
(drawing)
Okay.
I feel like our terminator needs one more pass.
(drawing)
Also for the sake of
clarity, I'm going to start removing even
more of our construction lines.
(drawing)
And just slightly establish a
little bit more of our - the darker half tones coming off on the
the
terminator on the sphere simply to now -
simply to not have too sharp of an edge and to kind of
give us a little bit of -
to sort of start
the process of the half tones before we actually begin them.
You always want - and
something on the paper to imply
what's going to be
happening in the process.
So it's kind of as if
you're just sort of putting
a mark on the paper that is
allowing you to
pick up from where you left off, assuming that you
(drawing)
step away and come back after some time.
(drawing)
Okay. So
we have a little bit more happening on our
sphere. We're going to
polish up all those curvatures like these
softer curves of the terminator
as we begin working on our half tones. But
before we get to that, let's talk about
and let's spend some time on the nonagon.
Okay so now it's time
to differentiate a little bit more between the
planes of our nonagon.
So let's begin, as always, with our
core shadow plane. And we need to make sure that
is properly
dark
and heavy enough to read as a core shadow.
(drawing)
And here I'm going to remove some of these construction lines
because I want - I'm focusing on my shadows.
And as you remove them and as the shadows begin to appear the objects begin to
appear a lot more solid.
(drawing)
So just - I'm working with that plane and
so I'm not too concerned with that cast shadow just yet. I just want
to get this core shadow plane and the reflected light plane
as clear as possible.
(drawing)
And the reflected light plane, at this point, just in
relation to the reflected lights that we already have, I think
is at a good place. Maybe it just needs a little bit of a tone over it.
Just kind of
make it a little more even.
(drawing)
Let's clean up these edges
and then emphasize this
part of the core shadow plane and
the terminator line as it comes off of
this plane right here that's catching a lot of light.
(drawing)
Okay. And now we can
differentiate a little between
these two planes. So, I see
that this one right here that's sort of turned
towards this area that is in
a general cast shadow is not catching as much light as this plane here.
So we did mention it in brief but
of course your cast shadows can also
have interference.
So they will, essentially, be - they will act a lot like the
reflected light. The plane of the reflected light. Because they're
catching reflected light. I know it can get a little confusing
but I think
my point is coming across.
And so what we have
right now is some
differentiation within these
areas but I'm not sure we need as much as we currently have. So you still
want to for the cast shadows to read a little
more evenly. See as
I'm doing this I'm actually accomplishing a few things.
I kind of moved into the plane here, which
allowed me to tone down all of the
these relationships as opposed to just
a single plane and then working on all the other
ones in order to adjust them. Here
I already made that a little bit darker, which is going to be
quite helpful.
(drawing)
So it's actually - in essence it's
hard to differentiate
between what we have here and what we have here. Because all of this
is in a cast shadow.
Except the only part that actually is in a cast shadow
is here because if we were to remove these objects this whole part would be
in light while this whole part
would be in shadow regardless because of the form.
But
you're always sort of balancing
between variations
within a shadow and always keep in mind that you have to keep
all of your areas of shadows like in -
like within an object and also in all the objects
consistent in one tonal range.
But, as we also spoke about earlier,
this is easy to do when you
have no half tones. And all the half tones are just
the white of the paper.
But we're
going to encounter some half tones quite soon.
So -
(drawing)
and I don't - actually I like
how some of these parts slightly haze out
because I want to emphasize the objects that are closer to our light.
And I want to slightly
simplify and remove
accents off of objects that are farther away from our light.
So now I'm going to
remove some
of these construction lines.
Just help make
these objects more solid
and prepare these surfaces
for half tones.

So now that we've placed our shadows, let's move on
to half tones. Now as you see
we've broken up this process into
clear steps. We start off by
establishing the placement of our objects, then
we analyze and figure out their structure,
then we move on to finding where all our shadows are
and then, finally, we move into half tones.
Now I think for the purposes of learning, the best way
is to separate everything into these clear steps.
I think as you gain more experience
you'll see that you might be
switching the order of them and
you might be working on multiple steps at the same time.
Okay so I'm going to
continue in the way that we practiced
and covered when we were working on these objects individually.
We began with
thinking of the darkest half tones that we had. But
here, before we work on that,
let's establish where the lightest half tones are.
So, this plane of the cube right here is catching the
largest amount of light. Our strongest
highlight however, or possibly not even the strongest,
our largest highlight is here on our sphere.
The other strong highlights are going to be
on the edge
of the plane of the -
of the nonagonal prism on
the plane that is angled most perpendicularly towards
our light and along the edge of this
plane of the cube.
We also have a strong light that I see along
the edge here on our -
closer to the top of our cylinder.
But even if it appears as though that light is on the
edge, we're going to have to indent, move it in a bit, and show
a little bit of a half tone moving off of the edge to turn
the form.
So let's just take it piece by piece.
So let's establish the tonality of
plane that we have here, catching the largest amount of light, followed by the top plane
of the cube, followed by the plane
of this ellipse. And we see that
this is catching the largest amount of light
then we have the top plane and then we have the -
the plane of our ellipse. I'm going to sharpen my pencil
a tiny bit on my sandpaper block.
I'm just moving it up and down and
rotating it as I go. I also have added
to my arsenal our kneaded eraser and I also have here
a blending stump
that I'm going to be using at times
instead of my hands. Now I prefer using
my hands but sometimes the oils in them can get into
the paper and do more harm than good.
Okay. So
we're going to keep the plane of the cube here the white of the paper.
At first at least. And we're just gonna start
to tone
down the top plane
of our
cube.
I'm gonna use the blending stump to even out the tone of
a little bit.
It depends on if you enjoy this quality
of mark making, this sort of softer edge.
I tend to use the blending stump but then I feel the need
to go over and hatch or
place a tone on that plane.
So
here we have a tone.
You can step back, think about it, and I would say
after you have it
in essence it's not - the relationship that you're thinking about is pretty much
the shadow to the tone that you've placed.
If you've established that as the correct one, then you keep that
and work off of that in placing the half tones everywhere else.
So, to continue, I'm just going to
adjust this relationship, not by changing that
tone but actually by
pushing the contrast
between them from the shadow side.
And now,
once that's in place, it's time to very lightly
find the tone of the
plane that's catching the largest amount of light. So you're gonna
have to be - gonna have to have a very light
hand here because you don't want
to go too dark. So just -
you place the tone very gently.
Don't worry about any
of the variations that you see there.
And then integrate it
with the paper.
Integrate it into the paper rather.
So see, there's a tone
but it's so slight you can hardly see it.
You can see it when you really compare and really look close to
the white of the paper.
And here I wanna clear line.
We'll be going back into this in
a little bit but I just wanted to have a line that's
a little more even, a little lighter.
And there it is. So
here, use the sharp
part of the eraser that I recommend you keep -
you keep carving and you keep cutting that eraser to keep it sharp. It's -
think of it as the same kind of
tool that your pencil is.
Like you wanna keep them sharp. You wanna -
you want to
use everything it has to offer.
(drawing)
Just going to
clean this up a little bit in order to get it as nice
flat
tone of the paper and a clean edge. Now
you can see my hand keeps slightly smudging
because I use my pinky to anchor but that's no problem,
you can always go back into them and it's not a big deal anyway.
Okay so now that we have those plans of the cube
let's move on to the surface of this ellipse, which we can clearly see
is a darker value
than that plane.
Erase that number.
(drawing)
Integrate that, smooth that out a little bit.
And you see now they're about the same,
these two are a little too close.
So we're gonna have to
go in again. I would begin
with the part that is tangential to that
plane
(drawing)
so that you can really compare
this relationship from
here and then if you establish that you're fine
with it, you're happy with that relationship, then you just
extend it outwards and you don't need to compare as much anymore.
You already have the tone you need
(drawing)
Okay, so
now that we've placed these values, these tones, let's
step back and compare a little bit and see.
I'm just gonna use - before we do that we'll just use this
kneaded eraser to get just a little more even.
(drawing)
I don't think that this contrast we have here is strong enough.
I think we run into the problem that we always tend
to run into and that our half tone is falling into our
reflected light in terms of tone. So
I first want to push this contrast between the
plane of the ellipse and the terminator line
in core shadow off of that edge.
(drawing)
I'm going to put
that terminator line up there also.
Just sort of establishing that
(drawing)
core shadow and terminator line.
(drawing)
Again, so
okay. So -
(drawing)
and now all we really need to do
is to adjust this relationship and make sure our reflected light -
even though on here
is a darker value than our light.
(drawing)
But of course, once that happens -
ooh -
get a little bit more of an even tone here,
which will also, of course, help to get a darker value
in these areas.
Just using the side of the blending stump.
(drawing)
Clean this up a little bit. And so, obviously,
we've lost our reflected light right there.
So we're gonna have to go
and work around it again.
Because on its own it reads properly in relation to
this tone of this ellipse plane,
but we're just gonna need to work out way around it
to make sure it reads as if it's considerably lighter -
(drawing)
considerably lighter
than our core shadows.
(drawing)
And then we're going to continue
to make adjustments as we move
back into our shadows.
A large portion of work in the half tones is actually
work that you need to do in your shadows
to make sure the relationships are correct.
(drawing)
Let's do this here, clean this up, keep
cleaning your surface. So here
let's
reestablish that line for clarity.
(drawing)
And
let's work out from our terminator into the dark
half tones. And then move
into our lightest half tone
and finally into our highlight.
which will be along this edge.
(drawing)
But not all the way to the edge.
Work from that edge, slightly in, in order
to make sure that there's a tone that's rounding off
that's wrapping them around. Here
let's make some corrections to your
ellipse, or
rather I'm making corrections to my ellipse.
But it's always
so good to go
back in. And that's kind of a part of what
I was talking about in that
we are clearly
breaking up the process into
logical and sequential steps
but at any
point, you might be
going back
into one of the steps that you -
that up until this point you thought was completed.
(drawing)
Adding some contrast there
and so here, right now, I want
to push that occlusion shadow we were talking about
because a similar
problem is happening here. You have this half tone and it's
sort of a little too close to our reflected light right here.
(drawing)
In value. A little too close in value.
(drawing)
Then use your eraser
to get a sharp, clean edge here. Really using it like
a pencil.
And here
we're not so concerned with the actual
value as much as we see it.
For the same reason that everything we have here is
hazing out a little bit and that
we don't need this edge too accented because
the close edge, right here, is the one that should be
catching our attention.
(drawing)
Let's
reinforce that cast shadow because now our cast shadow
is the same value as our core shadow.
Get that in place and
just making sure this line is
straight.
Cleaning this up. And now let's get into the half tones on our
sphere.
So in terms of our sphere since there's a continuous curvature
as we have seen,
encounter that
we have a wide range of
values in the light. So somewhere here the dark half tones are going to be
pretty much the same value as
the plane of that ellipse while
the lightest values are going to be as light as
this side of our cube
and then we have the highlight.
So let's begin to move out from
(drawing)
our terminator.
(drawing)
I think we've hit a point where we're about - these values
are close, they're
working. And now we have to quickly because of
the - they're either sort of
abruptly move into the light,
these half tones have to come up
(drawing)
very quickly
to seamlessly move into our
highlight.
(drawing)
And make sure to get that soft
gradation
as you move out of the dark terminator, into your half tones.
But
keep in mind that here we have to have a tone, because our highlight
is always indented from the edge, we have to have a tone that's very close
to what we have placed on this side of the cube. So here we have to be very light.
(drawing)
So it's hardly noticeable.
(drawing)
And then move it into
our highlight and then use the
kneaded eraser because it does not -
you can just put it up against the paper and pull it away,
it does not give you such a sharp edge.
(drawing)
And here I'm just
gonna combine that shadow a little bit.
Now that I'm here we can see that we're having a similar problem
that we had here and here. We see that this reflected light
is a little too close to our half tone. Even
on the sphere on itself. See so
obviously there's considerably more to think about
when you have multiple objects. You aren't just comparing the values within one object but
you're comparing the values on one object to the values on another.
And then
just - so as we go through all
these assignments, all these exercises, we're gradually
increasing the level of difficulty.
But I think you got it.
(drawing)
Alright, we've toned down
that reflected light a little bit.
Now it reads like reflected light.
(drawing)
And we clean up a little
bit.
Okay what we have on our paper,
analyze and think where to move
next. I don't wanna really jump off of
this group here just yet
because there's still some more to do here.
There's always - and also if you're at
a loss of what to do after -
after half tones, always come back
and reevaluate
your edges, your outlines, your contours because
you're
always aiming to get
as precise as possible with the contours of the form.
This is a process that continues the entire time
that you're working. You're always
reevaluating your contours. And we will see a lot of that
when we're working on the figure.
Okay. So
I think we're at a good place
right now. I actually feel that even this edge that I made
I can slightly lift up
and even introduce a little bit of reflected light into it. So you
can, at times, use your eraser for this. We have to be very careful
because you can easily run into that same problem of having your
reflected light, the tone of your reflected light,
be a little
close to the tone of
any one of your half tones. More often than not
it'll be the darker half tones.
(drawing)
Here we have a little bit of this.
We're just getting a flatter tone on some of these planes.
(drawing)
Just getting a
softer gradation from our
terminator, accentuating our terminator.
Also a thing that always
requires attention.
And right now I think we just need to go and
hatch
along the terminator of the sphere, remember what
we were talking about, that this is maybe one of the darkest areas
that we have. Even if it's not the darkest area that you
see in front of you. But it is the closest -
it's the closest point of the closest
object. So we wanna make sure that that reads.
Okay. So we'll probably have to
come back into some of these things
but let's move on to our nonagonal
prism. Nonagonal prism.
(drawing)
So here, before we -
I just wanna move into this shadow
for a moment and get a little bit of clarity on it.
I think
that works and we can sort of extend this out
a little bit and
do a little more there.
Okay so now it's time to compare
across. It's - across
a group of objects. Like from one object to a group of objects. On the one hand
this could be harder,
mainly because you don't have a value
here that's coming right up against the value that you're comparing
it to, as was the case here
for example. But the principle remains
exactly the same and you're just gonna have to
move your eyes across and just
keep your eye over here for a minute and
move it over to any other part that you're comparing to and then
move them back and forth. I'm thinking that this plane
is actually in value quite close to what we have right here.
You can squint, it'll help you see them. But
I'll go with it. Gonna correct
the line of that cast shadow. You might be able to see that that
cast shadow is not as sharp of an edge as I'm making it, but we're not gonna
concern ourselves with that at the moment.
(drawing)
Alright. And then we have the plane
here. Remember that we are going to show that edge
with a highlight, not with a darker line
and then here we have a light plane
and that highlighted edge.
Here you can use the point of your - oh no, don't use the point of
your blending stump. Here
use the eraser
to really go right up to that highlight, right up to that edge.
And then we have
something a little bit more complex happening
up here. So we actually have a soft
sort of end of a cast shadow along the top
of this plane on the right hand side and
then on -
and as we move to the left hand side
we're completely in light. Now this is
interesting so we're going to keep it in.
But it's not
really a dark shadow so it's just going to
slightly move off of it and move into the top plane
which happens to be a darker value that either of these two.
So start by placing a tone and I think
you can already see that we're encountering some confusion.
in terms of our
light values and our shadow values.
That is not a problem. We will go
into them and correct them.
And then to get that little bit of more
of a gradation.
I'd say that's all we go for at the moment.
So it's clear that these two values are very close.
So it's not reading quite well but this is all
a cast shadow.
All we need to do is go into these
shadows and bring them down.
(drawing)
Just gonna use the blending stump
everywhere here in order
to get a darker value.
I really need to get these tones into the paper.
If it's not perfect obviously don't worry about it because we're going to be
going back over them with our pencil.
(drawing)
So now it is beginning to read a bit more
like shadow. We don't have any
conflicting values. But I do want a little bit
of texture and I want to accentuate
that terminator, that edge, the beginning of our shadow.
(drawing)
Let's find a clear edge
where the
bottom is. Here we can now maybe
get a little bit of a softer edge so just kind of - the same way
you would move off of your terminator,
you could do the same thing on -
off of that
line of the cast shadow. But then you're still gonna want a little bit of clarity.
(drawing)
And see so the interesting thing is that even if you don't have
a line there to give you that
separation of planes, you have it with this
small part of it and this change of angle in the
way the cast shadow's falling in that part of the form.
(drawing)
Here I do want that edge
because it is an important one. And even here you wanna show it but not too much.
It's actually it's like
slightly off but yeah.
And here I'm just gonna get a little bit of a darker line
to get this plane to read more like reflected light.
And so
what you do want to do though is if you remember our cast shadows
should in general be a darker value than our reflected light. So here
I would keep what we have here for reflected light
and go over this one more time.
(drawing)
If they're close, in this case it's alright.
Here just bring this up a little bit with the side of
the eraser or your kneaded eraser
and let's
(drawing)
get a clear edge.
And so here we have
our objects and
shadows and half tones.
So the thing that I would like to do to kind of complete
this is
I want to make sure that this is a cast shadow
that's reading a cast shadow so it has to be closer in value to
the tones that we have on the nonagonal prism.
(drawing)
And here a long hatch can accomplish a lot of this.
(drawing)
Uh huh.
(drawing)
Mm hmm.
(drawing)
Use your eraser
to get that sharp edge at the origin of that
eraser to get that shadow coming off of the objects.
Let's not worry about the end of the page. And now
I'd like to introduce a little bit of a tone for
the background. Because as you see, we are
in the sense ignoring the background as we see it. So we're only going to use
a tone where it can help us. So in essence
it'll help pull out the objects that we need to accentuate
and sort of
create a haze around objects or parts of objects
that are - that we don't
need our eye to go to right about. So - but the other
thing is that the value of the background has to
not interfere with our
shadows. Or the majority of our
half tones so it has to be essentially -
it has to be the value of
like a medium
half tone.
And then here I don't think we need
this area to
read like a gap. And if we keep it the white of the paper it might.
So we're just gonna slightly tug it away
and here I just hatch in one direction and then I change the angle slightly
and I hatch in another direction, a lot like we have been doing everywhere else but I just keep going over it
I'm even gonna
see and you can go and work over the objects.
The particular tone here is not
going to really affect
(drawing)
the shadows.
So you see that's beginning to create a little bit of atmosphere.
It's not - this whole part isn't
sort of jumping out at us like it was.
Here I have a curve for some reason so I'm going to correct that.
Make sure that's
a proper line. We'll the do the same thing on the other side.
And, huh, I didn't
fix that curve. So you can always
go in, erase a little bit,
and make your corrections.
And the other
area where I would -
where I would place a background tone
is around here because I want to show that there is a strong
contrast here that this plane of the cube is
catching a large amount of light and
right now it's hard to see that because it's practically the same value
as our paper. So just gonna
begin by getting a little bit of a tone. And I'm going to -
here I want to do a similar thing with the edge of the table
and I'm gonna use the tone to establish
that edge and here we need it to be
a darker value than the top plane as well.
So here the tone's a little bit stronger
than it is over here.
(drawing)
And the same actually will
go for our cylinder - the ellipse of our cylinder.
(drawing)
And the reason why we're doing this -
especially around the ellipse, the top plane or our cylinder
we want a darker tone, is because
this tone we have right here is, in some ways, considerably -
considerably darker than
our paper. So it's not reading as if it's actually catching as much light as it is
So we're just gonna go over it
(drawing)
and just keep applying
the tone whichever way. This is a great time
to practice. This is the practice.
I'm doing a freehand
hatch but locking it into
a particular area.
Use the stump in some of these
areas to get that clean light.
So we're getting
closer to what we need. And then here
just go back and maybe even lock it in place with a
line.
I had to switch
hands.
And then in order to not have
it seem as though you're working around it - so this is kinda
a little bit of a - you're moving
out of the object, you're carving into the object and so on so
this is a technique that we will be using a lot -
step back, analyze - that we will be using a lot
in order to really get a
clear outline. And this comes
into play especially when we're using softer media.
But it also comes into play when we paint. Because
this sort of idea of carving into a form
and then carving the form out into
the background is an important element
of painting. And here I'm going to just push that to get
that to look a little stronger. And the same thing I want
with that top edge.
I'm gonna take it all the way up
there.
And reinforce the corner.
This edge.
(drawing)
Here we don't want that
much of a contrast.
And it's okay to have those hatch marks,
they actually add an
interesting amount of chaos
to some of the more sort of analyzed
and precise parts that we have here. Here I do want to get
just almost like a darker line
to establish that as the bottom edge.
And even though we see that
there's a black piece of cloth on which
the objects are on our table,
we want to kind of ignore
(drawing)
the color of it. So I'm just gonna slightly tone it away
once again to push the contrast between
the values of the cube and the values
of the table.
(drawing)
Here, maybe a little bit of differentiation between
the plane of the table and the background. Not much.
Just enough to make it clear.
Here we have a group. And just so we don't have
this strong contrast of this edge. So here we would place
the tone in order to have that contrast. Here we're gonna place the tones to
minimize that contrast. It is an area that is in shadow
and
it's away from us, we don't need it
to be accentuated. So the contrast of that
tone to the paper was just a little too harsh.
(drawing)
Let's see.
Now that we're almost where we need this
we're just going to go back
once again make sure our outlines -
our contours rather - are
where we need them.
(drawing)
Make sure we have -
And by contour I
mean the contours that are
all around an object, but also sort of the
contour of a individual part of an object, for example
this ellipse I'm working on.
So here we have completed our still life
study. This was a great opportunity to see how
everything that we have been working on up to this point
finally comes together.

For this assignment, using the photos
provided, you'll be taking your drawings to a finish.
While working on the still life in geometric solids, making sure to work
through the three main steps in order. Begin with construction, apply your
shadows, and only then your half tones. Good luck.