- Lesson details
In this first lesson of the series, artist and veteran instructor Erik Olson introduces perspective in a complete and unabridged pictorial form for artists. Erik walks you through the process of integrating compositional thumbnails and sketches with perspective all the way through to fully formal, measured perspective. You will learn how to use perspective as a tool for the artist, to serve compositional and conceptual goals. The practices and proofs that you will learn are derived from the Renaissance all the way to present day methods.
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In this first lesson of the series, artist and veteran
instructor, Erik Olson, introduces perspective in a complete and
unabridged pictorial form for artists. Erik
walks you through the process of integrating compositional thumbnails and sketches
with perspective, all the way through to fully formal, measured
perspective. You will learn how to use perspective as a tool for the artist
to serve compositional and conceptual goals.
The practices and proofs that you will learn are derived from the Renaissance
and are as applicable in present day.
my name is Erik Olson and I'll be doing the lecture series on perspective.
The type of perspective I learned and want to teach and be really thorough with
is based on some simple principles. Here in this diagram are some of them. These are our
ideas that are from our vision looking out into the world. And we'll talk a lot about
that later, but they're very important so I want to constantly refer to them and have them in the
background. Kind of burn them into your heads because this is really, really
important. Not all of this is gonna be really technical. This is about drawing so
this is perspective for artists and for drawers. The idea
is keeping the art of drawing alive and perspective
of course is a big part of that. But I want to make it clear from the very beginning
we're trying to subordinate the perspective with our artistic
desires and composition wishes as artists. So we're gonna
always work backwards from a narrative sketch or something that already declares what we
want to do with the picture, or with the objects, or with the composition,
and work backwards to the formal so it can help us do that. That's really, really important.
Otherwise you feel like you're limited and you have to fly all this kind of mechanical
system. We're not doing that. We're gonna learn a lot of mechanics, don't worry about that, but
in measuring and in the whole nine yards, the idea is it's gonna be driven by
compositional desires and an artistic vision. Meaning I'm gonna learn how to do this
so I can do what I want with it in my way. And that will be
achieved by basically, of course, many diagrams. And I'd like you to draw with me on the diagrams
in real time and keep your own notebook of diagrams, which is critical,
with explanations, which I'll provide and talk about and have at the end, you know,
recap at the end of diagrams. Also, we're gonna be doing some digital draw overs
and some very simple 3D movement through space to explain perspective and look at
some master paintings of course. The main thing though is you keep that notebook
and your drawing with me. And you're drawing on your own, by the way, after that. You are
taking these ideas further, doing little sketches, trying all these variables you can
after I maybe give you the main idea. Keep inventing of why it works
after you think you have it down so that you really get how to do this and memorize this stuff.
It's not that hard actually when you realize this is actually how we see
it's just a system of geometry broken down to replicate it. But it's incredibly
close to how we see, almost exactly. So it works quite well.
Another thing I wanted to mention is, I want you to realize that you can
use this for your own style. The idea is, this is not some thing
or lecture series on we all want you to draw
this way. This is not a perspective or drawing technique. It has nothing to do with
the word technique. That's a poor way to put it. These are concepts
that are related to how we see very clearly and they can be taken
and stylized, they can be stretched, they can be bent, you can use Curvilinear
perspective once you understand how to achieve these scenes. The whole point is for you to be able to take
it into the direction that you want to. So even if you want to be a German expressionist
and only use perspective and views based on that idea, this will
still be incredibly helpful because you'll understand how to do any type of view
and then abstract from it because you know actually how the perspective works. That's what my goal is:
everybody on every level learns the perspective and this is
critical. I wanted to also mention observational drawing. I'll be looking at my notes occasionally.
Observation drawing is extremely important as well. Of course
that's how to express and start getting your own sense of how you want to draw. There's many ways
to draw representationally and paint representationally, or even semi-representationally. You know
hundreds really. So let's just be
clear that this is information and that's what it's meant to be. It's not about
being a technician only and it's not about saying, "Oh you're supposed to be drawing
correctly like this." This shows you how the world appears to us in an incredibly close
way to it. So what? That's what the system is to understand
how the views are achieved by looking down, three point, up. Why can I look straight up in the air?
What's the difference, how do I change, where do the vanishing points go? Those are all questions
you'll still have to ask as you're sketching and drawing, even in a semi-stylized way.
So, I just want to make that extremely clear, that we're not trying to make anybody
draw one way. I've taught this for a long time and I certainly was a big fan of it
when I learned it because it allowed me to do anything I wanted in any style I wanted.
So, that's really the point I wanted to get at. Observational
drawing is very important. Sketchbooks, trying to draw objects, trying
to understand how to do these different variables from landscape drawings. You know, drawing
rooms, drawing people, putting them in perspective. All that you can just do in
little exercises for yourself, as well as work on your line quality, how you like to draw,
replicating an artist you really like. You can still do all that while practicing the perspective.
It doesn't have to be a separate exercise. That is an incorrect
way of thinking I think. If you want to learn perspective, you can take it and you can
bring it, the perspective, into the realm of what you like to do. And practice
it and get to know the views and really get technical with it. We'll be getting quite technical
on the diagrams in some cases. In other
ones we'll be simply, you know, how to place figures on a correct scale.
So we'll be covering all that and I'll be getting into that in the diagrams and we'll be getting more into
the explanation of what this is all about in the next segment. I just wanted to make some ideas
clear to you at the very beginning that, you know, this is perspective for artists again.
I want to make that super clear. Okay, drawing's a language, let's be honest.
Visual art, drawing, figure drawing, transparent drawing,
drawing through objects, understanding them as transparent things first so that you understand what's on
the other side. Volumetric drawing, figure drawing, landscape painting,
perspective drawing. All of it's, you know, saying the same thing essentially. You're trying
to express that color mixing, mixing real color, actually physically seeing color
mixing many variables on it. All these type of basics are really important so
perspective of course is a big part of that. Again, it's information. And what
you do with it is the exciting part and the new part, frankly, because you'll be going into the future
in new ways than others have. This is just classic information
that is about how we see. It's very analogous to music, it's very
analogous to writing. There is still sentence structure, words are still spoken in
order, there's an order to writing, and there's a, you know, an art to it. There's also
in music of course, you play scales. You have to be able to read music. You have to be
able to understand and play an instrument well. There's things and facts you actually have
to do in order to be a professional musician and then compose new music.
So, we're thinking of the same thing. This is just the basic of like -
an analogy would be this is more maybe along the line of classical
music as opposed to jazz, whereas jazz took classical music and all the rules
and all the sophistication and pushed it in another, very exciting, direction.
That's exactly how this information should be used. It's not about itself only.
It's not an ends to the means, it is simple a way to get there.
So, you know, that's an important idea. We'll be doing a lot of
thumbnails and freehand sketching before we get into the diagrams to kind of feel out what we
want to do or make an example. Little sketch diagrams, a little bit of value here. Talk about
lighting later, all that kind of stuff. Then semi formal perspective drawings of where you
pretty much are doing mostly freehand with a little bit of straight edge assistance
and really drawing to vanishing points. But we won't be measuring, necessarily,
all the time, we won't be measuring depth. Then sometimes we will be,
the full on formal perspective is measuring depth which, you know, this apparatus
has to do with as well as very simple thumbnails. This is always present no matter when we're drawing.
Actually, if you didn't know it, kinda like the constellations. They're invisible sometimes
but they're always there. So the idea - we will go all the way to formal perspectives
but there's ways to cut down the steps and procedures to measure in three point where you can get it
down to just a few steps. It's very simple. Very - we're always gonna be
talking about the frame and the composition first, then we're gonna work the perspective into it. So that's
important because it's not gonna become overly mechanical
except for the actual execution. That part gets mechanical at first because you have to
understand why things cross each other, where the vanishing points are. But technically
we're using it for a higher purpose. And that is: to get the composition and views we want.
That's critical. Okay. How do we see the world? We see it with
binocular visions. Obviously perspective, if I'm standing in the station point here, kind of
where this is supposed to be viewed from and the size of my cone - which we'll explain in just a few
minutes. The idea here is that, in perspective,
unlike how we see, it's from a single viewpoint. So you have to almost close an eye and
imagine you're never moving and you're absolutely stationary and that's how
you see everything moving consistently. So we're not seeing binocular vision
necessarily when we're drawing in perspective. We're from a single viewpoint with a single eye.
But effectively it doesn't matter. We just say it's right between the eyes, the station point, which
we'll get to in a bit. So the camera's the same thing. The camera lens adds to
distortion. Camera work is its own thing, it's not exactly how we see either
but it's incredibly close. Of course it's a great illusion. And so is
when you're in perspective. It's a fantastic illusion. Both are practically the same,
and for our purposes as artists, they pretty much work
exactly the same. So the nuances really don't matter. We'll be discussing
lens frames, everything about how to frame out and why we can frame around the cone. All sorts of
stuff having to do with composition, art, and figuring out what you want to say with the
composition. So remember, it's about helping your concepts and your ideas about what
you want to do. And the more freedom you have to do any view you want is
the more freedom you have to come up with any concept you want. Because concepts are directly
related to narrative and painting and drawing much of the time. Especially in semi-representational
and representational art, obviously. So that makes sense. And again, I just wanted
to cap off again, this is compositionally based. And what I mean is, lots
of variables. So we're not gonna teach some formulaic way and say, "Oh well if you want to do this
and you're kinda looking over here, here's a way you can do it, here's a trick." We're not gonna be using words like
that, or I'm not gonna be. I learned the full monty basically, the all the way up
everything you could do with perspective. Basically there's eight different ways you can do it.
You can remember them half the time, that's why, you know, you write the notes down.
The notes, the lectures, a few books you like, all that stuff is
helpful to go, "Oh yeah, I wanna kinda get this view, but I've forgotten exactly how do I
approach it, and what are the general outlooks of that? Oh yeah I forgot." So you just, you know, you refer
to your notes. But compositionally, how do I get, you know, five, six,
ten variables on a kind of a scene I want, as I'm compositionally
sketching. Just as an artist in a sketch book but with the rules, here, in mind. Kind of invisible
cobweb thin ideas, you can do a lot to go toward
just mapping out a real view. And then you can start stylizing it immediately
and you can transfer that onto a huge canvas or a mural and you're off to the races.
It's like, instant. It's not like you have to, you know, go through a lot of
transitions here. If you can do a really nailed composition in a sketch, you can
enlarge that sketch, either by simple griding, however you wish, and then you can get
right on it because you know the view is solid because you know perspective. And that's what
we're really gonna - you know, that's the goal of the lectures is to really get you feeling
one, two, and three point and all the different factors and variables that I can have thrown at me.
I can create an infinite amount of views is the important thing. And I
really want to stress that. And again, this helps us do it. These are the
four items that are ours when we look into the world. I'll just
name them: the eye level you're familiar with, which can be the horizon line where the
ground and the sky meet forever if we're in traditional one and two point. But we can also
be looking in down in one and two point and straight up in one and two point as well as
all around the sphere. The idea of the center vision
is always the plane at which we're standing straight in front of vertically.
Of course the station point is the point between our eyes in the position we are actually looking
from with our eyeballs, always. And the cone of vision is a projection that is always present
because it's our view of basic distortion here and the reason
we distort is because we are making a two dimensional
statement from a three dimensional idea. So in our own view, we can never divorce ourselves
from our own cone. It's always with us, along with the rest of this set up.
In paper you can look at a distorted area that is outside the cone
where perspective gets real funny. You can't do that with your own eyes because by the time you
switch over to a new view you've already changed all that information
over here and then you're looking a non distorted view again. So you can never escape
your own cone of vision. You can't really see
the distortion in your own view. Which I guess, philosophically, is kinda tragic, but you can't.
So we can though on paper and on two dimensional translations okay.
So, that's about it. I wanted to just make it clear again that I'm really
happy about doing this and I want to give you everything I know just not parts and
I don't want to make it the abridged version, I want to, you know
really give you more than I've ever done in
a - even in my own notebook or anything - and really put it together carefully because
I'm excited about the fact that more than ever these days we, you
know, we want to convey that drawing is it's own form and perspective, linear perspective
and drawing form is really important. And I wanted to stress also that of course digitally
people are drawing all the time in two dimensional, digital programs. So the computer screen,
this wall, a piece of paper, it's all
about the picture plane, which is the flat wall here
we're looking at an actual wall with a diagram. But that, again, could be a wall, a piece of paper,
a computer screen, it can be anything that you want to do a drawing on and give the illusion
of form in three dimensional ideas. So again, it's open to
anybody, no matter how digital you are, it's not technically a 3D program, it's the
original 3D program of course, from five hundred years ago and more. But the idea is
is you are a big drawer and painter digitally, these ideas can be
you know, drawn up and made
two hundred dpi later digitally and simply drawn out to everything you
need is information and you can crop in on the frame, you can blow it way up in size and
start painting. There is nothing you can't do with this stuff digitally that you can't do
traditionally. It's all the same. Okay. So with that we'll continue on
in actually this stuff and getting started on the definitions and that part. Alright
so we'll see you in a bit, okay.
well let's start some of those definitions now. We're gonna walk through it
literally, physically act them out and and we want to identify them. So we're just gonna start by
introducing the idea that this wall is considered the
picture plane and then everything else on it is the illusion that we can look through it like
a piece of glass and we can see into an infinite distance or a scene. It could be anywhere.
We're gonna be talking about mostly, traditionally one and two point, in which
case we're looking straight into the horizon and our eye level
is the same as the horizon in that way. But not in three point, we'll get to that later.
So the important thing is, this eye level is set to my eye level. Since I'm a little
over six foot I just said, "Okay, that's about a six foot eye level."
So we'll start there. And that's the important part of beginning to learn how
we step into it. I'm not there yet. I know you can see the floor, so the idea is I'm still kinda standing to
the side of it, but I wanna explain what the picture plane is a little bit more. It's
infinite. This flat plane can go on forever, up, down, it doesn't matter.
We can use it anywhere we want, as far away as we can so it can be a very distant
vanishing point way, way down there and the eye level would still hook up to it if it
was a ground plane vanishing point. So the idea of the picture plane is it,
as I had mentioned before, it could be the little piece of paper you're drawing on
in sketchbook, it could be a diagram on a piece of
paper, it could be this wall as a mural, it's this sheet of paper and the wall together
and the whole diagram together as the picture plane, it could be the computer screen
is your picture plane. And we'll go more and more into how the cone is
relating to those ideas as well in different ways. But for now, the picture plane
again, if you can imagine, is always straight in front us. Now I have
picked a point that is straight in front of the same eye level, this is my
actual eye level. EL: Eye Level. And I also have PP, believe it or not,
but that stands for picture plane. And from now on PP is picture plane, eye level
is always, you know, EL. So
now I'm coming to my center of vision, which I'll explain in a second too. Either way
I'm standing straight in front of it now, and that exact eye level is
in fact my real eye level, standing in front of this real wall. So we're gonna use
real examples of this actual wall. Also,
if you can look, the center of vision is directly what I'm facing. So we could say that my body
right now and my head and my station point is directly perpendicular
and parallel to the wall and all these items. So let's start.
Remember, the entire wall plus going on forever, down forever, up
forever, to the sides forever, is the picture plane.
Secondly, the eye level. My eye level again, I'm a little over six
foot so my eye level extends out and the plane we can imagine goes on forever
and ever and ever. Thirdly, the center of vision.
The center of vision is the plane that goes vertically as
the eye level goes horizontally. That cross is always is exactly
where the center of our vision is our entire life. And I'll explain that
in a second. The idea is if you look at the idea of the
picture plane always being straight in front of us, so if I turn my view and turn toward you
now my picture plane is facing straight toward you, anywhere, it could be right by
your camera, it could be back. I could have a picture plane way behind the camera, it doesn't matter.
But I am standing, looking straight into the horizon right now where the earth meets the sky
but my eye level is also straight across where I am. So it's roughly
where the camera is, but this is my picture plane. If I turn this way, this is my picture plane,
straight in front of me. But now I'm on my spot again, right in front
of my tape mark, it goes and runs all the way up the wall like this.
And I'm standing right in front of it. So, the picture plane travels with us
everywhere, as do all of these elements. And I'll explain why. So the picture plane is the first.
Picture plane up like this in three point, that would be bird's eye, looking up.
Picture plane straight in front of me this way because my head's down, it's straight in front of my
view looking down, that would be three point bird's eye. Then I return to one and
two point which I'm looking straight into the horizon. I can lower, I can
go higher, I can tiptoe. Each time I do that, my eye level
rises. My center of vision stays the same until I turn my body. So the eye
level is changing, lower or higher, if I go ahead and crouch
all the way down to being, you know, like a hamster, all the way up to being a giant
that changes the eye level. But the center of vision doesn't change until I actually
change my direction this way. So it's this type of movement for the eye level
this type of movement for the center of vision.
Also, the picture plane plays a roll later in being
able to be flattened out like a flap. We're not getting to that yet. We want to discuss the
station point is in fact right between our eyes. We are the station point.
The very level, exactly between our eyes, right at the point of our eyes is
always our station point our entire lives. And if a camera is looking into things, like
you're camera, the camera is the exact - the lens of the camera is the exact
station point you're looking from. But my station point is right here. I've run
a line down, continuing to the floor about a foot below the SP marker there,
continuing down to the floor and runs all the way here to a spot. That spot is
the same distance to my eye standing right here
down to there as this distance is to there because it's been flattened.
We'll get to that in a second. But to review again, I've picked a spot
that is four and a half feet in front of this wall exactly at a six foot
eye level because I'm about - a little over six feet. And I've also
picked a center of vision as you can see right there. I'm not standing on it now
I'm talking to you. But now I've positioned myself and now this is the actual
eye level I really have, as I mentioned before this is the actual center of
vision and this is the picture plane I've chosen to talk about.
The station point again is right here. Now I have a plane going
to the floor is exactly where I'm standing. You guys can't see it because I wanted to crop in closer to
try and explain some of this stuff better. But actually, if you can just imagine the center of vision line
continues to the floor, which is right here, the floor line and continues out.
And I'm exactly four and a half feet in my station
point, straight out. Okay, the cone of vision is the blue
circle you see. That is the mark of where distortion starts.
So anywhere in this picture where I'm standing here
right at four and a half feet, that is my actual cone of
vision because I've taken a 30 degree angle and a 30 degree angle from center
and projected it out until it strikes the eye level picture plane. Here
What that does it allows me to understand where
distortion will start. So distortion will start out here,
out there, above, out here, and around here.
Things will look pretty darn normal in here. You can play with the distortion but that is the
general marcation especially in one and two point perspective. In three point perspective actually
distortion starts pretty much about ten or eight percent in from that.
To be technical about it. So the station point for what we're referring to
at this point is right between my eyes at my eye level where my center of vision
crossed. So wherever that cross is is also and always dead in the middle
of the cone of vision. That's where the cone of vision emanates from is this point right here.
Okay, so because this is my particular eye level
in this picture again, if I stood back another 20 feet going back like
this more and more and more, the cone would get bigger on the same picture plane because
the farther away I am that 30 and 30 degree cone up,
down, to the sides grows larger and larger. If I get
closer and closer to the wall at this same eye level and center of vision
the cone would get smaller because the projection of 30 and 30, 30 and 30
as a cone would be smaller. And then I return to my position here at my spot
and the cone would resume back to its size that you see in blue.
So, what we've covered so far is the idea we have this imaginary
picture plane that's actually transparent and we can see the whole world in front of our
view here or whatever scene we create. Because of that
I need an eye level because it's at the level that I'm viewing it at, which my eyes are
actually at. In this case which is true to the black line marked eye level,
I also have a real center of vision because I'm standing right here. So to
rehearse again, that's that plane and it goes on forever and it also comes out to me at a
plane and returns here. So you can say there's a relationship between
the ground coming up and the station point right here where my eyes were.
That whole plane is called the distance too. So that could be
considered the distance plane to the picture plane or this is a line of
distance from my eyes right to here. And the same thing is true
for this distance to that station point because again,
that station point there is the exact same thing as my eyes
being here. It's just a flap, it's been flattened. And that's how people can judge
perspective from real angles, which I'm going to explain in a minute. But I want to keep going about
the basics on the diagram. At this point I wanna go ahead
and talk about one of the diagrams. So
at this point what we'll do is we'll fade in a diagram and we're gonna take a look
at that and see how that can really show us where the
ground plane and some of the helpful things. So let's go through all the definitions again looking at our
first diagram. We'll call it diagram A. Okay, alright.
Okay, with diagram
A you can obviously see the figure standing
straight in front of a particular eye level, which also acts as
the horizon line at this point only because it's in one and two point. But it's actually
is eye level all the time. The figure is standing on a ground plane
so no surprise that eye level is the same as the height as the figure is. Because again
that figure's station point is right between his eyes.
There's a projection on the ground you can see is the ground difference and the distance from the eyes to the middle
of the eye level crossing the center of vision.
So as before, that plane exists for the distance plane from the figure
to the picture plane. So the standing picture plane can be anything again. It could be us
really close to a piece of paper, it could be this person standing that far from the wall, it could
be me standing here in my studio this far from my wall, as we just showed.
All that is relevant. Also, we can look at
the fact that the station point is the same distance on the flattened version,
which we're gonna get into in a minute, as you can see goes down.
We always can think in terms of that flattened point. The main thing is to always
remember the four things that are ours are the most important thing we can think about.
And of course those elements are: the eye level, the center of vision,
the station point, and the projected cone of vision are always ours.
So, we'll come back and talk to that now. But see, look at the
diagram and the way we are kind of above and three quarters and can see the entire
ground. We also have a ground plane as you can see in the diagram
and we also have a ground line. You see where the ground plane connects to the picture
plane wall? That's called a ground line and that's right where you can put a measuring line
easily and figure out true height. What we'll do is we'll come back into
the film now and go away from the diagram here and come back.
And now what we're doing is we're gonna look at
the true height. And what does that mean? Well, if I look at the fact that
there's a ground line here that's just off your camera, I can measure a true height
here because I have real scale. Standing here, that's about one foot, two foot
three foot, four foot, five foot, six foot, because we were talking about having a six foot eye level.
So when I'm standing right here and looking at my scale
of the picture plane standing right in front of me, the idea is that, at this particular point,
my real measurements are actually foot marks, or could be foot marks,
against this actual wall and the real scale as opposed to me. And those are a certain
distance away and a certain size, those foot marks across the wall
because I'm this far away. They'd become larger if I stepped closer
and they'd become smaller if I stepped farther away. So the idea is
from the ground line to the eye level here, we could call that a
true height line. Because that's - and that continues up by the way, you can get true height.
Why can we get true height and what does that mean? It means when we're on the picture
plane, when we move around the picture plane as a flat surface, and we don't
move in depth, we don't gain any size. So as long as I say
one foot equals a real foot going down to the ground line,
a foot is a foot is a foot everywhere here. It could be going across the picture.
One foot equals one foot going up. Anywhere on here as long as we
stay straight on the picture plane, or flush to the picture plane, we don't
change scale. It's only when we cast things further into the picture they get smaller
like when we look at the world, and if they come closer they also get and that's where
our measuring system comes in in a little bit when we do a few more diagrams. So the idea here
is: remember, if you set a particular
scale at the point of the picture plane, on your
true height line or even anywhere on the picture plane as a flat piece of
glass like you've marked on it, that scale is only true at the point of the picture
plane. So one foot down let's say, as a total of six to my ground line because I'm
six feet tall, the SP mark is about five feet up but don't worry about that right now,
the flat picture plane here is telling me that if I put a foot mark there
that everything else that falls right flush up against this picture
plane that I want to start at this position in space, the picture plane, would also
be a foot. It's only if it goes back farther or comes forward would it get larger
or smaller going into the picture. And that's really important to understand.
The last concept I want to talk about is the fact of the four elements
that are the most important to remember that are ours. So
if we rehearse again, the eye level is with us since birth, the minute we open
our eyes. Everywhere in our view the eye level exists. What does that
mean? Anywhere I look the eye level is always at that center
of vision for me like this. It never moves no matter what I do. I can flail around
or whatever. It's like permanent head gear. Also, the center of vision
is always like this no matter what angle I'm at and it always stays.
So since we have this cross with us all the time like a periscope in a submarine
it never leaves. The cone of vision like a periscope is also with us,
it is a projection continually going out forever at 30 and
30 degrees for a total of 60 on either side of the center of vision plane.
And it also goes up, down, everywhere projecting from us because it's a round cone.
So the idea of that is no matter where we look in the world,
when we wake up and open our eyes or go to sleep again,
we are looking at this set up. We might not know it but the eye level,
the center of vision in the cone. And of course the cone means we have a particular station point so that means
that viewpoint right between our eyes when we open our eyes is always our station point.
So obviously we are always our own station point and the camera, in your case, is the station point
right at the plane of the lens. So what are we saying about this?
There's a permanent package that you bring with you as permanent headgear you wear
your whole life, if you can imagine. And that literally is the eye level,
the center of vision. So the eye level, the center of vision -
and remember the eye level change and the center of vision changes every time we change our view.
And the eye level is not equal to the horizon all the time. Only in one and two points
perspective when we happen to be looking straight into the horizon on the earth.
But if we were in one point perspective and looked straight down, then
our eye level would be crossing the ground and buildings coming up would become the
depth of the picture. So it's not true that the eye level is always equal to the horizon line.
It's only when we're looking straight into the horizon basically
with the ground eventually meeting the sky. So here we go,
we always have our eye level no matter where I look it never changes it's always right here, our center of vision.
The cone also is always everywhere I go at that projected angle I
talked about. And our station point is always right here. So no matter where I'm looking
into the world, those four items are always together. The eye level, the center of vision,
the station point, and the projected cone.
So no matter what picture plane I pick, far or near, that
set up right here on the wall, why it's so important is it's with us our entire lives. I know
it's like, what's the big deal? The big deal is, that's how we know how to
start a view no matter if it's the simplest thumbnail all the way to a 100 hour technical drawing.
Doesn't matter. These ideas
are always there. Like I mentioned before, like the constellations in the stars,
we might not see them all the time, on a cloudy night, or during the day with clouds, or the blue atmosphere
we can't see them. But all these parameters, inside and outside our
picture frame are always there. And they're never not there, it's just we might not
think of them. So another analogy before we go on to the next
explanation of the station point and how we can see it flat and in person and 3D
at the same time, I wanted to talk about. Perspective
I look at like a warehouse. You can have a hundred booths inside the warehouse that have a
little bit of different information with a little light above them. And you can walk in the door in this large
warehouse with these hundred booths that all have a single light above them. So a hundred lights, a hundred booths,
different information. You can walk in and have a light switch that has
a hundred choices on it. You can go through the rest of your art
career basically turning on just a few lights that you know about or understand and the rest
will stay off. The point of this program really, and the lecture
series, is to try and turn on all the lights in order
and understand everything in the warehouse. And then when you need certain booths
because you know where they are and what they do, you only turn on a selection of lights as you
need them when you're doing different projects or different artistic endeavors.
The idea is, if we know how the entire warehouse works, or the entire
amount of things to know generally about one, two, and three point
and the distance and the picture plane and how to scale figures, all this stuff, you have
the choice to go in and just flip on as many switches as you'd like to
when you need them. But if you don't know much then you're always
dependent on other people's opinions what a good diagram is or, let's say, the
cliffnotes I call them of perspective. Oh yeah let's just give them a few things, it won't take that
long, I don't want to be bothered with it so you get to know the cliffnotes of perspective.
Whereas other people know the entire story. So this lecture series is about
the entire stories as much as possible. So that being said
we're gonna then - we're gonna now go on and explain what
the station point is again, but how it can be flat to us
as a flat part of the picture, but also still representing where we're actually
standing in front of our picture. So we're gonna get
on to that in a second okay. Alright.
Okay, let's talk about the station
point now and what we need to do is explain how can the station point be
something that's out front here where our actual position is in front of this diagram
at our true eye level, center of vision, at a true, you know, particular distance.
Always right between our eyes. That's us looking in. This is my
true station point right here. Also though, because of the abstract
needs of the geometry for perspective, we can flatten the idea of the station
point. So the SP, that black box that is x-ed, station point
with the cone of vision 30 and 30 degrees. 30,
30 equals a total of 60, going to the marcation of the cone of it.
It turns out that if we simply take a flap and flatten
what was this distance down to that
flap, we can measure all the exact same real angles as we could from our
actual head. We can't show our head because that's
three dimensional and we're working on a two dimensional surface. So in
order to make that abstraction, it's simple. The idea that you
can flatten it, but still have the real same angles coming and striking the picture
plane eye level are the same angles, striking at the same place,
on the picture plane eye level as if we were standing out here from my head.
So just in short, to begin, let's just take the two
angles coming off of the cone of vision that come off at 30 and 30 from the flattened
flap representative station point there, coming up as you can clearly
see and striking at their points where we begin the cone of vision.
The cone of vision was drawn like a compass, out and around
from the center point, equal distances. The idea is, "Oh 30
and 30 for a total of 60 strike there." Well it turns out that if I struck those exact
same angles from my standing station point right here
between my eyes, the exact angles would also strike
the picture plane and continue on forever as 30 and
30 degree vanishing points. Because not only do
those strike against the picture plane, not only do they represent where we're drawing
our cone of vision, but remember our cone goes on forever as a growing and growing
and emanating cone. It goes forever. Therefore, that striking
against the picture plane at 30 and 30 degrees for a total of 60, actually
is exactly to vanishing points too. And in that
case, because I can actually cast real angles
from the flattened station point, it turns out I can cast
those exact same angles from my real space, three dimensional space head
also. And they strike exactly at the same place on the picture plane
and then go on forever. So the difference is here, they have to come
up to the picture plane and turn in and go into the picture and go on forever
to represent vanishing points, or the illusion of them. The difference is with my head
I don't need to do that. They just come straight off my head at those same angles and they go on
forever to become the vanishing points. They just go straight, they strike the picture plane
eye level and then continuing forever. The difference here again from the flattened flap
of the SP is that they have to come up, strike the picture plane eye level,
then turn and go into the picture. So they're coming up and then going boom, into the picture.
There's no difference though, as far as the business of actually measuring real angles
from the single station point, the viewer, the apparition
is exactly the same. So once again, striking these same real angles projecting
off my head, striking the picture plane eye level is the same thing as
doing it from here, at those exact same angles coming up. Striking
in and going into the picture. So it's the same. I'll use this
curtain rod, magical wand thing and I'll demonstrate the idea. So it's like a
hinge. I'm actually standing here, where my station
point is. So, here's my - remember my distance line again.
My first distance line right here that's exactly me looking
into the picture, right? This is, this entire
flap, including the angle of the cone and even some vanishing points in a very flap
it doesn't matter, can all be taken down with this as the hinge point, the eye level picture
plane. And it can be turned down and that
exact distance is the station point flat. And that
idea, because that whole thing can be flapped down as a hinge, we can get all the real angles
we require to our angle of vision because this represents us
from above. So I'm really here looking in. But also
we can be looking at ourselves in third person as well as in first. And I'll explain that in a
second. So, this view of the station point is actually the distance
we are to the picture plane. It's just that this is the top of the picture
plane and it's flat and thin, just like this picture plane at the top.
Up here is flat like a flat piece of glass. So once again
we're looking at both: into the picture
as the first person, like this. I am the first person in my own story
looking into the view. But when I'm actually looking at the flap down
and looking at the flattened SP person, me looking into the
picture, or us, I am now the third person observing myself looking into the
picture. But there is no height to it, it's just a flattened out
plan view basically of real angles going to my station
point. But that's exactly - in future diagrams very quickly, where we
actually get real angles to project into the perspective. But I wanna, I wanna be
really clear and not draw anything in this circle until we understand the perimeters
of this stuff. The reason I'm not showing really nice perspective
drawings or anything complex and look at this incredible perspective, isn't it beautiful? Yeah
great, but the idea is we wanna learn why this works.
And all we're saying is yes, I could draw a little mountain scape here for the horizon and the
desert and the salt flats of Utah, or rolling hills,
you know, a pagoda or something. Fine, we all know that, that's in the picture plane, it's the window.
Remember, the picture frame is the off
white paper. Fine, we all get that. That's pretty easy to remember. Like, I could look into this
picture and see any kind of view we want. What most people don't get is that
our actual position to the picture plane as a real viewer in three
dimensions can be represented equally by taking this flap and
making it two dimensional. And then, therefore, this station point we're gonna see over and over in our
diagrams, we'll explain it, we're gonna use it for the whole course. You can even use this
for fast thumbnails. You can do a window, flap, in these parameters just by freehand
and you will now, you know, you will make your pictures look much more real, much quicker because
you're actually using the real angles we actually see at when we're
standing out here. And it's really helpful. So, even though it's kind of an arcane point
I wanted to still keep this diagram blank and make sure you understood
that the real us, standing out here at the station point, with
the distance line going right between to the red dot
that is this distance again, can be abstract
and flattened out like an entire flap, down like this
to become that station point. And the whole flap can be carried with it because the
hinge point is the picture plane eye level. Why? Because that's where we are standing
from at the height we're seeing. Because we're the viewer, that's why it flips down at that point.
Ideally, all you have to do is have faith that it works and understand it generally.
The big thing is that it greatly helps us set up a picture really quick
even in casual drawing all the way to fully measured drawing. So
that is the explanation of the station point. And I wanted to make the point again,
if I went over it a little too quickly before, is that the
eye level, the center of vision, the station point, and the projected cone of vision
again are ours. We own them, they're always with us as I, you know, pointed out
before. No matter where we go, that package of four items is
always with us on our heads like permanent head gear. The rest of the
things we look at, like the horizon line, where the earth meets the sky. Mountains, trees,
cougars, gorillas, you know, architecture, whatever,
grass, clouds that move, things that float through the air,
at different angles, flying saucers. It doesn't matter. Those are all things that are part of the world.
not us. So make it clear to yourself that the eye level,
the center of vision, the station point, and the projected cone of vision are ours
always, the same way, always. The station point can change in our imaginations.
We can pretend we're way back from the wall or we can be an inch away, like an ant.
We can do anything we want, but the package is the same. it is the eye level, the
cone of vision, the station point, and the center of vision.
They're always together, they're always a package, like a periscope
or motorcycle helmet that has a cross in it and, you know, the station point,
however you want to think of it, please discern the fact that that is a package that we
own. Everything else, all the objects we'll be drawing, all the angles we'll be talking about,
all the other things that we're referencing to in the picture, invisible,
and vanishing points and other things that we go to and measuring points, that's all
part of the world, not us. So this is our stuff and then
everything else that we have not represented yet in this blank diagram is that
rest of the world. So I'm not really that concerned with that yet because my priority
was showing you our stuff. And our stuff again, eye level, always
center of vision, our station point now that we're gonna be representing
there. I no longer have to use this station point with you guys
because now you know that no matter what I want to project from my actual
head and what I want to pretend that I'm seeing from standing out here in this picture
can be equally represented now by that station point, because that's
me. We're looking from above and we've flattened the idea of myself,
standing the same distance as I am here, the same distance down
now, flattened out, from the picture plane. So I can measure all the angles I want
and that now represents and speaks for me as the three dimensional viewer. I have just been
flattened to become the two dimensional viewer. Why? Because we're trying to get three dimensional
ideas translated into two dimensional surfaces, just like the computer
screen, paper, murals, a large painting, whatever -
a sketchbook, as we mentioned before. So that is why that's
very helpful and certainly a great tool for being able to figure out quick,
correct perspective on the fly, as long as you have a little room. And as I said, digitally
at the beginning of the introduction lecture, digitally it's actually
easier to do this stuff because you can create all this room on a layer. Do a line drawing at
two hundred dpi, you know, close it out, make that your bottom later
and then bump all the resolution all the way up when you have all your measuring and your perspective
worked on. If that's what you choose to do. No matter what, this stuff is extremely friendly
to that as well. So okay, the next thing we want
to go on and talk about is framing. How do we decide
what frames and what context does that work in. So I'm just gonna continue with this
because I still think the best way to describe this stuff is with no subject matter
and it's almost like a blank stage at the beginning of the play. We're not starting a play yet.
Actors aren't coming out yet and the curtain is not gonna rise until we get a few
things clear. So I'm the little guy that walks out in front of the curtain and speaks
about something. So we're still at that for another few minutes. The
idea here is framing works in different ways. Before the
camera was invented, which basically becomes us. Like, we walk around in the world
as I talked about, with this package with us. The idea is
traditionally, even though we see like this centered in our view, because if I'm
at the station point here, looking in, you know, with my distance line
or I'm represented by the distance line to the flattened SP person
that we're looking at from above. That's, you know, that's the - we're the third person
now looking at that, where we were the first person viewer. If we look at the now
and say - okay traditionally you have to understand that when you look
at the world, we are in fact centered at the eye level crossing the center of vision
and the cone emanates from there. So that's in the middle of the cone, SP is a particular
distance that we choose, always relating to that same point. That never changes,
The reason all this doesn't have to be centered in a view is because
artists abstract the idea of having to be in the center and we don't
have to be. Because we're not moving in sequence like film, we can actually
make the frame for a picture any where we want. So I didn't center this white piece of paper
exactly on everything. As you can tell, I really couldn't
make it past my ceiling and I didn't want to go past here, so I just cut off the border here. So
essentially this represents now our frame, the paper.
Well that's a random choice. So the cone still continues up above
into my ceiling here and back down again, as you can see. So what's the point of showing it? We don't need to,
we just know it's there. That's all we have to know. The idea is, if this is our scene -
I could actually have a whole scene drawn out here. So let's pretend there's
mountains here, and a river, and little houses, and people running from something, whatever.
The idea is, no matter what that scene dictates, let's say that stays the same
No matter what that scene dictates I could actually only show this much of it.
Because if I'm Caravaggio or traditional artist of any kind in the past
I can just show you what part of the frame I'm gonna cut in and show,
choose to show you, the world or the scene through this. The
rest of the scene is still there. So what Caravaggio and other painters you like
your whole life, before the camera came along, and continued afterward in traditional
picture making. Before the camera or other than the camera, traditional
picture makers can choose any frame within the cone or around it they
want and just show the view of what is all there in that
little frame. So that doesn't change the world any, we just changed the framing. So the
traditional way that painters and book covers and commercial
art and horizontal and vertical paintings have all been done
is that if I want to do a horizontal painting and I don't want to show the one point vanishing point
which is always, by the way, at the eye level crossing the center of vision. Let's just say we're talking about a
one point scene generally. I might only decide to do a picture frame right
here as a horizontal landscape painting and I don't even show the one point.
It's just off frame to the right. And that's my
frame because that's what I choose to show of all this world we can see or I can
choose to show you, I'm only gonna show you, or choose to draw, what I
choose in this smaller frame. Or I could do a frame just off center here.
Or I could still be centered and do a very, very long vertical frame
that's very, very narrow and tall.
Again, as you can see my white paper frame happens to be a certain configuration
but it's not centered on this. It is, of course, only a little bit above here, and a lot
below here. It even goes below the cone of vision. So again, let's make it clear, the camera
can't do that. When you're behind a viewfinder and the viewfinder itself
is the only frame of reference you have in the movie theater or in
video games or in your home video camera or in your camera or anything that is
a camera lens, you have to be in the center of this
because the frame is always about being centered around those elements.
It's never not, okay. So that's the difference. We are too of course. Our view
in the morning when we wake up is truly centered on those elements. But we can
choose, because if we're not doing sequential storytelling with like
film, frame after frame, moving around things and they all, in perspective,
move around. In a movie theater you could do that, by the way. The camera shot you could
choose to blank out the entire movie screen except a chosen square.
Oh, you could show the whole movie like that. The film roller, the film
took the entire picture, but we decided to matte out everything for the
entire film. You know, it would almost be like some kinda cool hybrid art film
thing frankly. You know, Andy Warhol like. We'll choose to show only a little frame
for the entire movie and black out the rest of the screen. That's exactly what Caravaggio
all the traditional painters did. People that did, you know, all the way back to
the antiquity. That's what people were doing. They were just choosing
what attempt they were making of showing the scene. They didn't know perspective
back in antiquity but they had some mighty beautiful
sculptures. Obviously, they have beautiful tiling
work and everything and they were still attempting to do this. They were saying I choose
to only show this part of the entire scene and that's my artistic
choice. That's my conceptual choice of the human, we can make these abstract decisions.
So once again, traditional work, before we leave it and go to camera
film frames in a second. Traditional work could choose any view. I
could do a horizontal view right here. So part of my view could be
out of the cone of vision. Part of it could go way out here and come back. It doesn't matter.
It would be distorted out here as we mentioned, that's gonna be distorted out of the cone of vision if you're using
traditional one and two point, that being the horizon and stuff. Doesn't matter.
You can frame your picture - I don't want to beat this like a, you know, over and over
again but I want to make it clear because some people do not understand the concept of
why still art, non sequential art can just pick
any frame they want and just pick apart of the bigger picture in the cone.
That's what we do traditionally. So remember, traditional means you can make a frame
any where you want in and around the cone anytime you want, still showing a
full picture. That doesn't change your vanishing points. There gonna still behave, you know, the way
the scene is designed. The fact is you're picking a frame within it.
In a sense, when you're designing a scene traditionally, a lot of times
you really have to be thinking about this and knowing with your vanishing points should be or could
be or want to be so that you can an intelligent, interesting, creative,
framing choice. That's an artistic choice. It's part of the composition.
The very essence of design and the very meaning of it is that the frame and the border
and composition is designed into the frame as well as the interior picture. That's a -
obviously as you know from creating imagery, or if you don't know,
your framing choice and your proportion of frame is an artistic
choice as any of the others. That's why, traditionally,
still single picture paintings and such
are basically picking a frame wherever they want. So let's go to film.
We're now talking about a camera. So now since we can't divorce ourselves from
actually being in the middle of the viewfinder, just like if you picked up your camera right now at home
and walked around with and jammed your eye into the view frame, you can't suddenly just
move over, you know, to the side of the view frame. No more than we can divorce ourselves
from the cone of vision. And that's what I'm gonna talk about in a minute. There's a related thing
with movement with the cone of vision and why there's distortion on the edge that kind
of makes sense when you're talking about film frames. So, film frames
are stuck in the center of the cone of vision. But at different proportions.
So if we're using long box, we could be at a really telescopic
lens. Why? Because it only selects a little bit of the information because it's
scoping way into the picture. 50 millimeter in
lenses is about just touching in a three by four frame the edges of the cone
of vision. We're gonna go into diagrams, explaining this thoroughly, during the process of
lectures, but I wanted to get to it. Film frames, again,
they can be sixteen by nine, bigger sixteen by nine
huge sixteen by nine. We can do three by four.
Traditionally, larger three by four. All of those would
represent different millimeters. So the aspect ratio of course for the lens
is the sixteen by nine as opposed to three by four as opposed to two
point 39, which is real long box. All those are centered around here
but yet of different proportions. But they have to be centered both by height
and width around in the center of the cone.
The idea again is what do you choose? Now, do they
get distortion? We know wide angle lenses and film do. So again, really quickly to wrap up,
yeah, some of those film frames are so long they come out of the cone at the
sides, come back up, especially long backs, and come back out. We might be way
out here with our film frame when we're in a movie theater. So the
idea is, that's great because if you ever watch
a DVD just freeze frame it during some wide angle shot and you can clearly see the distortion.
It behaves very much just like your picture will distort if you draw outside the cones. It's the same thing.
So, just to hit this information home again and again,
there's different choices in framing depending on if you're doing traditional,
which you can put the frame anywhere you want around, or all through it. Or film,
where you have to start from the center and grow it out equally. But it can still be a
certainly different millimeter choices, which will make the framing larger or smaller,
centered within the cone. Or different aspect ratios, which we
basically again have traditional three by four, sixteen by nine, which is basic
television, and then long box theater is about two point three nine to one.
So, those are our choices. So that pretty much is framing.
It's important because a lot of people
get confused about this. So let's see if there's anything else I want to talk
about. Yeah, it's just - since we're on framing
let's just talk a couple minutes about composition. Since framing is
part and parcel to composition, it really is important that you've
figure out within the possibilities of what we're looking at here and what scene you could
create. Not only what you draw inside the picture and how you draw it
but what aspect are you showing it to in relation to these ideas
in the view. So a cinematographer using a camera for a film has
to be very careful because he has more restrictions on
a cinematographer, I should say it correctly, has many more restrictions on
them then the traditional framemaker because a traditional framemaker - we can
show an old album cover format that's a square,
we could show it halfway out of the cone as I mentioned, we can do anything we want. But the filmmaker
because of the low or short
vertical and long horizontal they're caught with, they
have real problems. They have to get way back to show someone standing at a party,
for instance, you have to get something like 22 feet back even to show a full figure
when you're in long box. Restrictions come into play, so a cinematographer
have to be even more precise about how they're showing it.
Setting up film shots is a real big deal. It's a lot of work because
they have to really think hard about these ideas. And by the way, these ideas we've been talking about:
the cone and restrictions and how we look at the world, those all come true for those people and
they have to realize those restrictions. Just like we'll be talking about them
when we're designing things that are more from a camera view. But mostly
we're probably gonna be doing more traditional because that's more the choice of an artist
or someone that's making a single view picture. So basically
to wrap it up, we'll be starting diagrams now that just
talk about these exact perimeters but we're gonna probably start with sketches, kind of at the
upper left of the page. Then talk about maybe the top view with no perspective
and then elevation, which is a side view. And talk about well what kind of thing are we creating here if we just make a
plan of it without any perspective. Then we'll start the diagram. So the typical routine
is gonna be, what do we wanna do? What set up do we have to think about? Are we
just doing simple reference figures maybe, then we won't use a cone and we won't use an SP and we won't
measure. Other ones we will. We'll actually get very into it.
But it will be all sorts of kind of thinking. But we're always gonna be talking about these ideas, even if we're
not actually drawing them. And this is the big - I think the big advantage of an
education is, it's the thoroughness of how people
understand concepts that's important. Whether you use them, or speak of them, or are constantly
referencing them, which you're not always, is irrelevant. The fact is that you
know all of it. So again, to wrap it up, for this kind of -
well we're actually gonna do some basic shape stuff a little bit too but it's kinda separate from this.
We'll talk about - in the next segment we're gonna talk about, you know, what is
one point and two point and how to look at a basic cube and stuff like that. It's real basic stuff but I want
to go over it before we jump into the diagram so we can still express
and, you know, in real terms and a real space what that means. But to wrap up
the definition part more, it's real important to understand that
again, when you're drawing and doing your work as a drawer or as a designer
you don't have to always refer to all these rules and put them in all the time.
If you just know what you're drawing to because you know perspective thoroughly
whatever you need is whatever you use. Just like that warehouse analogy. You can just do what you want.
But people that don't know it are limited, it's that simple. So
that's about it for the physical kinda of explanations of the terms. But
we will - we'll do a little bit of looking at basic shapes turning
and we're gonna put, you know, we're gonna put the camera actually in front of this, like where it would actually be
in view then for those and kinda look at some basic shapes. Okay, so
great, we'll continue on that in a few minutes. Alright, alright. Thanks a lot.
now we've reset the camera obviously so that we're basically having
the camera have the effect of being straight in front of the diagram where I was
before. It's a little further back, you know, I was about here, but
because of the way the lens works, you actually need to bring it farther back to see about the
same thing we were before, or I was. We're a little behind our own cone but that's
fine. I've also raised the ground level to this table. So we can consider the table top just like
a second ground level, or the ground level now instead of being down there
we're up here. And that means, as we discussed in the diagram before, in part
three, or in the previous lecture, physical lecture,
we now have the ground plane meeting the picture plane here
and we can consider this, you know, ground line meeting the picture plane
and continue on that way and this way to be a measuring line. And we could measure all this
and the whole perspective. Because what you're seeing here is very real to what, you know, we could do.
The cube is in front of the picture plane now obviously. It could also be back behind
it, we could go way back with other cubes back here to eventually they'd get so small near the
horizon line, eye level, we'd never see them. A whole grid could be measured, things could be brought
forward more into space here. We could do anything we want. So we're just having
a cube, an actual cube slightly in front of the picture plane for the same illusion to make some points
about how we know, and why we are in one point, two point, and three point
perspective now. So we'll use the simple object, the cube, to explain that.
And hopefully that will help you visualize, as we go into the diagrams, why we're looking
and seeing and talking about what we are. And also, if you get confused later, it would
be really helpful to probably come back to this idea. So even if we're in the middle of the diagrams
many, many lectures from now and you are still not quite understanding why something is,
it might help you come back to the physical lecture with a real object with me, kinda moving
around and acting out why it works. So that's the reason why we're doing it. Okay.
So this cube is in one point to you the viewer now so it's
all about you and viewercentric from the camera now. We're in one point
to the cube because this plane and the back plane aren't in perspective,
they're parallel with the picture plane and the sides are perpendicular. And
because the sides are perpendicular, the sides go back to that
vanishing point. Or should, if the camera was in perfect - in view, compared to this like a drawing.
These would diminish exactly and go back to the one point vanishing
point. Of course which is always on the eye level at the point of the center of vision.
So again, even if we had diagonals drawn across the plane of this cube, they would have
no diminishment or no perspective to them because they would come
straight down at real angles because this plane has no perspective. It's flush or
flat to the picture plane, or parallel to it. Same with the back, you know,
same with the table at this point as well. So again, that's why we know we're in one
point. So you could be looking at a photograph with many, many, many objects and
as long as you're identifying as many of them, or most of them, in your design, you want
to have this effect, that the front plane and the back plane and all those planes
are parallel to the picture plane then you know you're in one point. And of course, again, the perpendicular side plane
would be going to the one point vanishing point. Assuming that the things are flush
or standing on a flush ground plane. If they're tipping that involves auxiliaries, which
I'll explain in a minute. Secondly, we want -
it's important to understand that all verticals, when you're standing normally on the ground are going to
the core of the Earth essentially. They go way, way down all the way to infinity.
But in that case they're passing through the core of the Earth, which is important. So any true verticals
standing on a flush ground plane, perpendicular to it,
we can consider going to the core of the Earth. Which is important because it kind of embeds it in your mind
like, "Oh yeah, right, true verticals are always straight up and down, perfect, okay."
Again, this is - look at how foreshortened that becomes.
So imagine if you think there's really long squares coming toward everybody in perspective.
Look at how foreshortened this actual square is on the top plane to your view
of the camera. It's actually pretty foreshortened. It's surprising, the further it moves up
toward the horizon line, eye level, it will become more and more foreshortened until it
just disappears and becomes a flat line up here. So
we know we could get down a little further in our cone view from this and then this would become broader.
But again, the main thing is, if we know these are flushed to the picture plane and
these are perpendicular, behaving to this vanishing point, we know we're in one point. Or we
can create it so in a design. So, the odd thing about
when you go slightly into two point, sometimes it's better just to adjust your design
to be in one point. It can be a more powerful idea. For instance, this cube is no longer in
one point, but it's so close you're like, it's almost annoying what a tiny angle that is.
So if you draw things, or redesign them anyway, you know, from your own
artistic skill, your viewpoint, the way you wish it to be, you might decide that things
that are barely in two point might as well be brought back to and be in one point.
Because it might be just a stronger design and less confusing for the viewer if they're so close to
one point anyway. Another thing is, one point - we're still in one point
if this just slides back and forth and up and down. So if I go over here with this
still in one point and behaves to that vanishing point, and this still has no perspective.
If I slide it over here, same thing. This still has no perspective,
neither does this plane because they're still perpendicular and should be going to that.
No difference, we're just sliding it back and forth until it dissapears out of your cone or completely out of your frame.
Okay, that's important because
no matter what - or up and down by the way, I don't want to forget to mention that. As long as this is still straight
towards you in the same manner, it can go anywhere around here - ooooooo floating -
that's still all in one point and will still behave
to that vanishing point and be having no perspective
on this plane. Okay. So one more thing about one point -
well we'll talk about auxiliaries actually altogether. Let me skip that. Let's go to two point now. Why do
we know we're in two point? Because suddenly we're not in this position any more. So I'll turn it
slightly like this. That's not even. There's much more length
to the vanishing point to our eye level this way than there is here. This one ends up
about here. Why do we know they go to the eye level, picture plane,
or typically the horizon? Because we're still on flush ground here
and that means that their vanishing points for these planes
will end up somewhere on that eye level, on that
actual angle they're striking out toward it. The other one would be able here.
The interesting part is because this is a true 90, if we were looking from above like when
we have our flattened SP, you can project a real 90 at these same
angles as here. Longer, shorter, same angles
from your station point, that's the flap that we talked about last time
because that allows you to have these angles in your
picture, using the station point that's flattened out, will travel and strike the same
vanishing points this real object would. That's the whole point is, because the station - the flat
flattened station point that did represent this one, that has been flattened
like we talked about in the last parts, that will allow you to
take the real angle and situation this is to the center of vision
as a flat idea and project up and hit the same vanishing points as this actual
diminishment does, landing here and way out there. That's
why the flattened station point is so useful and helpful.
Okay, so now we know that
the cube can be turned more. So this is more 45 and 45, that's
more even, roughly, from your view. I'm just guesstimating. But then we could say
45 and 45s because it breaks the 90 in half. So now if we were to take it down to that
flat SP, or look at it, it's about even.
And that would be true when you project from the 45 and 45 from your station point.
Only meaning that you get a, you know kind of a centered look to your cube in two point.
Still flush with the ground plane, verticals are still all, you know,
they're still all traveling straight up and down. You can still move this over here -
over here real quick, we can still go up and down.
No problem, as long as it's still straight onto you at the same angle
and I haven't turned it like this, I'm just doing this, that will still
use the same vanishing points the whole time for the cube. Verticals
are straight down into the Earth and I haven't changed the direction of the
those side angle vanishing points at all. Okay. Turn it like
this, turn it like this, all different directions. I'm just turning it in different - to different
vanishing points. Which will in fact be closer and farther out as I change the angle.
So as I do this, those vanishing points are going way out there and then coming back, shallow here going way out
there. That all changes each time you change that angle. So we know we're in two
point when we no longer have any of the planes of the cube facing the picture
plane flat. We know we have true verticals if we're still in a flush ground plane but
now we know that these certainly aren't facing flush to the picture plane
or you, the viewer. Therefore, you have to lead
some way back to get a vanishing point. Way back here off camera to get a vanishing point because
the ground plane is flush again. We know those vanishing points appear at
the point of the eye level horizon line, okay.
Let me think. Okay we talked about moving it around. Again, doing this they stay the same as long
as they don't turn. So now let's talk about three
point perspective. Three point perspective -
we'll go back to the simple view of this.
Three point perspective now is when we're not changing our view at all,
we're just changing the object to us. But in a sense you can still describe the same effect.
Later, in the next segment, we'll talk about actually changing our view
a whole bunch, but right now we're gonna stick to this. So three point -
one point perspective - and as long as I tip this straight toward you, the viewer, because
we're perpendicular and parallel to the picture plane,
then what happens to the vertical, these which were going into the Earth
now. Let's just take it and flip it down. As long as I'm tipping it straight towards you
these same verticals now actually take and reach a
vanishing point way down or closer to for more severe, on the center of gravity
of vision. So less tipped, further down, they diminish to a
simple vanishing point, called a vertical vanishing point in three point, at the center of vision.
And more severely there'll be much closer up this way because these converge even
steeper and they come up the center of vision, closer to the eye level
in the picture plane. And again, very severely, they'd be very close, just below the table
if you did that. That is, basically, tipping down
and looking at the top of things which is typically called the bird's eye. Worm's eye
is the opposite. Now we'll tip it up toward this. Now the verticals are going up
and up and up and diminishing to a point above the eye level
on the center of vision line. And why does that vanishing point happen on the center of vision line?
Because we're agreeing to tip it straight up and down
like this toward you or away from you. We're not turning it yet.
That will be a different situation when we turn it. It would become auxiliary vanishing points
or slopes and inclines. Which is weird, they seem like the same thing but they're actually different.
Okay, so again: bird's eye from above,
tipping back, straight towards the camera, back toward the picture plane. Worm's eye
view, vanishing point for the verticals goes somewhat, or very, up or a little
up on the center of vision line to create a vanishing point - a vertical vanishing point
for the verticals. Okay? Now, we'll turn it like this again
in two point. Now, verticals going straight down
into the ground. Now if I tip this I have to tip it again straight
off the balance point of this front corner, straight toward the camera, or in the back
corner, straight back toward the picture plane in order to keep
the vertical vanishing point to keep it appearing on the center of vision line.
Otherwise it's gonna kick it out somewhere else and become something different. So I'll just try to
imagine these verticals are going straight into the Earth now. If I tip it
straight towards ya, without tipping this whole little table over, which
I'm about to, these verticals, all four corners that were the verticals
now, these four planes, go down to a converging vanishing point somewhere under the
table on the center of vision line, just like
they did for the one point situation. If I tip it back,
same thing. If I tip it straight back toward the picture plane, these vanishing -
these vertical still tip and converge to a point up there
on the center of vision. Again, so that would be bird's eye
and worm's eye three point with a simple cube. We're not changing our angle
of view, we're just changing the cube. So it's at a different angle of view to us, but we're
staying the same through this whole basic set up here.
That's inherently different than what we do when we have auxiliary vanishing points. And again, I
don't expect everybody to understand this exactly now. This is really for a reference
point when you get confused later or have questions and refer to other material, you can
go back to this physical lecture and say okay, how does that match up
with what I was talking about and physically demonstrating this in this same perspective set up
that very closely matches how you'd set up a perspective drawing. Especially when you include all the
this information. Then you can match it and maybe you can confirm yes,
I'm doing the right thing. Because this source here says it, a later
diagram might say it. But also, this confirms that kind of behavior. So
let's take the cube again, now in two point, and say
let's say we don't tip it straight forward toward the camera or straight back toward the picture
plane. Now if we're talking about these angles here on the
cube, if I tip it this way the interesting thing is, is that these
were going all to that vanishing point over there on the horizon line. Why?
Because this is a flush ground plane, the cube's flush with the ground plane,
and so therefore the vanishing point from the planes will go back
and hit somewhere over there. The interesting thing is if I still mark that
vanishing point on the ground plane and I tip this like this
these angles all converge towards a vanishing point that is drawn
directly under that traditional ground point, vanishing point. And that's called an
auxiliary vanishing point for inclines. And this in fact is a decline. So you could
say this is a declined auxiliary point. That's how that behaves, but if I
do this it's the opposite. You would go to a vanishing point that
goes up and converges straight above the ground plane vanishing
point that appears there because I tip it straight above that with a line.
These converge to a vanishing point straight above that on a line
called an auxiliary incline vanishing point. Okay.
Same here, if we do it in this direction or we do it in this direction. Then we'd come over
to the ground plane one over here. And if we tip it up or back the same thing happens.
If we went down, then it would go down toward here. And if we went up
it would go up toward the vanishing point this way. Same thing.
That's incline vanishing point. So again
down toward this, with a line below
it would be a declined vanishing point - auxiliary vanishing
point. Woah. Incline
somewhere up here. Incline, I don't want to tip the whole table over. So again,
confusing now, I know it's a lot of information but I only have - you know
I want to explain as much as possible so people can refer back to this
physical explanation in different parts. So it's not like you have to take the whole thing in at once.
You'd want to refer back to this lecture or this entire lecture one as
you need to when you come to areas in the diagram or other draw overs
this physical lecture of the entire thing parts one through five would be helpful.
Okay. So again, that's pretty much it. Let's see if I've left
anything out - oh we're gonna bring that little cylinder up here too. Also, draw a lot,
especially if some of you haven't drawn much than just draw a lot of different objects that are like rectangles and
things in still lives from all different angles. You'll really see these concepts
as we go forward with the diagrams and the more technical perspective. You'll see these concepts come
alive all over the place when you're drawing. And again, it's critical to draw from observation.
This lecture series is mostly about why perspective behaves, but again
as I've mentioned before it's critical that you're matching and pairing that with your physical
observational drawing skills and your knowledge of the world from that standpoint. It's critical.
Okay. So we'll bring - I think that's all I wanted to say
about the cube. Um, yeah. So
bring up the cylinder. And
the cylinder. Okay, so
if I brought this - look at how foreshortened that is as an ellipse.
It's flat up here, as I turn it obviously it becomes more of a flat
circle right up there. Turn it more flat when we bring it down. More
foreshortening. Also flat, flat, turn,
ellipse, ellipse, ellipse, straight on, turn. Real simple
stuff. We'll learn all about ellipses, technically how to create them, why they work, why the
illusion of a perfect oval with a line in the middle appears to also be a circle in
perspective. They're the same thing. We'll talk about all that stuff. But I wanted to make you aware of again,
be clear about the fact when you're trying to learn and construct ellipses in your
- kind of in your imaginary drawings when you make them up and try to construct them
or are constructing them, you know, think about taking an object like a soup can or a
anything and keep turning it like this and really draw from it to help you understand.
Where is the major and minor, why do they happen according to the diagrams?
It's very helpful to draw real objects and practice that way. It's pretty critical there. Okay
great, so next we'll just do a little bit of reviewing how we change
angles all over the world in an infinite way by changing our view
with the cone of vision and stuff as we walk around the room or spin around the room a little bit. So this, in this
case we change the angles of a single object and kept our view the same and didn't move
the camera didn't move. Next, we're gonna talk about how to be the station point
viewer and then move all over the place and then what perspective we'd actually be looking in
much as the same way we described what perspective we were looking in when we changed the cube
in a little bit with the ellipses here. Okay, alright so we'll see you in a bit.
we're just gonna review again, real quick. We're back in this
view but we're gonna talk about how to change our view in infinite ways and what perspective we'd be
looking at while we're doing that. So instead of looking at the cube before change
and the object changing in different directions to us staying the same in view, we're
now going to be talking about how do we change view. And I'll discuss as I'm in that view
what view we're looking in and why at all different directions. Because, again
if you're thinking of using perspective in a way where you can turn 360 degrees
around and around, up and down, and side to side, just like you're inside
this infinite sphere then you need to understand, you know, all the ways you can use different
things. So I just wanted to explain that briefly, it will only take a few minutes. But I think it's important
so that when you start feeling a little liberated by knowing some of the facts we're teaching in the diagrams
and some of the draw overs, you can understand okay, what if I want to get this view
in looking down here like in a comic book or if I want some drastic view here or I want
a really subtle view this way. Hopefully this would help you realize where
would I start with that view and what would it be replicating. So again to review
quickly. We have, again, we're always at our own eye level,
our own center of vision. We're always at our own SP
and the flattened SP now represents us here, is now represented
there like we talked about before. So again, if I'm standing the correct distance away from
this particular illusion right in front of it, that same station point down there
and on the flat wall there's a flap coming down, represents those same -
that exact same distance and idea of me standing there with a real projected angle.
And of course, the cone of vision is my field of distortion
and that doesn't change. What we're going to do now is talk about a lot of different changes.
So for instance, why is it when I look into the world I don't see
distortion? If I look over here quickly that's not distorted, that stuff in the corner, or way over here or
anything like that real quick. Why is that the case in a single? Because in a single view on a two dimensional
surface of course. In real like each time we change our center of
vision rapidly or our eye level, we're actually like this. So let's say I'm
saying over to you by the camera, this stuff in front of me is not distorted
but you are actually, I just can't see over there. By the time
I change my view to you I've changed my center of vision and I've changed my eye level
so instantly I'm refocusing on things that are always in the cone.
So we can't escape our own cone of vision. It's always right in front of us. So no matter how
fast we turn our heads to say I can't see any distortion, I can't see any distortion,
what are you talking about when there's distortion out of the cone, I don't get what you're talking about.
The idea is we can't see it in front of our own eyes, because by the time we change the view
fast enough we still repositioned again our own cone of vision,
rapidly as we change view. So that - we can never escape it. So that's why that happens.
The distortion happens because in a single point of view
on a two dimensional surface that we can back away from and view our own view,
it's gonna get distorted at one point. We just can't see it because this peripheral
is about how much we can really focus on before we have to change our view.
And by that time, again, we've changed our cone of vision, we've changed our station point
and direction and we've changed our eye level and center of vision. So, because of that
we can't see the distortion. I just wanted to make that clear. Okay, so let's start out
here in our traditional view, where we were before. That's our station point
straight here, there, and represented down there.
How else do I look around the world in this same view without changing my horizon
line eye level? Let's just say I want to maybe step back,
go forward real close, but in particular get out of this view. How do I
change it? Well, if I go ahead and look with my center of
vision and my eye level and I change like this. Just rotate like this
of course I'm carrying this whole set up with me everywhere I go. So I can have a
infinite view of the horizon all around me, just like when you're standing in front of
the middle of a field. So obviously that's easy to do. So
that's pretty easy to understand. And of course, any new angle I strike
the fixed objects around me if that's the case. Let's say I'm in a fixed environment,
they all change perspective too like the cube was just doing in the last part. So you have
to consider not only how our objects changing to our view angle, but how
you've changed your view angle too in relation to the
environment around you. Now you could do a blank slate and say, no, no I'm just doing this out of my imagination. Then I
I'll do it. But you have to have reference points or else all you'll have is this blank which
really doesn't mean much other than reinforcing the rules of what we have as
our - what we own in the world. And remember, like we talked about, all that other stuff
is part of the world. This is ours. So again, if I'm looking over here and then
suddenly want to look over there, I'm still in one point - I mean I'm sorry,
I'm still in traditional one and two point because the horizon hasn't changed like this. That's
normal, I'm looking straight out in the world like this. That doesn't change.
But everything else around me changes going from one point, two point, maybe
even three point depending on if an object is tipping. So keep remembering
that when this moves with us, which it does, if everytime I move this
entire set up and the station point, being here, represented by that
all moves with us exactly, because it's always exactly parallel and
perpendicular fixed right in our center. It never is not. Okay, so again
pretty easy to see that. If I change this again in a rotation
anywhere I look is always going down me. So we'll discuss three point now.
Actually no, I wanted to discuss looking down straight in one point.
I eluded it to in lecture one or two but I'm gonna do it again.
Let's say you say I want to look out here. Okay, I no longer - I wanna
be in one point, there's a city coming out of the ground let's say, or a lot of objects that grow out of the ground.
I don't want to be in one point perspective looking out this way. I wanna
look straight down into the ground like Superman flying. Well again, if I - my picture
plane suddenly goes from here, traditional, looking straight down, what happens is
all the tops of the building, if I'm situated correctly, are still going this
way and this way to me. That's rather obvious if I
situate myself, but now the verticals are the things that are diminishing
to the one point vanishing point. Because my view if I'm in a true one point, looking down into the ground,
my vanishing point is the core of the Earth. The one point vanishing point
has to be the core of the Earth if you're truly looking straight down, like Superman,
at the Earth. It must be. So going from here to here
really has to be your one point center. If I turn my head like this to those straight
up buildings coming forward and do this or this
just to the side, I suddenly turn it to two point. So again, traditional
one point into the horizon. Let's just say I'm looking at a whole bunch of things in one point this
way. These things are still perpendicular and parallel to my
situation, but I turn straight into the ground. I am now looking
straight into the core of the Earth with things coming up toward me, going to the diminishment
of foreshortening. And the other planes are all going down, it's
width and it's height. But if I turn it like this,
or swing it like that, suddenly I have those same buildings that were coming up straight to me
kind of in a one point situation, now have turned and are in two point.
So you can easily do one and two point perspective of looking straight down
into the Earth, with can be a really effective thing. Happens in comic books a lot and stuff like that, but you still have
to understand: the entire set up and all the rules are completely
carried with you the same way, they just are carried 90 degrees down from
that view to here. So zero, ten, twenty, thirty, forty, fifty
sixty, seventy, eighty, ninety. Ninety is straight down.
Zero degrees would be us considering ourselves not at an angle - at a down angle - but we're
looking straight into the horizon. Ten, twenty, thirty, forty, forty-five, halfway,
fifty, sixty, seventy, eighty, ninety, straight down.
And that explains a down angle basically, if we're talking about in degrees, okay.
We're considered with one point and just being either here or at
ninety straight down. Anything in between is three point. Also, another way
to look at one point, if we go from here and then suddenly, looking out here,
we're going okay, I want to carry that with me, I want to look straight up into the sky
and everything changes and becomes the same. All you're saying is that buildings that are coming
way above you are still acting in one point. Just like towering - if you were in the middle
of the tallest buildings in New York, those towering buildings would be moving away to the ones
point vanishing point. The one point vanishing point now that would be in the sky of course,
straight above you and everything would be diminishing to it. But you'd still treat a lot of the other
side planes of the buildings the same as you would in traditional one point.
It's just that the objects are doing different things because now it's the verticals that are going straight
toward the vanishing point if you were looking straight up. That would be the difference. So play with these ideas.
Don't just sit here and listen to me and go, "Okay this guy says that, okay." Go ahead and
play with the drawings. Formalize them and just do little careful drawings saying, I'm lying on my back
at a picnic, falling asleep, and I'm looking straight up at these tall buildings that are right next to some
trees because the buildings have true verticals. Go ahead and draw some of those scenarios.
Okay. Same thing as you spun, if you were at that picnic
and then you turned your position on the blanket, looking straight in the sky, then one
point would then turn to two point in that case because you're no longer
straight and you'd have to tilt your head. So essentially you would imagine if you were to be looking
straight up at the buildings, turn a little bit if you wanted to, but then cock
your head this way or that way it would suddenly turn into two point. It gets confusing but if you work
it out using these elements and carefully thinking about the rules, you can
actually work out a pretty - really involved view once you're
head kind of snaps around the confusing angles and it works. So one point looking
straight out, looking straight down, or straight up follows the same rules.
And same when you cock your head this way or this way will be two point. Looking straight up
two point, one point, two point, two point.
If I am looking at one point at my wall in my room right now but I cock my head this
way, only straight over, I suddenly am drawing it in two point. One point
wall, two point corner, wall. Okay, same thing. Looking
straight down, two point, one point, two point, one point
two point, two point. Same thing, okay. I know it's weird and annoying
but the physical explanation of this is a hell of a lot easier than
doing it on a page sometimes because we're really looking at it. Okay, so
if we're kind of covering the complete spectrum - so remember if we're some
kind of huge hamster ball here like a giant sphere, then we've already covered
looking all around the horizon in traditional one and two point like this, okay.
That's been done. We've also covered - turned any angle in that sphere and
then looking straight down or straight up, so that's been covered. And then even
straight down cocking our head like this, we're no longer - we're at an angle and at an angle.
But because we're looking straight into the Earth or straight into the sky and just sliding and
sliding we're not particular going into three point yet. How do we know we're in three point?
Well let's rehearse that now. We're in two point
as we discussed, standard two point, one point, two point, one point
two point, one point. Any angle that is between zero and
ninety and zero and ninety looking straight up is technically
in three point perspective. Therefore, if I'm just two degrees
down, technically there'd be a tiny diminishment to verticals just like we saw with the cube.
But instead of the cube now, that was tipping forward before, now we're
changing our angle to the world. The world is not changing like before. We were taking an object
from the world before that was the cube and tipping it. Now we're saying
the world isn't changing, our view is. So I'm traditionally in one point
like this and then I look down ten percent, twenty
sorry not percent - ten degrees, twenty degrees, thirty degrees, forty
degrees, forty-five - forty-five would be right between ninety. Halfway between
these two angles would be a forty-five degree down angle with my picture plane.
Ten degrees, twenty degrees, thirty degrees, forty degrees, forty-five,
fifty, sixty, seventy, eighty, straight down would be ninety. No
longer in three point. Zero is no longer in three point, ninety is no longer in three
point but eighty, seventy, sixty, fifty, forty, forty-five,
all the way to ten is still in three point. Go back to zero, you're in traditional
one, two point again. Same thing when you look up. We're not in
perspective now, but ten degrees up, twenty, thirty, forty, forty-five, all the way up
to eighty, we're way up there at eighty and we're in three point but then we would
go to ninety, we're suddenly in one and two point again. So it's kinda weird but think
of yourself as existing in a giant sphere and those simple angles
changes allow you to understand how you draw things. I understand you have no idea
how to approach that yet, but with the methods we're gonna cover in the
diagrams, along with these very clear thoughts of being inside this kind of giant sphere, it becomes
easy to actually figure out from oh, this corner of my room or
that part of the city, how do I put that into a different view than I'm seeing. I want to be
underneath that stuff and looking up. Well if you can kinda sketch out the stuff you want to draw
then imagine what it might look like at a different under angle, we'll be able to
show you, real easy, how to draw some of those three point angles to
figure out your real, your real
down angle and up angle, your real degrees to the world. That part's easy actually with the measuring.
It only takes like less than a minute. Very, very fast. The hard part is to keep
the visualization going well so you understand it.
So remember, it's not just the angles that can be confusing, that
part actually if you step it out goes very well. The important part is that you realize
that if I want to measure myself in three point with this set up, you can do
it easily. Saying I want to be 47 degrees down angle for some reason, like an
exact camera. Easy to do in three point, but you have to be able to visualize
what and why you're carrying into the picture compositionally. So again, composition
is the most important thing. Not only do you have to figure out the view, you have to figure out how would I
block out an interesting composition at 47 degree angle, down angle
looking into this picture. How close do I want the corner of the building?
Or the person walking down the street or the corner of the scene and looking into it. That all
is a lot of working out compositional variables. So all we're talking about
here in this last segment quickly is variables. These are all variables
of view you could turn around in a real environment. And when we're talking about going into
one point and two point straight down or straight up, those are all variable ideas you could bring
to the table for composition. As well as every single one of these little
rotations like this, all have that complete variable of all the three
point angles in between the zero and the ninety and all of them going up. So
it's a huge amount of selection you have to go through if you really want to do different
angles. But again, once you understand the perspective and can kind of play around with
thumbnails, kinda throwing these ideas out on thumbnails, within a few minutes you can actually get
a really great view that's really quite complex. And other people might just say, "You know, how did you ever
with that, how do you even know how to draw to that?" Well people figured it out hundreds of years ago.
So again, to cap off the physical lecture I guess, the big, main point is
this stuff, most of it was proven and figured out five hundred years ago,
three hundred and fifty some of the harder stuff. You know, the proofs kept coming as artists
and the mathematicians figured out the angles and stuff. But what we're left with
luckily and happily is a lot of the institutions across the world
in the early twentieth century, kinda got all their stuff together.
Architects and stuff and a lot of this stuff has been common proofs that have been kinda translated
by a few people and I was lucky enough to have one of those people as my instructor
and a few other people around the country obviously. And that kinda culminated into
rediscovering and retalking about these ideas, which are fully measured three point
which allow any camera angle you want. Not just one and two point. So the good news is,
I'm excited about passing this stuff on in very simple form and
all the way to complex measuring to everybody. So as many lectures as it takes, that's what I'm gonna do.
Alright, so let's get to the diagrams now. We're pretty much done with the physical explanations
lecture part and we're gonna go with some - mostly
some diagrams next and then eventually draw overs and all that kind of thing. Okay.
So we'll see you in the diagrams I guess, alrighty.
we're here with this diagram again and we just wanna review everything
before we start. And I'll start with the tools actually before we go to the diagram just
to familiarize. Here's a T square. Wave that across, standard T square.
Over on the side of my table. Alright.
This is a 45, 45, 90 triangle.
45, 45, 90. Transparent is always good
because you can then when you're making alignments you can see not only above and below
but through the triangle and the plastic. Very, very helpful, much easier.
There is a 30, 60, 90. So a 30,
60, 90 triangle we have to have as well. So there's that.
A protractor to be able to gage
angles from zero to 180 and determine
a lot of actual degrees of angle in
perspective obviously. I like
these mechanical pencils and they sharpen by twisting them
and grinding them in this. But those are great, they stay really
sharp and they're great. So that little spinner actually spins.
Okay and as I recommended
also, the two sided red and blue Prismacolor Verithin
So you can find those - these are real handy too to do the color.
And my old brush when I was 14, still have it for sweeping
away any erasers you have. Real easy. So pick an old favorite brush.
And you got that. And typically just
kneaded eraser and a Staedtler Mars kinda white eraser if you really need to get hard on it if you make any mistakes.
and stuff. Okay, okay.
Let's review, we've got our picture plane as we've describe plenty before. I just wanted to make sure
we're all on the same page again. We're not gonna really do formal diagrams at first
after this one, but I did want to make the point that I just wanted to review and
look at the tools. Picture plane as we know. We're standing here.
We're a particular distance away and that distance
projects that cone of vision. So there's the station point, there's the eye level,
horizon line, there's the center of vision line and the center of vision point in the
middle. We have the distance line from the actual station point viewer.
to here. But we also then have the station point
that's down here. And if we want, we can actually put in
the fact that this goes from here and we'll do that
right now. Slowly turns
and goes to there. Oops, of course I broke my lead.
So there we go. So that's
the actual station point going down from its original position from the
eyes all the way down to the flattened station point we talked about so much.
Then of course we have our ground plane and we have our ground line measuring
line. So you can measure real horizontal widths
right there on the picture plane, if you want to imagine. And this is our true height
measuring line where you can do real height. Anything behind that space
will have smaller scale. Anything that's giving the illusion of coming forward will have
larger scale to those increments. So only those increments are only true for
whatever you designate them as on the picture plane. You can slide all around the picture
plane up and down, side to side, and you won't gain any size. Once you
wanna go into deep space or out toward the viewer you'll gain size
or lose size as you go back. Again,
the cone of vision of course is 30 and 30 on each side,
projecting to these points, which you clearly saw in the diagram and, you know, in real life on the wall with me
with me in front of it. And then it's a total of 60. It also goes down to
the bottom and the top as well because it's a cone. It's actually, you know,
all the way around. What else? Anything else, oh yeah and
this is your distance line as I mentioned but this is the other distance line of course, down here.
And that's about it. You've got your ground plane, you've got your real station point, you got
your flattened station point like a flap. So again, this whole thing falls away
like a flap and continues. And that's about it. So we're gonna get into
some simpler ones on referencing now. Diagrams on referencing, reference point,
and scaling size and perspective. Okay, alright. So we'll
dive into that right now.
This time we're gonna call this one diagram two and what we're gonna do is
we're gonna reference three figures that are the same height but they're in different
parts of the picture plane. Meaning, one's gonna be further back, one's kinda in the middle, and one will be
forward. And we're gonna talk about how to do that with reference points. So this is about reference points
and achieving things of equal scale in different parts
of the picture. Okay. So I'm gonna start out with a basic premise. I've already driven -
I'm sorry, driven - drawn a horizon line. So I'll call that the
HL over here. That also happens to be
my eye level because we're going to be one and two point for quite a while.
So at this point the horizon line will equal the eye level.
We're not gonna bother setting up the cone and all the other stuff we had in the physical walkthrough
yet because we're gonna get right to these really simple breakdowns of referencing and
and scale in the next few diagrams. So we're just gonna forgo that and just
deal with direct pictures like you would when you sketch. But we're still gonna use T squares and triangles and such
because we want to be precise and make sure we convey exactly as to why - how we do this.
Okay. So the premise is, it's your composition and you might decide well
I wanna figure kinda standing in the middle of somewhere
like maybe right here. So I want
one figure that big. That's a purely random compositional decision. I wanna start there with
a figure. You might be supposing because that's where you want it compositionally because you have a frame worked out
and it's proportionate and everything like that. So I'm gonna go ahead with my T square
and I'm gonna go ahead and put a little base
and a little height for that figure.
I'll draw my little midpoint there. That pelvis, a little waistline.
I'll go ahead and put in a simple head.
Kinda sitting in pockets there,.
Draw up some legs, some simple shoes.
Very, very simple diagram.
Alright so, we have figure A.
Figure A could be seven foot tall, five foot. Let's just call him five
eight or this figure five foot eight. The idea is we're replicating his
height with different positions on the picture plane. So figure A.
Now I say, well I randomly want to put someone over here that's a little
further back. I think about here feels right. So I'll go ahead
and say I want them only being
smaller being here. I can't decide their height because I have to reference that.
So I'll go put their base on, just like I started with the base of figure A. I'm gonna say
this is where base of figure B is gonna be. I'll go ahead and make it official and say
okay they're standing right there on the ground. I'll go ahead and put with my triangle.
I'll go ahead and put an absolute vertical just for the heck of it. Remember these lines
that I'm setting up for you are all cobweb thin and
basically invisible and very light ticks when you draw. And then of course you do your drawing style over it
or whatever your art is, your painting, it doesn't matter. I'm making it very, very clear as a
lesson obviously, to make it a good diagram. So
there's the vertical, we don't know how tall figure B will be quite yet in that space
yet until we do some referencing. So now, because I already have established figure A
I can simply reference B off A. And we'll start doing
that together. I'll pick my red pencil up and I'm gonna go from the base of A
through the beginning base of B. Even though I set B randomly and I set A randomly
now I've got some things that will actually help us.
So base A through base B. I'll go ahead and draw
and that line will lead us to what's called a
reference plane on the horizon line. Reference point I should say, excuse me.
We'll call that reference point number one.
And that's possible because this is a flat ground plane and
because the horizon represents the infinity of the ground plane meeting the
sky I'm gonna make a plane that goes on between A and B and then goes on
forever. And that becomes a reference point. It's actually a vanishing point but we'll call it a reference point because
that's the purpose we're using it for. Now, how do I figure out
what the height would be, which is the goal. We'll I've already got established Figure A and I've got
Figure A's height. So I'm gonna from Figure A's height with my red pencil again
and I'm gonna go ahead and pass through the vertical plane of where B
wants to be from the height of A to the reference point. All three of those points.
So here we come down. Arrow
going to the reference point, where that line cross the
vertical, where I want B to be, will represent their height. So we've just go the
height, the proper point of figure B standing that far from figure
A in the picture plane. So now we can go ahead and draw figure B in.
Top, bottom, about halfway point for the top. About half way point for the
pelvis. Go ahead
and draw slightly smaller head in.
So again, these figures are standing straight up. If someone was leaning over you'd probably take their real standing
height and then you'd have to then proportionality go less for if they're doing something else.
But you're standing with a full standing figure at its full height. It's easier because then you
can proportionality make that person smaller depending on what action they're doing. So now we've got
a real figure B, a real figure A. They're both the same height as each other
they're just standing in different parts of the picture plane. And that was done by
referencing. We first established the base of A through the base of B
after creating the area we wanted B to be in
and we made a reference point. We then came back from the top of A to cross the
vertical that was unfinished of figure B to the reference point. That gave us
figure B's height. Now we're gonna say we want to add a
third person of the same height of these two people. I'm gonna go alright -
I'm gonna do it somewhere over here. It's gonna be larger, they're gonna be further forward than
either figure A or B. I don't want to put the person compositionally
really dead even with them right here. That would kinda create a pattern or a tangent
I wouldn't want. So I'm gonna put the figure a little closer so there's a smaller gap in between these two.
Something like that. So I'll just sketch that idea in. But let's see. How much larger do I want
them? I dunno, maybe quite a bit large. So I'm gonna say that's the basis
of C right away. Just say okay, I wanna figure C sitting there. Let me go ahead
and put in the base officially with my T square just to be official.
Then I'll go ahead and use my triangle to draw
their vertical. And I'll go way further than I need to, or that I think I need to.
Same idea now. How do I get the height of C? Well I could
reference through A and go way over here if I want to. That's pretty far,
that might be off your page. So, since I already have established B that's also
the correct height for a figure at their position, I'm just gonna ahead and reference C
through B instead of A because it's more convenient. I could do this but it goes out here a bit.
But just for the sake of good practice, I'll say I'll pick the most convenient one
that's in the picture. So I'm gonna take base C through base B to establish
reference point two. I'm gonna do that with a blue pencil.
Base C through base B
another reference point on the horizon into infinity. And I'll call that
reference point number two. Okay.
Now, same thing as we did before.
How do I establish the height of figure C? Well
I already am referencing the base of B, now I have to reference the complete height
of B to get it. So I go back from the reference point with my blue pencil
through the head from the reference point
to create the height of C. I'll mark there with my blue.
And there we have it.
So I'll go ahead and mark what I think is about half way down again. Something like that.
Waistline might be there, I'll make the head bigger this time.
I'll go ahead and make the shoulders.
Draw down real quick.
Arms in pocket again.
There is figure C which would be the same height
as figure B and A. And I've done that with another reference plane, but I had to
start out with the base of C and go through the base of B to create the first line to make the
reference point two. Then I could come back from reference point two through the total height of
B, which was already established to mark off at the vertical of C
to get the height of C. I create effectively two planes
that you could imagine are made of Plexiglas that are tinted a color. I'm gonna go ahead and
let anybody catch up that's behind. I'm gonna go ahead and tint in the first
plane we put in to get A to B referenced.
Real simple shading, no big deal, when you go back later -
remember this is about you guys drawing and taking clear notes from what I'm
saying so please be pausing the lecture occasionally to write down notes down
here in your drawing or in your own way that
make sense to you about the process. That's why I'm going to repeat it even one more time before we
leave it so that it makes it clear. Alright, because it's easier for you
to pause and write and for me to just make the points clearly, verbally.
That will get us to more material, more quickly, for more complete lecture
series. Okay, there's that plane that I was talking about
going from A to B to the reference plane. It's like a standing, thin Plexiglas plane.
And now I can do the blue one overlapping that one
And I'll just do it lightly so it doesn't get too confusing.
But these are where those two planes overlap.
Okay. And I'll go ahead and darken up
figure B a little, trying to get out of your way here
with my head. Alright, there is B.
So, once again, we wanted
three people standing in the picture plane at different distances from us, the viewer. And I wanted them
to be all the same height. How do I achieve that? I established A, compositionally saying that's where I want A
I then said okay, there's A, I want to now create B
I put the position of the feet only with a vertical only for B because I had to make
a reference point from A's base to B's base to make reference point one.
Come back through to A's height and I get the height of B. Now I've got
two figures, totally drawn out, that are in proportional height to each other
depending on their position in the picture plane. Then I wanted to create figure C,
I made the base, made the vertical. Decided instead of going through A way over here,
we decided to go through B. Base of C, just made it up
through B to make reference point two. Then, because B was already
established, I could come back from the reference point two, to
the top of B's head, which was already established to strike and make
height of C. even though we just started C at the bottom, we couldn't get their height until we referenced
it through figure B. And that's basically it. You can do this all day long
essentially with many different ways. Objects, trucks, cars,
anything. Trees, it doesn't matter what you're drawing as long as they have height, width,
and volume and space, you can reference one similar sized object at the same angle
to you to another all day long all across the picture, anywhere. Rise them up
and rise them down. As long as they don't come forward or backward, things
stay the same size. The reason these guys are different sizes is because they're at different
points in the picture plane. They've come forward and they've gone back. And that's why we needed to use
the reference point system. Okay. Alright, then we'll get on with some other diagrams
now. Alrighty, okay.
we're going to use a constant eye level at three feet,
that's our height at the picture looking in at things.
So we're gonna have a three foot eye level.
Horizon line, three foot. That will help us
in gaging where we want people at various points forward and back in the picture
plane how to gage their height properly and quickly. So just remember
we're always at three feet, so this line not only is behind
representing the ground plane meeting the sky in infinity but it also
can be thought of as striking across and in front
of people to gage how tall they are. So we'll just start and I'll show you what I mean.
Let's say I want a six foot man here. I will then
randomly assign that person, you know, where I want them to be.
Let's say here.
I want a six foot man standing here. That's where they're touching
the ground. And I don't know
how high they are but I'll put in an official vertical just to be clear.
So now I'm gonna stick a real vertical up, longer than it needs to be. So
this person is supposed to be six foot tall and I know
that the eye level is at three feet. That means it's gonna strike this
person right there at the three feet mark on a six foot man, which would be right around
pelvis height. So I'm gonna divide this evenly into three.
That's critical because this is the ground.
Ground. That's where that
is. And I'll go ahead and use my red pencil to make it clear
that this is three feet.
Okay, then I have to add because he's six feet tall.
So now ground up till the point of the eye level, striking at three feet. One, two,
three. One, two, three. And add another one just
approximating. Four, five, and six.
Let's just estimate. Yeah, that's about right.
Okay, so that's six foot knowing that from the
ground - I randomly picked that ground placement compositionally that's what I wanted
then I can go up and reach the true height by one, two, three,
four, five, six. So I'll go ahead and draw the man in.
About pelvis height so you can say the waist might be
something like that. Shoulder.
Real fast here. Hips.
Feet, real simple.
Hang around with arms in the pockets.
No big deal.
Alright. So that's our six foot man.
I'll go ahead and use my blue pencil.
Say, six foot man.
Next I'm gonna have a five foot woman.
She's gonna be standing slightly in front of him though. Kinda close.
So again, I'll make an official vertical just to make it clear
it's a diagram. But again, all these really
clear points I'm making are invisible tiny, light lines when you're setting them up.
It's just the idea and then sketching. But we're making them very official.
Formal. So everything is clear.
So that's the ground again. Just abbreviate it.
Once again, we're left saying that's three feet even
though she's only a five foot woman, the fact is she's standing further forward
so let's see where that puts her. We have to rescale the three feet though.
Only at this point of the picture plane is a foot this large
as with the man because he's standing at this point of the picture plane. These are flat planes.
As they come forward they become larger in scale and
as they go back they go smaller in scale. So she's got large one foot
increments because she's further forward towards us. Therefore,
we have to carefully kinda say okay, is that about right?
Yeah, that looks about right. And then I have to add two more.
About like that. Yeah, that's about right. So there she is.
that's a five foot woman's height. So she's coming forward toward us, since we're at a
lower eye level at midlength, if she comes forward and she's shorter at the same time she's gonna end up
not being as big as the man. So five foot tall, let me go
make my red pencil mark to make that clear that that
the important part is the three feet horizon. And then we have.
the important part is the three feet horizon. And then we have.
One, two, three, four, five. Just like we had six
here. Okay. So I'll go ahead and draw her in real quick.
Get the feet in there.
Alright so the idea is
we've got a
five foot woman.
Now we're gonna have somebody even smaller back here. Let's say right there.
Not sure how far back, maybe
this far back, way back there. Okay, I'll make a little vertical just to be official.
And let's say I haven't made my mind up
yet, I'm like alright whatever I want somebody compositionally but you know, alright
okay that's a four foot child let's say. So now I do the same routine now.
Now it's gonna be even smaller scale because this person is standing even farther back in the picture plane
therefore demanding a smaller scale to feet. So
she has the largest scale so far of feet. He's
six foot tall but has a small scale to feet because he's standing slightly farther back in the
picture plane. Now we're gonna have four foot child. We still have to do the
increment guess like this: one, two, three.
Then we'll continue with one more for four.
That's about right. Okay.
And we'll draw him in.
Alright, so that's - he's got a bigger head because
he's a little person, pretty small. So let's see
that goes down with the feet.
Alright, not that small but either way, you get the idea.
That is a total of a -
mark the head of everybody, get my head out of the way.
Okay, so that is a four
foot child. Farther back than
any other figure. The woman and the man are farther forward.
That would be a four foot child. Let me make their ground really clear. So that's
just to make it official. We'll definitely say remember that's the
this point of the picture plane. So that scale is only appropriate -
that scale right here is only appropriate for one, two, three feet way back there.
Three feet is larger here, a little smaller there. That's the way it goes.
So that's important. Okay, next
let's have something smaller in there that's standing again forward again, but not quite as forward
as the man. Let's say right there. We'll go ahead and put that
somebody over here.
scale would then be divided by three
because we're going to three
at that point of the picture plane.
Three foot I should say, so there we go.
Three foot, but that's scale slightly bigger than with the child, but not quite
as big as these two because it's between them. So the scale is somewhere in between
these two groups. Okay that's gonna be like an 18 inch dog.
So let me mark it off with blue and say, okay, we can say that
18 inches is one foot
two foot, three foot, is one and half feet. That'd be right there. So I'll
carry that over.
Some sad looking dog there.
Okay. That's 18 inches, so
an 18 inch dog.
But further forward than the child but not as far forward as the man and the
woman. And that's at 18 inches because again, we carefully counted increments.
One, two, three. We could keep going but we don't need to because the dog
is only half the distance to the eye level.
Okay next, let's have someone that's really tall, that's even taller
than anybody. There'll also standing more forward.
Oops, paper adjusted there. Okay
here we go.
I'll have even a taller person standing a little forward from everybody, even the woman or
the man. Right there in the picture plane. And I'll go ahead and put that person
vertical in. Okay.
So again, this person's gonna be really tall. Seven foot. But we're still gonna divide
at the scale and take a guess, something like that.
Right. And then I'm gonna keep going and add feet.
And take - that's three and add three so that's about right.
That's six. Must carefully point that out. One,
two, three, to the level there. So I'll go ahead
and point that out as three feet. But this is the largest scale. Let me go ahead and write
ground under here, ground
under the dog, and ground under our large person.
Okay. And we keep counting. One, two, three, four, five,
six, oops we need another foot. Let's see, hopefully we'll fit on our paper, we should.
Okay, about there. So that should be seven feet. So let's draw
in somebody. So, three and half would be
about pelvis, so waist would be something like there.
Alright, so this is a pretty tall person.
Okay. So that is a seven foot person
that is standing further forward than anybody.
Standing further forward than anybody.
So let me clear the diagram. So to review one more time. We randomly created a six
foot person and said I want them standing there. And
because of that I counted three even increments up and split it into three
and then continued that scale. That scale is only valid at this point of the picture.
Our eye level strikes the man right in the middle because he's six foot,
three foot being half. Next we have, standing forward from that a little bit
is a woman who is five foot tall. So we have to strike one, two, three again to the
eye level then add one, two, and get her height properly. Then we
say compositionally I desire to have a small child or somebody standing back there
The child is - not that small - four foot child standing that far
back. So one, two, three, up to the eye level and then one more is four. So there's
a four foot child standing furthest back in the picture.
Next, we decided to come forward again a little bit and have a dog
standing there. I just made a little reference plane off to the side here. We still had to
count one, two, three back to the eye level, but we didn't need the three feet,
we cut it in half because the dog is only 18 inches off the ground, it's a pretty small dog
So that's an 18 inch dog this far away. And again that scale is only
appropriate for this part of the picture plane. This scale for the child
only at this part, this scale for the woman only at this part. And then we come
to the farther forward on the picture plane, where this scale
is only appropriate at this part of the picture plane. Only sliding to the side, moving
around but not going back or forward into the picture any. And then we
counted up three, one, two, three, and then had to add four, one, two, three, four.
And that's how we got our seven foot person. So
that's pretty much how you can scale an infinited number of people. Just a note, of
course, when you're - all this work is extremely fast
and it's also extremely light. You would do, again, you would do
cobweb thin lines to get these references and then you'd draw from your reference or whatever
you're using your drawings or paintings to get the exact style
you know line quality, all that stuff goes into it. These are just, obviously, done
very quickly and basically to get the idea that this is how you scale.
The rest is all up to you, figuring out proportionally how to draw. For instance
if people are leaning over, tying their shoe, doing anything like that, and they're not at
full height then it's your job to figure out how much shorter than someone's true standing height
is that same person tying their shoe, or bending over laughing or something.
Then you have to figure out how to scale them to that.
But everybody standing straight up is a great way to get them shuttled back to their position quickly.
Then you can make those changes for their actual standing posture position for their
narrative action. Okay, so six foot man, five foot woman,
four foot child, 18 inch dog, seven foot very large person. Okay.
And that's how you do different size people in different parts of the
picture plane, all gaged off a particular height of eye level. Our eye level
in this case was three feet. Okay, okay so we'll go on to the next
we're going to do a diagram in one point perspective. Very simple, we're
not gonna worry about the cone of vision or anything like that. We're simply gonna imagine that
there's a serious of pipes that are the same length that are coming towards us
and going back in space in one point. So in flat space, all the
pipes are laying parallel to each other going straight back from us like this.
But because we're in perspective they'd all be emanating from that one point,
vanishing point. And so they'll come toward us and diminish
as they go backwards. So I'm gonna draw a
initial line first.
My initial pipe.
And I'm gonna call that pipe A.
I'm gonna put it in in blue.
And I wanna make it clear that it goes back
to the vanishing point, so I guess I'll put a trailer line on it.
And the length of pipe A is going to be the length of all of our pipes.
Now since I'm gonna do a various other pipes here, I'm gonna also say I can take
a picture plane - straight across the picture plane I can make a reference
plane of the length of pipe A all across the picture plane, straight
back and forth like this. Could be helpful later. So I'm gonna do that right now
by simply taking horizontal lines.
And I'll call that line
one A to represent A the pipe.
And 2 A.
Those are just for reference. So now if I had pipes going
next to this, here, they'd all change going to the vanishing point like this,
all across. Because even though they're laid straight across from each other
in a row, in flat space like that, because
again we're in perspective in this ground plane going to the one point vanishing point, the pipes
would behave like this going to the vanishing point. So that is a reference plane
for any pipe of this length laying right there lined up going across
our picture only would all line up to these front and back
ends going to that vanishing point. Okay, so now I wanna do
a pipe in a different position. We'll call that pipe B.
So what I'll do is I'll say pipe
B is here.
And I'm gonna start the head of pipe B here
and I'm gonna cast it
back there. And I'm gonna clearly call this pipe B.
And I'll make the
start of it in red, but I don't know how long it is because we haven't referenced
it yet. So let me get out of the way here. Okay.
Now, let's say I wanted to reference the head of A going to
the head of B, kind of like we did the figures in diagram 2.
I'd go way out here, so that's going too far out of my picture. Because to get a reference point
to reference what the true length and depth B should be since we've already establish A
I can go from the head of A to the similar head I've just created for the head of
B. But that would take me in a straight line way out here and I don't wanna go out that far.
So what I could do is pretend I've shuttled
with a reference representation, shuttled
pipe A over just to be convenient. Because I already did that
reference plane. So I could basically do this and say
I'll call that
RA, meaning reference A
So that is our reference version of A, which is a ghost of it but works too.
Now, what I can do is create
a reference plane. I'm gonna go for the head of reference A,
doubled over. In fact let me make a couple arrows, it'll be easier.
Let me get my head out of the way again. Okay, so I've taken kind of the
referenced A and now I can do the same thing. I can say alright, let's make
a reference plane. We're gonna go from the head of reference A
through the head of B to make a reference point on the ground
all the way to the horizon. Let me make that darker.
All the way.
And I'll say that's reference point number one.
That's the first one we needed to make and if I come back from that reference point, no
surprise because I'm referencing the back of reference
A as it slides over from A. I can get the back of where B
belongs by coming from the reference point now, reversing it,
going through to the back
of reference A. I now get where that
crosses, I get the correct length
for pipe or rod B. There it is.
That's the correct length because I made a real reference plane from the
reference A. So I'll go ahead and do a little shading.
That's all flat on the ground, so that reference plane is not standing
up, it's flat to the ground. It's just a plane between reference A that has been brought
over and B, we just started but didn't know how deep in space
so we just got that. Now we could do another pipe
that is coming out, let's say, right
here. And we could
say how far forward would we want that one? So I'll say we'll start
here, something like that. And now I'll do
the back of this pipe and say, I want the back of the pipe here
and I don't know how far forward I want to come
with it. But that's the back of the pipe coming forward. Okay, the
idea is, where can I, you know,
how can I reference that? So, I take -
I could easily take the pipe, we'll call it C I forgot to label it, sorry. That's
pipe C. And I could say, well I could easily reference B,
it's close enough, I don't have to go way out into space to do that. So I will do that. I will do it in blue
and I will say C has a certain
length. And I will go through the back of B. The back of B
and the back of C, I should be able to come forward and reference.
Go through, continue on to make a reference point
right there. And I'll call that reference
point number two.
And now I can come back
from reference point two, and I'll use my blue again
through the front head of already established
bar B to get the new head position of C.
From here, up through the head
And this then becomes the correct length of
So C was referenced from B and B was referenced from A
being shifted over as referenced A. So referenced A we actually
referenced B from, but it was originally A, shifted over straight on the picture plane to
represent kind of a ghost or a phantom of itself. But we can do that because we can
imagine all these pipes laid out like this on that reference plane. So 2 A
and 1 A represent a reference plane we originally put in.
So now we've had C and, you know, let's
do another one. Let's do another red one again and call it D. Where do we want that?
Maybe I want it way back here. So
why don't I go - let's say I want the back of it, you know, there. And we'll say
well - like that.
Actually I'll just do the back
of it here. There we go. I'll do the
front of it. We'll call that D, why not make it
smaller. So in red again, I'm saying now I want -
I'm just starting with the head of D and it has to go toward the one point vanishing point. Because
remember, as weird as it looks, even if we're a little out of the cone, the idea
is what we're saying is that all these pipes are actually lined
parallel to each other. Because they're behaving to vanishing point one.
So that's the kind of diminishment you can get if you're fairly low to the ground in one point. Okay, so how -
again, we use
reference D, using C which would be pretty convenient. Again, we use our
blue lines again.
And I can go from the head of C now to the head of D.
Make another reference point.
That will be called reference point three.
And then now
RP number three. And then no surprise
we can come back from the reference point, going
through the new pipe D on our way to
get to the back end of C. And we strike what
the proper length would be for D.
So let me make the pipes really clear now.
That's pipe D.
This is pipe C. This is
This is reference pipe A.
And this is original pipe A
which we made a reference plane from.
Ground. Okay. I'll go
ahead and shade those in as well.
Those help us cast back, make reference points, and
get the size of all the pipes. So again, we have
at the same length as each other, in this simple one point set up, we have
pipe or rod A, then referenced from rod A,
reference rod here, we have rod B. And then we get C
and then D. So all we really have is objects
with all this very light line work you'd put in your work. You know, again,
cobweb thin would be rod A, with a reference, rod B,
rod C, and rod D. But we know they're all the same size actually
and they're all parallel to each other because they're really on flat space lined
up like this in a parking lot or in a big, flat ground surface
going to vanishing point one. Okay. So again this is just
you know, we could call it referencing four rods of the same size from the original
rod A. And you could keep going back and forth and doing this all day, and then if you
reference one that takes you too far out with your reference point out of your picture, you could always drag
straight across the picture plane a reference version of any one of the pipes.
Or objects, you could be doing boxes when we get more complicated, things like that. But the
whole point is you can always scuttle straight across the picture plane without gaining any size,
you could scuttle across a reference representation of
an object. In this case, rod A was referenced
to reference A. Okay. And that's pretty much it and that's referencing some
rods there. Okay.
Here we are again. We're gonna do a very similar one to the last one except
we're gonna give these objects height now. So instead of just rods coming
forward, all again in one point, we're gonna have three objects that are also parallel
to each other coming straight forward but we're doing it to one point. So they're still gonna converge
toward the one point vanishing point. We're gonna do some standing fins like the
back of airplane wings or the standing fin of a tail wing, let's say.
So I'll go ahead and establish my first
rod type shape.
Let's say about here.
And I'll call that A.
That's the front of A.
Okay. So first I establish the length, that's random.
But I'm also gonna apply a vertical
to the rear. You'll see what I'm doing in a minute.
Going a little bit above our horizon line.
And apply another point.
So that has a particular point and then I'm gonna
close it out.
So I've got a standing triangle now.
And I'll go ahead and fill that in with blue.
So that's our shape. Imagine it's
transparent and it's a standing fin.
And let's say I want another rod
forward from that, that also
has a tail coming out of it. So it's going to make a fin or a triangular shape as well.
So that one will be coming this way.
I'm gonna say that one's front
is here. So it's just a projection from the one
point vanishing point.
And I want to make it clear that this one also came from there.
Let me just trail it back there. Okay, so now we have a completed
fin, fin A. Randomly - completely randomly drawn and sized.
Just what I decided to do, just as a good demonstration. Now, I'm gonna take the
front of the second fin. So I first want to
reference the actual depth of what the fin is. Because remember, all of these fins are lined up
together if we were to be straight above, all parallel, and they're
all going back here to that one point vanishing point when we get into this perspective.
But I still need to find equal length to this, up front, further forward.
So, how do I do that? Pretty simple. Now that we're getting used to it
I'm gonna do - this is B. And I'm gonna take new line B,
what's representing the front of it, going through the previously
established fin front A.
I'll just make an arrow.
And that gives me reference point number one again.
Because we wanted to go through there. Now I simply
come back, you know, through the back of the original triangle
to here. And that gives me
the length of the rod B
as it projects forward from this position. The more forward than
triangle A, or rod A, in the picture plane.
So don't get confused, this is totally separate now. We drew that independent,
completely randomly. But then we decided we want two to three other fins,
probably just two others, that are of the same length and depth
in height as triangles. So I completely started referencing B
once I randomly decided I wanted B placed here, which is a random decision.
I then can start matching its depth here.
That's rod B. Now we're gonna come up and we're gonna
say clearly there's a vertical coming off the back
of the second fin, or triangle B as well, in the same way it did in A.
So we'll just draw a vertical higher than we need.
And then how do we reference the height? Same thing. Now I've got the height of
the back fin, or the back plane, of triangle A. I can simply use that
to reference how high this one needs to be forward of it by going back to the reference
going through rod A.
on until I strike the vertical of the back of
B. And I've got it. So that gives me the height of triangle
B. I gotta close it off now and I'll make that one red, because we did that second.
It's more foreshortened as well. So there's
I'm gonna make that clear. So that shape, if it was made of transparent
Plexiglas or tinted color plexiglas
that would be that. So now we can understand that reference points
don't - not only help us with scuttling across the ground plane like in the previous diagram
but it also just as easily, for many things in perspectives of course, can give us
height as well. Because remember these planes disappear back to an infinite
space or vanishing point. But we're calling them reference points, okay.
So now we have A and B, so we can say that
triangle B was referenced completely
once we found it's front position randomly was referenced completely from triangle A.
And now we're gonna set, you know, a second triangle, I mean, I'm sorry,
a third triangle. And I'm gonna randomly place that
over here. And it's not gonna be nearly as far forward,
it's gonna be farther back in space. Let's say, I wanna start the back of it here.
And bring it forward. So here's the back of a triangle a good deal back
from that. Okay.
I'm gonna first find it's length of the rod coming forward to match these, because
remember all three of these triangles are the same size in different positions from
forward to back. but all parallel to each other. So this one's
further back, the second one's further up, the other one's over here, but they're all parallel to each other
and they're also all the same size. Okay. So
I'll go ahead and it's more convenient for me to use B to reference C. So we'll call this
one C and then we'll take the back
of B. Why? Because we're representing the beginning
of a new triangle coming forward and we're representing the back of it first. So we need to
use the back of the triangle we're gonna reference from. So I'll go
ahead and go from the back of triangle B
go through the beginning of C.
All the way to the horizon line again. And that will give me a reference point.
We'll call that reference point number two for our purposes here.
Okay, that reference point then can be taken all the way to the front
of B. And where that intersects
the plane coming forward for C will get
that. So let me draw that on the way
So the arrows help. And that's it. So that's not very big is it because it's back
in space quite a ways. So
that's only that tall, I mean deep. So
and we'll go ahead and draw the back - oops.
We'll go ahead and draw - let me clean that up a bit.
Make that clear. That's the back of C
now. Triangle C. Goes straight up. We don't know where to cut it off yet because we haven't referenced
it right. So let me get out of your way.
Okay. Now we can say, oh well
I could, if I used B to reference C, I could use the top corner of
B to reference back to reference point two and cut
across. So in a sense I can go like this and
and that gives me the height of C because it cuts across it.
So essentially we first got B by referencing A and now we're also getting
C by referencing B. You could technically get C by referencing A but that would
bring you much further here out of the picture. And as we mentioned in the previous diagrams, why not
you know, use what you got to be more convenient in the picture and not have to
go so far. So essentially now let's close off that third triangle, triangle
C. We've got it's height now, right there, it's front
its back, so let's close it off. And we'll also shade that in as blue.
fairly foreshortened and of course we could put another in there if we wish.
Not a problem. We could still use B to reference that, we could bring one over here if you wanted to.
You know, that makes the point. But let's put another one for the heck of it just to say well
alright if anybody's confused, you know, let's bring - what's one -
start one right here. Fan one out a bit.
So I'll use the vanishing point right there. Remember that's our original vanishing point.
Shuttle it forward. Okay. And where does that
bring me? Well it brings us fairly far out but, you know, let's try it.
I'll use B again and I'll quickly reference this last triangle,
D. I just decided the back of it's here so I'll randomly say alright
that brings me to here, all the way out there for a reference point.
Real quick. Reference point number three.
Alright. And if I come back from the reference point to the front of B again
that gives me the depth
of D by coming back. Now this can get confusing
so that's why the videos you can pause and go back and take careful notes because I'm gonna
carefully go through the order again so for your notes and how you're writing -
if you're writing on your notes here in lines - I would just rule the lines here, then I'll carefully
step back about what came first and you can just keep pausing until you have all those notes written. Okay.
So, not we've got the depth of D. So I'll make the
front and the back as a rod. We'll go ahead and make
that back come up as well.
And again I can just
reference here again.
And I can reference B, the top of B. Now I have to
go all the way over to reference point three to use that one.
There's the top. Right there. It's confusing, I know, it meets there but you know
what, if you understand this and you can look through things that's how you
understand it. And we'll tone that one in red for D.
And there's our referenced fourth object, D.
Which was referenced again from B.
We coulda done it from C but it would have taken us over here and gone through the other
objects, so I decided to do B again to D. It was pretty convenient. So again
to make it clear, we got the top of B
to get the top of D. So let me make that go like that.
I got my head in the way here, gotta keep remembering that.
Okay. That to that reference point gives us the top.
So let's go through it again. We've got four standing triangles now, there'll all
the same size but they're in different positions in the picture plane. Like some of the previous
diagrams. We started with A as a standing fin or triangle
and we totally established it randomly and decided on its size compositionally.
To then say we wanted similar size fins also, I went ahead and
referenced B from A. After I'd referenced B, I then referenced
C and randomly decided, and B was also randomly decided in position,
A was randomly decided. They all were, after the last one was finished.
So, B was randomly decided and then
finished. Then C was randomly decided on the back side and I went from back
of B through new back of C to get reference point two.
So we got reference point one from referencing beginning
of B from established A. We got reference point
two from taking the back of C, randomly just coming
forward. This, going through this
gave us reference point two by coming forward to the front of B,
striking across the plane coming forward for C, we got its depth.
And we also went from B's height to reference point two
to cut across and get C's height. Okay. And again
play this back a few times until you get it. Once it snaps into your mind you'll get it. Take a
few notes, make them worded really concisely and clear. Don't go nuts with the notes.
It's a visual thing. So I encourage you to take notes, but I'm not gonna
take the time to write them out. I'm gonna repeat clearly, verbally what's going on and I want you to
extrapolate your words for correct behavior by playing the tape back
or the video back and getting it correct with as few words as you can correctly, but it's
the visual idea that I want you to memorize and that three dimensional platform
to start sewing into your head basically. Then from C,
I didn't really want to reference D from C. It wasn't as convenient, you'd have to go way over here
so I went ahead and used B again and completely referenced D from B again,
creating reference point three. So go ahead and review
and that's pretty much showing you that reference points on the horizon line
or created on the horizon line can help with height
just as well as they help with some of these depth issues in the past diagrams. Okay
so that's about it for this one. Just four standing triangles, all referenced
from A, B was made from A, and then C was made from B
and then D was also made from B. Okay. Alright.
so we're going to do one now that is still using both the
referencing method from reference points on the horizon line as well as
a little bit of referencing from a particular height of eye level, like we did when we counted
down from the eye level and back up. So we'll do both in one diagram. Let's say
and we'll have a person lying down in this one, not feeling well, as well as a distant figure.
Just to kinda mix it up a little bit and showcase how they can be used together.
Okay, so I'm gonna go ahead and pick a spot where I think
I want a, you know, standing person. So I'll just say okay
about here. And I'll say that person is, let's
say, six foot. So I'll go ahead and pick some place I want them standing.
Maybe a little bit below that here actually, we'll do that.
Okay. I'll give them an official vertical. So
here we go.
We don't know how tall they are yet. Okay, here's their
base on the ground. Okay.
So we'll split that in half again, about there.
And we'll add another one,
a little higher another one, another one. So
let's say we agree that's about six foot. One, two, three, four, five, six.
Okay. We'll make it clear that this is
two feet. So I'll go ahead and write that in. That's a two foot eye level.
We'll put in our horizon line eye level at two foot and we'll also say over here
eye level two foot. Okay, so now we
know for sure that we're sitting on a flat plane looking out
at two feet. We've just found two feet at the beginning of our six foot person.
I'll make it real clear, one foot in red, two foot,
three foot, sorry, three foot, four foot, five foot, six
foot, basically. Let's go ahead and draw that person out real basic.
Then we have the body coming down, a little bit of waist.
Coming down to the feet. Okay
There we go. Some hands in the pockets so we can do this quick.
There's our little person.
that was figure A, that's the counting method from
the eye level down and up. So we've got a six foot figure. We'll want to put another one that's
let's say over here. Another figure here. This'll be also same size.
So again we'll give that person a vertical and a position on the picture plane officially
with our T square. Alright we'll shoot that up.
And first we'll count off with the
counting method. But this is still two feet.
And I'll go ahead and actually use my red this time.
That's one foot, two foot now, two foot eye level.
Go ahead and estimate three, four, five,
six. Just an estimate by hand.
And we'll call that figure B.
Alright. And again
there's the ground. So we've just used
and gotten the height of figure B using the counting method down from the eye level,
two foot eye level and up. But let's also go ahead and
rehearse the fact that we could take base A to base B and get a reference point.
And come back that way just to see how we did. I'll do that in red
as well. So, base A through base
B. Should give us a reference plane, or point, first.
Let's call that RP number one.
Then if we come back from the established A, down
to that we should get a height. So that's pretty close right there.
Okay. I'm a little off since I hand
counted real quick, that's pretty fine. Okay, so now we've got a plane. We won't
shade it in yet but now we've got both a reference plane referencing A to B
and we counted. So I'll go ahead and draw in figure B.
Woman this time, six foot
also. So she's tall, that's fine. Let's do it in six foot.
Woman and six foot.
man. Okay, so we got six foot woman
we entirely referenced by A, getting
the increments down from the picture plane at that scale from her particular point in the picture plane which is a
smaller scale than this person's because they're farther forward in the picture plane. We then
counted up the rest of the way to get her height but we also confirmed it
again by the reference point method as well. Okay, so now
as another idea, I'm gonna kick
a straight line out from figure B to the left on the picture plane.
Like that. And I'm gonna go ahead
realize her height, directly laying down
to the side of her, by using a 45 degree angle.
Okay, there's her height.
And I'll do that in blue. The point is, by using
a 45 degree angle I'm getting the same increment
I have for height as I have for horizontally
for length. So it's a fast way to do it. I'll just
mention that we do it here. That's 45 degrees.
And that gives us that.
So here, base of woman, to this mark
is the same length as she is tall.
So now that can become a reference if someone is laying down.
Okay. So what we want to do next is
we're gonna say that someone's laying down back
here. So, we're gonna say how about if I wanted to
put the head right here
of someone that was lying down and then have their body
going this way. They're obviously laying
quite a bit back in the picture plane again. Okay.
So it's not really on this reference line, it's a little bit over. So I'm like, how do I reference
what I already know is this
proper, laying down length from someone who's
head starts there? I don't know where to put the feet. Well I can simply go from
one end of this rod, which represents her height,
put it through to make a reference point. I'll call that
RP number two. And then if I come
back from that reference point there to
the end of what we know is the proper line length
over there we cross here. And that give us the laying down length
of someone in the background. So if I want, I can simply make
that a head. There's the
torso. There's the legs - feet sticking straight
up. Little arms.
there's the proper height, I should say length, of someone laying down
perpendicular. I mean, sorry, sorry, parallel to the ground,
to the picture plane. This figure is laying down a ways back that we
referenced from originally figure B's height
then laid them down and then that gave us a reference point or
plane that we could start with as kind of a rod. Then we'd randomly pick the
position of the laying down person, marking their head first and just casting them horizontally.
Then we made a reference point by the base of this at
the feet, going through the head position to make reference point two. Because we didn't know
how long to make that figure. Once we have reference point two, we can return to what we
know as the full length of the originally referenced plane for a laying figure
and coming through to here, crossing the plane of where we were laying down
a person, we get this mark here.
And I'll explain it once again. So the idea is
that in red we have a plane that's
started with figure A, randomly selected. We also counted down
from the eye level and up to get the height. We then took figure
B's position, randomly chose it, marked an area on the ground, and also
got that person from counting down from the two foot eye level and then up to
six foot. It's a woman. But we also said we'll confirm and then double that
idea by going base to base and making a reference point just to exercise
the fact we could do it both ways. We came through the same thing, so now we
have a reference plane and we have the counting from the eye level, for both of them.
Thirdly, I wanted to reference a lying down person back there
from figure B. And of course the laying down person we'll call
Now, figure C, I didn't know where I wanted to put them, so what I did is I made a
laying down reference with a 45 degree angle, which gives me the same
length here as the width here. Okay, so just to make that clear.
These are the same.
That gave me a reference. Just shooting straight out horizontally from figure B.
Now I randomly placed the position at the end of the
head of figure C. That meant, if that's the one end of Figure C and the other
one, end, is gonna scuttle over here horizontally then I'm gonna take
the ground reference of this end of figure
one, end, is gonna scuttle over here horizontally then I'm gonna take
the ground reference of this end of the figure
laying down, go through that point to make a reference point.
Reference point number two. Then, by going back to this point, which
is the end of the figure laying down in the larger reference,
these two together to make a reference point, I could come back from the reference point
and shoot through the plane of the laying down person to go through.
That gives me the length of the laying down person in the distant picture
plane. So now we have a six foot person standing,
a six foot woman standing, and a laying down person. And that's
figure C. The idea there, again, would be that we can use the different
methods and different ways. But it's still either way if you count down, or if
you reference, you're getting people to be similar heights if you wish. Or, if they're different
heights you can simply say, "Oh if a five foot person's
there then I could make, on the same reference point I used for reference one, I could make a
five foot person anywhere by referencing simply here." Four, three, two. So
you can basically interchange the way you use
these depending on what you need. So again
six foot man, six foot woman, laying down woman representation
is a plane here, using the 45 degrees. Picking
randomly position of the laying down person. Head there, referencing that from ground.
Figure B, making reference point two, coming back,
gives us the feet of the laying down person. And again, you can repeat these ideas as long as
you have your head clear about what reference points you need to use. And by the way, this can use
you know, these can be used in paintings when you're doing just wet to wet lay ins with a
thin brush. You can be doing this directly on your canvas.
All these methods, obviously, can be used in the middle of a painting. They're
very simple referencing and counting methods. As long as you have an eye level and you have an
understanding of how you want to scale people based on a couple objects in your
painting, already having a true height and width, you can use these methods all over the
place without having to do any real measuring or anything that
technically - even with the cone of vision. As long as they're reasonably in the picture.
So again, this is not just about doing diagrams. This is about the idea of what
you can do with many, many other things and finish drawings, paintings, and all sorts of stuff.
Okay, so again, two figures standing, one laying down
by two different reference methods. And the two methods are, counting down and up
from a fixed level of eye level, which was two feet in this case. But also
we used horizon line, eye level, reference points,
on the horizon to get some of our referencing. Okay, and we'll go on
to the next now.
This time what we're gonna do, we're gonna draw in an eye level, which I already did. Go ahead.
All the way across. I put a one point vanishing point right about there.
And we're gonna draw a one point side walk. First I just
want to explain we're gonna do a sidewalk using - knowing that the sections are equal by creating
a reference point off to the left. And then we're gonna lift a section of the sidewalk out and float it
over to the side but still retain the correct size of the floated section.
Okay. So let's start. So we're gonna do a
basic one point side walk coming forward.
And we'll do our front section.
That's random. The whole thing's random so far.
And I'll go ahead and fill out the depth, what I want the depth to be. Maybe that.
Okay, a little further, okay. So I'll randomly decide the depth.
So we've randomly made our first section of sidewalk
And I'll call this A, corner B,
corner C. Now, since I wanna
reference it I'll use my blue pencil
and I'm gonna take corner A, because I wanna go through kiddie corner to B and that will make a
reference point. Okay.
Right there. And I'll call that reference
point number one. And
what that gives me is a reference diagonally through my first square.
Into infinity, corner to corner. And what that will serve is how to
create all the new sections of sidewalk also from the same reference point, corner to corner.
So let's go to C and repeat.
So we've gone through it, we'll go back and through it again and where it strikes the side plane
on the left we'll have our next section. So
over, striking, over to make the reference.
Where it strikes against the wall is where we get
our new section. So I'll take my T square and bring it back up. And I'll draw
the second section. So, so far we randomly
picked the first section. We designated corner A, B, and C.
We went ahead and we referenced
diagonally through the first section to get reference point one. And that
will give us the rest - by the same referencing that will give us
our rest of our sections. So I'm gonna call this new corner D
and one after that E. And we'll do the
same thing again. Starting at corner A, kitty corner from the reference
point and going across, striking, going across.
And again, draw back
with our T square just to be clean, neat, and clear.
Third section. And we'll go ahead
just do a fourth for the heck of it.
So I'll take my blue pencil one more time,
cast it back. I don't have to label
them each time. I'm doing it for the purposes of our next move. Again, I'll leave that
one blank and just say kitty corner, through, gives us
our next square.
There we go, right there.
So now we've got four, correctly even,
diminishing squares of a sidewalk in one point.
And I could, you know, I could keep labeling.
This could be F, that could be G if we wanted
to. A, B, C, D, E
F, going through, G, on
and on and on. So it's a Z pattern. Z, Z,
through and through. First one's random. I could be over just as well
on the right, but I decided it's more convenient so I've made my sidewalk a little bit over to the right, a little more.
So we have room for that reference point. Okay, now what we're gonna do after
we've done this is we're gonna lift the second section of sidewalk out.
So we're gonna make it clear that we're concerning ourselves with the second section
of sidewalk. So go ahead and tone in that second
section. Simple. And
we'll go ahead
and lift that out of there. So now we've got
our second section of sidewalk. B, C,
D, E. Okay. And we're
gonna randomly say we want the new - what was corner B,
the front corner B - I'm gonna randomly say I want somewhere up here. Not
too far forward so we can stay in our diagram okay. But I'm gonna say I want the new corner
to be right here. Oops. Alright.
I'm gonna go ahead and draw what will be the new corner. So
the section will still be in one point, so we're gonna go back and draw.
We're also gonna draw forward, horizontally
to the new corner. Probably a little longer than I need to be.
Okay. So if that's my new corner,
that's my old corner because I'm lifting a section out, like I'm floating it
and placing it on top of the front one. What I need to do is I need to make and reference
point from my new corner through my old front corner left.
New front corner left, old front corner left. Go ahead and drive
a reference point
or drive a line to a reference point I can create on the horizon line. New corner,
old corner, reference point
number two. Alright, now that we have a
reference point, I should be able to logically say "Ah." I can come through now
the back corner left and also make a mark.
Back corner of the new square should be right there.
So there's the back corner of the new square. Now I know I have to draw
the horizontally to finish off the back plane.
Okay. Now the logic is, why don't I go ahead
and go through the old corner on the right. Back corner on the right.
And to create the new back corner right on the red square. Old back
corner right, E, going to the new square.
Corner. Also drawing forward
And then finishing shape off back to my original vanishing point of course is
important, to finish the square off.
So we can check it basically and say, alright, is it accurate? This corner
now, the new corner, front corner right. I should be able to go through the new
left corner back and still arrive at my reference point if I'm basically correct.
So let's just check that. Sure enough it looks pretty well.
Right back there. Alright, so
there's my new
section. Oh let's go ahead and label. We can just call
this process X. We can say
this is Y. This is Z.
Okay. So the important thing is we can still do the whole
zig zag thing. Front,
zigzag to get the thing. So we're gonna start from the front, we're gonna go back
and we're gonna go over. And we could do a whole raised section that is properly going back. But the whole point
of this was, we only wanted the one section coming forward. So let's
tone that in. And again this is all just ground referencing.
Pretty fast. And again this becomes much more
helpful on a large canvas even, or anything where you're laying in a large
image and just trying to figure out scale. And again this could be done with wet paint on a
painting. As long as you have a little raised straight edge you can draw a lot of this thing. You don't
have to necessarily do some incredibly - oops -
careful drawing as long
as you're paying attention to your horizon line and your image and you know basically where you're making a reference
points you can get a very good gage on proper sizing. Especially if you're,
you know, on a larger canvas. So, what did we do? Let's go back
over really carefully. Let me go draw a little harder on some of these.
I'm gonna recreate this square again. Okay. So let's
Okay, we started with
the original front section of the side walk. Completely randomly. We drew
the idea of the sidewalk coming forward from the one point vanishing point. We then
decided the depth of it. So we closed it off and made this first section. Then by
creating a reference point from going from corner A through B,
on the first section, we created reference point one. We then only had to draw
back and keep repeating that pattern going through the side, left plane. And that
gives us our next section, repeat, next section, repeat, next section. So we
drew four sections, a sidewalk. Then we decided to take
the second section, shade it blue, and decide to bring it
and lift it forward in our imaginations. But still wishing to retain the proper size
for a square coming forward that matches the size of the previous. But now it's
lifted to the right and lifted forward. But it's still flat
on the ground. So, how did we do that? Well in this case we decided
we could take the desired front corner of the new section, which
we had to decide randomly, and that's all we decided. We knew that front corner
would still run back and go back to the one point vanishing point, and we knew the other
plane would go across the picture plane horizontally. So we overdrew those lines a little
bit to start with just that corner. We then simply took this corner through the
old front left corner of section B
to use section B as a reference and we made a reference point.
Reference point two. That allowed us to come through the old back
corner of D, left, to make and strike that plane
to make the new back corner of the red section. We also could take
the old, right back corner, called E, come back
from the reference point through that to strike the back plane we now knew
when we got our new corner Z. So essentially, you're just
piece by piece putting together this new reference triangle. Then we just found that point
and closed it off as a square. So by this reference method
we just designed it. You don't have to find that corner first. Any one of these
three could be easy to find if we desired
to start anywhere within here. We decided to stay in this front corner, went back,
look over, then strike the plane, coming through old corner D,
through old corner E and originally through old corner B to get X.
Then we just drew the shape out and we have a lifted sidewalk
that's a properly sized section from what we had before with the other
four sections. So again, simple ground referencing.
But it starts giving us an idea of the different things we could do. These could be the
basis of much more complicated houses or rectangles
Imagining now, when we keep going into these diagrams that are simpler
for referencing and scaling, which we're gonna still have four, five, six more that are gonna be
you know really straight forward referencing and sizing and scaling.
The idea is these can of course be eventually raised
as footprints of houses or everything and, you know, obviously we could repeat the same shape
over and over by referencing the entire shape. But we're not gonna quite reference an entire
complicated shape until a little bit to the end. And we're gonna carry some rectangles around
like pretend they're little houses. And do a little referencing three or four different
structures around the picture plane that are to the same parallel vanishing
I mean, operating to the same vanishing points but are in
very different positions around the picture plane. But for now, we're doing these simpler shapes.
So there are four sections of sidewalks with one raised up. The blue one
raised, brought forward to make the red one. Okay, very good
on to the next.
on this one we're going to actually use some two point perspective and
just reference some basic shapes.
Some boxes and repeat them. So we'll create one box in the foreground and
try to repeat a couple in the background as a referencing technique. So we're still gonna be using
reference points. So I'll make one vanishing point here.
Call that VP one. And one maybe
over here. Call that vanishing
point two. Okay.
And now we'll just create
a vertical where I think I want my
first corner. I'll try back - well we'll try one right here.
So I'll just make a little idea on the picture plane of a
box. Right here.
And I'll make it kinda randomly sized.
Okay. I'll go ahead and
draw its planes back to the two vanishing points.
Okay. And to the other
vanishing point. Now we're in two point we have to consider.
Doesn't have to be in the middle. I'm a little farther over to the right,
doesn't matter. As long as I'm not too far out of the cone. Which we're gonna get to
quickly once we start dealing with more two point
things that get more complex, certainly we'll consider the field of distortion more. Right now
we're just kinda working in the middle, doing some simple referencing and scaling as you know.
I'll randomly decide how long the box is. Maybe I'll make it that long.
On the right plane.
We'll be getting to Xing and
you know halving and doubling and all that in a second here. But we're gonna - not in this
diagram. We're still gonna use purely reference points. Reference point for getting sides.
And I'll have the box a little shorter on this side, let's say here. So
there we go. There
Close it off. We'll also remember that all objects are really transparent
when we start doing more. So that's kinda where we're going with this one. We're also gonna
draw the idea of the inside of the box so we can really understand all the shapes
we draw. So most of the time in perspective, especially for the diagrams of course, we'll be
doing transparent objects and trying to remember that
we're trying to think volumetrically through things so that
we understand all of them. So we have a little box
and the idea is, if there are other boxes still on
the picture plane, on the ground, and they're still going to the same vanishing points,
meaning the boxes are eventually in flat space, actually parallel to each other
like that. That means we'll start
drawing in that idea. So the idea, if we draw in the top here, we can just do
a little idea that most of the boxes, even though they're not going to be exactly lined up, are still
parallel to each other. For instance, like this, actually. I'll draw down
here. So we might not have all the boxes
lined up right next to each other but they're gonna still be parallel and perpendicular to each other.
Okay. Alright. And we'll randomly decide this. So
let's just say we want a box somewhere else on the picture plane
that is parallel to this. Parallel and perpendicular
to this box. The same size as this box. But, you know,
sitting back a ways. So I'll randomly say
why don't we make one here. Its corner here. So what do I
know if I pick this? So this will be box A.
And this will be
Now, what do I already know about that box? It's still gonna go back,
travel toward these vanishing points. I'm kinda talking about the front
corner of the box. Okay. And I also know it has to have a vertical on it
front corner. So I can assume this and go ahead and start off
there it is. The front corner, box A,
front corner box B. Now we can get
the entire rest of this box
by inference of creating a reference point. Front corner,
box A. Top of front corner, so
here's the height, that's all we need. So we'll consider this a bar
that's sitting there. So if we want, we can put that in in blue
just for the heck of it. That helps us at all.
I'll be using that to create
the reference point. But I'll do that
in red. So front corner on the ground, box A
going through front corner, beginning of front corner on the ground, box B, which we have
haven't even begun to draw yet except for the standing front corner, makes a reference
point. That's my first
move. Front corner A through beginning of front corner of
beginning of box B. Makes a reference point. Call that
reference point one. Okay.
Alright, so now
why don't I identify the other four corners of box
A. That corner, that corner,
that corner. We've already done that corner. This is the first.
So let's just say first. Doesn't matter after that.
We can pretty much carefully take
back corner, right side to the reference point.
Where that lines travels through, on its way
to the reference point and strikes that
plane that represents one plane going back toward the vanishing point. Here's the other boxes,
right side plane going toward the vanishing point. It strikes there.
That's where I'm gonna rise the corner - back corner - just like that corner. I'm also gonna take
this front corner on the left side and drive it
toward the reference point.
Like that. So I'll line it up here and drive that
And that strikes right there. Okay. Now we're noticing something
that as things get further over to the right or the left, they'll change
and seem longer and shorter and things like that. Okay.
What do we need to do now? We need to draw those two corners back.
So we're gonna go to our object. And I
know this corner here is this corner here on the new one.
We've got to draw across to get our plane going back to the left side vanishing point over here.
That way. So I'm gonna carefully go like this.
My new length and go across and kinda
draw it out. I'll also go across to the right vanishing point
where the corner is like this.
So that new corner back there is just to the right
of the front plane. So now I've got the foot print
of this little box back here is just like the box here. It looks very
different though because it's much more foreshortened because it's going further away and it's actually
farther over to the right in our cone of vision. So we will
actually start foreshortening this side a good deal, which you'll see, and
lengthening this side a little bit. That's actually how we see and how objects
are. Most people don't draw like that but the more you learn how perspective actually behaves
like it does in the real world, the more you'll be able to draw more accurately.
If that's your goal. Or, if you're a stylist, you'll actually be able to exploit
and stylize and stretch the perspective more, knowing how it actually behaves
in front of our eyes. Either way. So let's go ahead and rise those
corners our of the ground now for
box B. There's the
front left corner,
rear right corner and back corner.
That's very close to our front corner but just a little bit over to the right.
And now we can only go, oh
that's right we're gonna use the height just like with those
jet plane tails, those triangles we drew. I can also carry the height of box A
to strike and get height of box B. But I have to take
the front corner height and go back to the reference point to also, as a
separate move to strike against the front corner of our little box, right here.
So top front corner,
box A, traveling to reference point, back
here. That strikes - let me double check - right
there. And that's how I know how to draw out the rest of the
top of my box because I got
that little mark on the little front corner of box B. So I can now draw
to the left - oops - to the left.
I can draw to the right.
I can draw back to the back of the box, back toward
the left. And remember, the back plane
is just a little to the right of the front, so it's back here. That's why I overdraw my verticals most of the time.
So even though, when you're, you know, when you are drawing your actual assignments
you'll be doing it very lightly. But I kinda leave it like this. And there is
completed box B, little box B in the background.
That we completely referenced because it wants to be sitting
parallel and perpendicular to this box, going to the same
vanishing point, still sitting on the ground. Now we could have it raised
and still draw it by reference, but we'd have to carry
our measurements up and we're not gonna quite get there yet, that's a little more complicated.
It's not hard to do, it's just at this point I still want to talk about Xing and halving and doubling
and a whole bunch of other things with basic referencing and scale. But
we could easily lift this box up and find its footprint on the ground like we have
and it's true height measurements. And as long as we're not going back into space
or forward into space we could actually raise this box straight up and have it floating
way up here if we wanted to. Just like we've measured it with a ladder
and could still realize the same size box up here, just by that reference point. As
long as we carry the idea of these invisible, vertical ladder
alignments up and measure scale going up.
How many times the box goes up. We can then still mark these same measurements
vertically off up here, behave to these two vanishing points and we've got it.
I'm tempted to do it but we'll save that for
another one. Okay, but we will do some more figure stuff. Now we could do, again, as long as this
is accurate, we could reference another box back here from here or we could reference
a box back here from this. Remember,
as long as the other boxes are perpendicular and parallel
to these, going to the same vanishing points, and flat on the picture plane -
I mean flat on the ground - you could reference them all day. You could have 50 different
boxes as long as you had a nice, sharp pencil and you were careful. If you were laying out a
canvas when you wanted, like, repeated box shapes or houses or whatever, you don't necessarily
have to measure each one. As long as you have an initial basic size size house, you can
reference that house as long as they're lined up to the same vanishing points, all day long.
Float them in the air, do anything you want. So this is actually very useful, more so than
the simple demo. I'm trying to just speak to it. So I wanted to get to a couple
people referencing too as well make some points about raising. So why don't we,
instead of rising the whole box in the air, let's rise a person in the air and see how that goes.
So let's do that on the other side. So we had box A, just to be clear, to re-explain
what did we do? We randomly, completely randomly drew box A
in size, length, and width, and height to these two vanishing points. So let's -
completely random. We then said no, but I want to repeat that same thing, in correct perspective.
So this one looks clearly more foreshortened on the right plane and a little elongated
on the left. And you're saying, "That's not the same shape." Yes it is. That's where a lot of people
make the mistake. If you move this box back that far and to the right
it is not going to look like that box. Even though most people draw it
just back here, looking exactly the same as that one. Well they're not considering the line
of sight change and the foreshortening happening to the box. So this is correctly
box B getting more foreshortened on the right and less long than this one.
This is longer, shorter. So the idea is, that's
how our site works, believe it or not. You could set a whole bunch of boxes out on a flat plane
in a warehouse or a gymnasium and you'd be surprised at how different they looked.
from being farther away and closer. But not only that, to the right of the cone of vision
and to the left. It changes a lot, the proportioning of the box. It's surprising actually.
Okay. Let's get to a figure. let me sharpen my little pencil here.
And we'll just randomly put a figure standing somewhere as well.
And we'll just really quickly, randomly put that together.
And say, okay, just to be clear, I'll make a person
standing right here. Oops, sorry, that's a
tangent, I won't do that. I'll go in and make him stand right there.
I don't know how tall they are, I don't know how big the boxes are. Once I decide
either the scale of the boxes or the scale of the person of course
then I'll have to kinda stay with that and commit to it.
So what am I gonna do? I'm gonna probably make the person a little bigger than the horizon line, like
this. For the heck of it. And say, that's the
total height of the person.
There's their halfway point about. So the waist is
probably about there. Okay, do the head.
Okay. So that's part of the picture plane that figure's on.
Let's say we don't know yet
how tall they are. Are they six foot, are they five foot four? We're not sure but either
way, we know now that we've decided to have the vanishing point cut across them.
Once we do assign a scale to that figure - well, basically it will be
logical to say we'll be able to figure out how high we are off this flat plane too. But we
can't say how high our eye level is in this particular diagram until we assign
scale like we did before to that figure. But I'm not gonna
do that yet, let's just keep it about referencing size. Just to say you
said alright, these little packing boxes feel right to the size of them because this guy's moving somewhere,
who knows. Okay.
So obviously we know how to reference. So let's say
I wanted to reference someone standing right back here.
Same thing, you've done it before. So let's do it
And we'll put in a true little vertical for that person's height as well.
Now let's say they're not necessarily
the same height, but they're near to the same height. Well we'll still use this as the standard and say
if that other person's a little shorter or taller, we'll know it by referencing this person's height to
that position. And then just add a little or subtract a little. That's easy too.
That's a typical way to reference. You don't have to reference same size figure. The idea is you
reference a standard size and then go shorter or longer depending on that actual
person's actual height and build and character. Okay.
So let me find a pencil here that's colored.
Okay. So I'll go ahead and do blue referencing
for our figures. Base of figure A.
Might want to call it, figure, I'll call it figure
So we know it was first and we referenced the
second figure from it. Okay. In blue I'll
go ahead and make that reference point, going for the desired beginning base of B or
two I should say, figure two, from the base of the first. Makes a reference point. No
surprise now, right? Reference point number
two. Okay. And then coming back
through the head of our initial figure gives us, striking across the vertical of the
second beginning figure. Gives us
their height back there. Okay. So we'll call that figure
two. There it is. So figure two is a good deal
smaller. So again, are they the same height?
Yeah, alright, we'll make them the same height. So, head's a little bit
Okay. So there's figure two behind
because we've made a little reference plane, reference point two.
But let's say in your imagination you're saying, you know
there's actually a hill here. And this is a steep little mound of some kind
who knows? Could be a balcony, but we'll say it's a simple mound or
raised piece of earth. I'll
go, keep going up with that figure's vertical.
And now, since I'm saying you know what
I think I want them standing above where they are. Well we know where they're touching the ground, that's our
ground reference point because that's where that person's based. We decide we want
them up in the - we want them three or four times higher maybe than they are. So
that could be relatively simple. So what we'll do is we'll find a scrap piece
of paper. This is what I do typically.
Just find a scrap piece of paper, fold it in half and say
okay. Since we're not moving this figure, smaller figure number
two. We're not moving them back in space anymore or forward, we're just shuttling them
up and down because we want him about. We could go across the picture plane too, straight, without gaining any
size. So, how high do we want them? Well if they're around, let's say, around
six foot tall we could say, okay, six foot,
double that. We could simply really say
okay, that's twice that high.
So let's say we want to go up a full six and half of that is nine
feet. Okay. So there we are. Okay.
So now we could say, well
here's the full height of the figure.
Doubled. So that's twice. So there's one, two,
then another half. So we know we're six feet in the air.
Twelve feet in the air, six times two, is twelve, plus another half
is fifteen. So that's fifteen feet, right up there.
Alright, so again, six, twelve,
plus half is fifteen. So now we could say
alright there's some bizarre reason why
Landscape here comes up.
Runs off like that.
So mountainous background or whatever.
Okay, so now we've got a
hill. And the hill happens rather quickly. And we could say
well this person's a decent amount in front but that mound happens quick. But we're saying we want that person
at the top of the mound. So now, we know that the mound, right here,
where that person's feet will be when we rise them. We know
that mound, basically, right at this
point in space is fifteen feet high because we have a reference point on the ground.
And we can actually figure out by the reference and size of everybody by Xing and doing all
this later, which we'll do when we do more pictorial diagrams,
we can actually understand exactly where that spot is high and then
roll down some diminishment and guides and figure out
how to section that earth. Anyway, let's take our person
and say, that's the total height of the person. Now we raise him 15 feet in the air
and we get the total height. So now I can draw a little person again up here and say okay
that could be a separate person or the same
person. The idea is
is now standing, because I understand how deep they were, they simply
went up a certain amount of feet. But I know how many feet because i just simply went straight up the picture plane without
gaining size. I simply doubled the math. As long as we're going straight up and down,
straight across on the picture plane, all around the picture plane, and not coming forward or
backwards, we don't gain size. So that's how you would reference a person up
in the air that you wanted to say was initially on the ground plane. So let's say this
is not a separate person. Then we could say, in our imagination we shuttled this
person from here back that far into space, knowing
that we wanted them on top of a particular height of balcony or embankment of earth.
We then doubled two and half times so we know we're at fifteen feet. So
now we know there's a platform at fifteen feet. So let's say your instructions to yourself were
that platforms gotta be about fifteen feet. Okay, done. I went back
a certain distance, which we'll talk about more later. But we can lay these people down when we
measure later and simply get their proper foreshortening distance in space
And then go up straight on the picture plane. So all we did was take
the figure up into space fifteen feet. So let's
review now. Because I wanted to make a point now as we're gonna get a little more pictorial with these
I wanna make sure you understand that
I will repeat everything three times essentially and try to move fairly slow. But because
you had the advantage, unlike a class on a blackboard or something or
on the computer when you're just doing diagrams, you can repeat this endlessly, so I'm
gonna speak clearly and about the steps like I have been. But it's then your job
to draw with me, stop when you're confused, replay and keep going,
and then I'm gonna speak clearly two or three times and in the order of what we did things.
You need to take notes of that to be able to get these correct and take notes at the bottom
somewhere. So on your diagrams up here, down here, wherever you have room
you should have straight ruled lines essentially and be writing notes in the order you
understand it. Because I'm gonna describe it slightly three different times, three different
slightly ways when I describe it. It's your job to extrapolate notes from that
that make sense to you by pausing it until you get it. And then you practice
this a little bit. So, it's totally up to you but if you do practice these ideas
and stuff and little sketches and rearranging things your own way, you'll get real good
at this stuff real fast. So it does take though repetition and it does take
some careful note taking on your part for the order of these. That's why I'm speaking a lot
and clearly through the diagrams so that you can stop it, rewind,
pause when you need to and write the clear notes in yours. I have my own
notes from my notebook when I was a student were very thorough, but I had to
conceive those. Our instructor did not stop and tell you exactly what to say. He just
went through the diagram very carefully and it was our job to draw and take
and then rewrite them later very cleanly. And that is my permanent record of
perspective. And so, in the same manner, that's why I learned it well. Because I
had to write the notes and figure out the diagrams by drawing them personally. And
that makes a permanent memory that's five times better than just reading and referencing
xeroxes in other people's books. You have to draw to
the exercises like you practice figure drawing or landscape painting and you have to
actually write out the explanations yourself so it makes sense and actually
connects in your brain. So we'll run through this one again. Alright,
we started with box A, completely randomly. We then
proceeded to reference box A to make box B. So
box B was randomly placed by its front corner, its front vertical, and its two
sides going to the subsequent vanishing points. We then, by referencing
not only the front corner, all four corners, and then eventually
the height of the box. We referenced the entire box B that way
in order to that single reference point. That being done
we simply placed a figure, and we really haven't even figured out scale yet to the figure, but we could.
If we know this is six foot we've just put scale everywhere.
But we'll get to that later. The main thing is we took a figure now and just
decided okay it's another six foot figure after that. And we said I wanna
have someone randomly standing this far behind. But then I had a fixed distance I wanted to
raise the earth above them and the idea now is that
this person is no longer standing in front of the mound because they're standing directly
under the mound that this person is standing on. So this person would be buried. The idea is
I use this person's height to then jettison back here on a plane making
reference two, reference point two. And then raised them to be on there. So
to understand scale it's easier to move to the position you want
the person to be in underneath, you know, higher or underneath
that higher position first. To be right under them like a plumb bob.
Like a little weight on a string. That person is right here, is above
the earth right there. I just took the idea of that person up into the air.
So in a sense we could say, the only real person might be the person on the
hill. Or we could say the only real two people are the first figure and that figure.
Or we could say, this one's real too but they'd have to be standing in like a carved out tunnel
because they'd be under tons of earth. Okay. That's
basically how you start referencing. This stuff will get more and more how to reference the figure back
you know to the boxes and stuff later. I still want to get to Xing and
you know halving and doubling and things like that. So, you know,
and we'll continue. We'll have one or two more reference pointing diagrams and then get to the more in picture
automatic perspective xing and double and things like that. Okay. So that's
all for this.
We're back. Now we're gonna do the classic method of how
you - with rectangles and squares - you X off or
diagonally X off, make an X through the middle to find the middle and then the half to find a
square or rectangle. And then we're gonna also
you know, show the method of doubling squares and rectangles.
We'll do that in flat space up here, then we're gonna do it
just building a row of boxes. And then we're gonna go ahead and do
a one point kinda bridge, sidewalk in the air, and another two point
side walk. So we're gonna try to show that in a number of ways.
So first off - first of all I'm gonna go ahead and establish my flat
So I can draw that up.
Also draw the whole line.
And I'll go ahead and use my 45 degree triangle.
We're gonna go ahead and cast down from the upper corner here at a true 45.
With the red pencil.
Because 45 is
as we remember talking about, bisects a square.
So we'll go ahead and do that.
So that makes contact right there
and we want to recognize
this as a 45 degree angle. I'll shade that in
And then we have - we're gonna strike our next vertical there.
We've got our first square.
Actually over a hair.
Realistically right there.
Okay. And then we can X that
space. Make another diagonal, we find the middle.
And I'm gonna drive that middle now
all the way horizontally through everything I'm gonna do, carefully.
Noting where it is. Okay, there's my middle.
In blue I'm gonna show how I can quarter the
square. Show the half, the quarter. There's the halfway point
of the square. And I'm just gonna draw down like this
to show you that. Get precise here.
Okay. And we found the horizontal half,
obviously with the horizontal line. Now the doubling technique.
What we're doing is we're coming from
this corner again, our first corner, top left.
And we're gonna come to the halfway point of the horizontal half way line
striking the edge of
the square where you want to find your next square next to it. Or rectangle.
Works with both squares and rectangles. That point becomes important because then I can
like this to find my half again.
There, little arrow there. So I get my next half
and now I've just doubled the space, I'm sorry, so I've just taken that method
just gives me twice this. I just found another one, I can strike it and make my vertical.
finding my second square now properly.
I'll go ahead and X that again with the diagonals.
Just with my pencil.
Now I've got my halfway point if I need it because I don't need
to keep making the 45 because now that I'm repeating the squares I have my
halfway point every time. So if I simply strike any diagonal
I can find the middle. So we can get our blue marks again.
And the blue marks represent splitting the square
vertically, and then we've got our quarters. So we got quarter squares, we have the half of everything
and we've doublef one as well. So let's double it again. We have to start the fresh
new squares upper left hand corner and we'll strike down the same way
to this point here. At the half way
point up. We'll strike down again and get another one.
I'll draw that arrow a little further and we get
that strike right there and that gives us our next vertical for an entire new square.
Again this can be done over and over with rectangles too.
Okay. There's our next
standing square, make sure that's right on the money.
Okay. And again if I want to put a
casual diagonal down there again I can, you know, either way.
Let me find my middle again. I coulda come down this way but I just wanted to show you since we're doing
projections. We did our original 45 to find our original square
then we kept doing the same corner, we kept coming through this half way
reference point we made here to get the entire new square, same thing, entire new square.
So I go ahead and reverse my diagonal to find the half again. Now I can put in my blue
verticals giving us the half
and then the quarters of the square. So now we can quarter the square.
Again, okay. And I'll go ahead
and do one more. So I'll take my red pencil again, find the new upper left
make that reference point on the halfway line
Line that up more accurately. There we go. There we go.
And once again
strike through, find my mark, come up,
make my vertical. And we've got
a last fourth square, right there
where we can still go ahead
strike a diagonal back and find the half to confirm it.
Right there. Yup. And then I'll put in my - and quarter it in half
with my verticals for the blue.
We'll go over that really clearly.
Just make a note that this is
one half, one half, and we struck it originally
every time I do a blue as well. We'll put this down here.
This is one half, one half,
one half, one half, why?
My original square, half, half,
second square, half, we already have the half, third square
half, half, makes a quarter, fourth square same thing. And
each time I come through, top corner if I want. I could also come through the
bottom corner, through here, and find it from the top. Either way works, so go ahead and play with these concepts.
But we're just showing the basic Xing or diagonal Xing
method to find half way and half way line and then the reference point on the
halfway point of the far wall of the square or rectangle where you want it
create next to, repeat another object.
create next to, repeat another object.
you go ahead and double over. So we just repeat, repeat, repeat. So
there you have it. We have one, two, three, four squares.
Okay, so that's a very ancient method of doing that in architecture
Okay and why don't we go ahead and create two vanishing points now. Ober here
and one over here and we'll go ahead and just do that with some boxes.
On the ground just set kind of in front of us. So what I'll do is I'll just set a vanishing
point right here, randomly. Since we're not doing
the station point and cone of vision right now I'm just gonna make them fairly wide so they're
accomadating what we need. And I'll go ahead and put one way over here.
And I'll call this VP two. And I'll call that VP one.
And we're just gonna randomly place a box where I think it will be. Pretty good.
Let's say about here. Okay, okay.
Like that. Alright.
And I'll go ahead and draw that out to the one
vanishing point on the left and to my other one on the right.
Making a little cross corner, kinda have it fade away. Okay.
Then I'll have a standing box.
since we're not measuring with measuring points yet we'll just simply guestimate.
how high I want the standing box. I'll kinda go well
alright, I'll guess that it's this bug.
Now in flat space I can find a real
square easily. Without measuring I have to guess at what a square is. So I'll go
ahead and try to make a good robust one and not make it too short.
Something like that. So I'll say it's out here. Right about there. So I'll go ahead
and randomly assign what I say my first square is in the particular perspective.
There's my first box. What I'll do, just like before.
I'll go ahead
and exit -
find the middle. I'll also
guess at my other dimension toward vanishing point one.
Just kinda as a
little bit of a guess. About there I'd say, okay.
Then I'll draw out my first cube, real lightly.
Drive those two to the vanishing point number one to the left. I'll come back
find my line down here,
And now what we're gonna do is
we're gonna continue drawing just the face of the box. We found one box but I've continued
the idea. I'll fill in my back corner so I don't get confusing.
I'm just gonna create the faces of the box on this side
we'll then repeat the rest of the boxes. Okay, so
just consider that a standing, random first square.
Then I turned it into a cube. I'll come back to this.
And I'm gonna say, alright I drove that by
finding this, what we'll do is we'll find that half way point. Remember
this is the half way point. We made a 45, X that.
So if I want, this represents now prespective
45 that I guestimated. So we'll replicate what we did
up here in the flat work, drive that down, and we'll
say that's going into space. So now we'll use a little cone, there is that
half way point. That's really important, we're gonna drive that all the way back. Now don't get confused
with this half way point. We want to make a, you know, be able to kinda tell the difference between them. So I'll go ahead
and draw in my half way point all the way down. And that
will serve me now when I make the same reference method. Now I'm gonna
double it over.
There's that point.
There that goes into space as well. Okay. Make my mark.
Okay, make my vertical back up. And then
we'll go back and put our blue work on our first square.
There's my second square, referenced from the first
with this halving and doubling method. I'll go ahead and take
my vertical. Now that I've got my halfway up the cube
Half, half. I'll go ahead and mark
vertical halving with my blue, just like we did
with our first square up here. And now I can find my
half by simple diagonal on my second square I've created standing here.
There we go. Alright, there's my center.
So I'll go ahead and create me blue half as well.
Just to replicate our flat work above.
Okay, I'll go ahead and use my red reference point again on the half
way point to remind you.
And this is a perspective 45 now.
So remember, this is a - I'll put in
perspective 45. And this is
a real 45. That's a 45 in
perspective according to what I said a standing square was that turned into a cube.
This is a real 45 degree angle in flat space.
Okay. Then this is this projection. It's actually going into
space now, into deep space. It's going down and far into space, down to the right.
Okay. And we're gonna do that again from being up here. Going down
through it to repeat. So I'll go ahead and be careful here to make sure I get enough
depth to it. Okay. Again, going down
and into space. Make my mark.
We'll go ahead and still make the four boxes. So I'll come up and get my vertical again.
Making my third standing square.
And I'll go ahead and put a diagonal through that, really lightly
to find the center again. We want to find that
halving point. So we can make our blue verticals
and quartering that square as well.
Because that could be very informationally
helpful later. Once again, I'll take my red,
find the far upper left corner in this case, come down,
there we go. Here to here will make the
fourth and final standing square. I'll go ahead
and reference that. Again into deep space,
down to the right. So we're going three dimensionally in our minds, not just
over to the right flat on the paper, but down and into deep space
to the lower right. Okay. And those - we'll talk about why those actually
all diminish together when we get into auxialiary vanishing points, 45 degree auxiliary
reference points, all that kind of stuff. Kinda like we did a little bit
when we talked about what space would be
with the cube in the physical lecture. When we talked about auxiliary vanishing points with the cube.
Okay, ah there's my mark.
Alright, we'll go ahead and put that last vertical in for the end of the fourth
standing square and then we'll turn them all into cubes. Which is pretty easy.
I'm not gonna put a lot of interior work into here, I don't want to get the diagram confusing.
But there's our last standing square, and I'll put
a light little diagonal back in, crossing
our middle line. Remember, this is our one half line right here.
One half, the height there. Not that one,
that's the back wall of the back cube. This is the half way line, so one half.
There it is. Okay. And then we'll put in our blue work for that last
square, standing square. And then we'll turn them into cubes. Kind of
lightly, I don't want to cause too many lines. There's the blue line work.
Now we know, that says that's a half, half, half, half, half.
I won't bother labeling them you can just refer right to that and everything's the same just in perspective.
Okay. So we've got our standing cubes so I'll
put - lightly put them into going to this here.
I'll make sure I'm doing my cubes, not my halves. Back to the back wall.
The idea is I'm just gonna
find them there. They're gonna be pretty light, I don't want to mess up the work inside. Main thing
is I'll mark really obviously is this top cube.
I'll make a row of boxes going back properly
here. And then again I'll put the work of - transparently put the
work of them coming down very lightly so they don't interfere with our interior work here.
I'll just kinda face that line away as we go.
And there's our back corner. There we go.
Alright good. Clean that up.
Meet that up, meet that up. There we go. Okay.
And I'll put those darker in so it's more obvious.
Real quick and then we'll move on.
Just get a little line weight in there.
There are our stacked cubes. They started out as the faces of four
squares, or actually the first square, then we made a cube, then we put in one, two,
three more standing squares, cubed them out. used the same
exact method here, as we described. Exact same method in actual there.
There's a one point vanishing point, or I'm gonna say it is. And I'm just gonna say VP
one point. And we're gonna put like a walkway bridge
completely randomly going up this way.
So that's in one point so it's going to behave a little differently. I'll
go off camera.
Go off camera. Alright.
And we'll go ahead and put our first sidewalk - well I'll do that
with a T square actually. I want to be accurate and good practice.
Make sure it's in camera, so it should be about there.
One end, there it is. That's
my first section. We're underneath, let's say, a bridge.
And again, I'm just gonna guess at what my square is. So
I'm gonna go ahead and sketch and say, well I don't want it too shallow, I don't want it too deep. I'd say it's about
there. Alright. That's fine.
Then I'm gonna go ahead and put a simple X through it so we can see the center.
So I'll try to carefully do that.
Let me get my X diagonal. This time I'm just gonna do it with pencil.
Do it kinda fast. Okay.
Find that, that's our center. And we're gonna drive that center
all the way to the VP.
Okay, there's my center. I'll use the doubling method
again. Where we can come
from this corner, through here and continue into space.
Okay. And that will create a
Okay. Right there.
I'll draw across from that point.
There's my second square in that particular perspective.
Now I can just find
this corner again, look at that for the reference, find the
next one that fast. And if you want to keep halving them, you just keep Xing them. In this
case I'm just gonna keep doubling them. But you can certainly go back
if you need to.
And you could certainly X this, find the center like we did on that one or
all these others. But I'm gonna go ahead and just keep going, make my mark, and that's
the third square I can close off. Or
its back edge, let me go ahead and do that.
Okay there's my third and we'll make one more.
that halfway point again,
Make it a little deeper, there we go.
Once again, back into space.
And finishing out the fourth.
So there's a little one point idea
of one, two, three, four squares. Like a little
bridge we're under going into one point forever. And, you know, we
randomly decided the size of that first and the foreshortening of that first
square because we're just using basic referencing methods here. So halving and doubling, halving by
the Xing and the diagonals Xing like this, making the half way mark.
Then doubling by the reference point on the halfway point of the far wall. Going
ahead, getting our next, getting our next, and getting our next. It works the same way here.
We'll do one more real quick sidewalk
in two point, laying down.
And remember, in a sense we did this same
thing that we're doing here and we're gonna be doing here with
our reference point with our simpler sidewalk. But now we're actually, you know,
we keep drawing now with the idea of it just being a reference
and Xing method. Okay, so we'll have this right next to here
like this. Running like that.
Running forward like that. And we'll just make a
real quick guess. I'm gonna get my bigger triangle here, it's a long way away.
I'll make my first random plank, or sidewalk section,
right there. And then I'm just gonna guess
what I think a square is. I'll say there.
Alright, that's what I
say the first is. And again, we can always
put a diagonal X in it, find the center, and then drive that back
toward the vanishing point. Okay.
There's the vanishing point, there's my center, right there, drive it down. Okay.
far corner, half way point,
it gives me a reference too, making the second. There it is.
Draw it in.
Go back to the vanishing point on the left. Got my second.
Go ahead, make the reference
through here again. Same repetition and we
got, we have our
next one, right there.
We'll go there. Alright.
And one more time.
Here, through there, to get the next
square. Alright. Try to do it accurately here.
Good, alright. One more mark. There it is.
Okay. Got the end of my last
section there, off to the vanishing point.
There we have it.
So we could say our first section was right here.
Okay, so make sure you make note of that. That's random.
The first one up there was random. This first
one was randomly sized the way we wanted it, here.
That was our first one. And the first standing square here was
random. Because we're just referencing, we're not measuring,
We don't have the cone laid down and all that kind of stuff yet. We haven't gotten to that quite yet. But
we're just referencing and doing all that kind of work.
There you have it. We have a real method of Xing and diagonals to find the half, and also a reference method
to come over, strike the half mark on the far wall, double, double,
double, like we've been doing. Reality here, in one point and then two point
again in the sidewalk. Okay, and all the same things about halving are
true here. We could keep Xing these and halving them if we wished, and we didn't do it here either but
we did here. The same exact thing. You'd X, find the half,
draw out any, you know, how you wanted to, like we did here on the original. Okay. Alright.
And that about wraps it up that way. So that's diagram nine for lecture one. Okay.
vanishing point one and two, for two point situation, down in this
area. Or we could draw up here. And also we're gonna have a one point vanishing point. So now
we know that this is where our invisible center of vision is we're not using yet, but it's
actually there all the time. Because our one point vanishing point is always
on the eye level, or the horizon line.
Crossing perpendicular to the eye level is the center of
vision. So when we have our one point vanishing point, when we are parallel and perpendicular
to everything, that means it's right there. Okay anyway.
What we're gonna do is we're gonna stack some rectangular boxes and, you know, still continue
a little bit of Xing and half and Xing and doubling space. Okay.
So let's just start with some simple shapes.
I'm just going to, let's see,
yeah we're just gonna create some
boxes going in this direction. Essentially let's do that.
So I'll just kinda start out with
a compositional feel out like, alright, let's do some
boxes going this way.
Okay, maybe put a vertical there. So
I'm just gonna start with some shapes and just keep
building and talking about proportions and lengths and widths
by just guesstimating depth because we're not really measuring yet, we're only
using vanishing points essentially. So I want my first box to -
I don't want it to be a square now, which would be right around there, but I want it to be
a box. So I'm just gonna - it's not gonna be twice as long, so I'm just gonna say alright.
But I could do that. If I wanted to I could guesstimate and say okay, there's my first box.
That would be a square. Then two squares would probably be about there.
Okay. So I'm gonna make a box approximately
one and a half deep. So that's just an approximation I'm putting in. So remember
the scratchier lines are just my guesstimation are what
two standing squares would be essentially with the next one being a little more foreshortened and then roughly
guessing this is one and a half by one. If I wanted to.
So that will be my goal. Okay, so there's the side.
So we could say that this box is roughly -
just by guesstimating with good standing squares, which is really how we base all movement -
we're just guesstimating with vanishing points and sketching freehand
and just knowing perspective and using reference points and scaling and all the Xing
and doubling we've been doing. But you're also guesstimating really good squares, drawing
flat and standing squares and then turning them into cubes. That's how we get
whole grids and just with a freehand method and assistance of a ruler.
So we don't measure that often unless we need it. And then, but
the measuring is what teaches us why the perspective works. So, you know, as a package it's
crucial. But let's say, we now know that this box is
one and a half times as deep as it is high. So one unit high, one
and a half units long, to here. So there it is.
Not to be confusing I'll make really clear corners there. Okay.
So let's go off to this and say how wide we want it.
And then I'll guesstimate that.
And say, alright, if that's a standing square about there
I'd want that to be about the other side. Roughly.
Alright. Something like that.
So, I'll just put it there.
the depth of my box, basically it's a little shallow but that's fine.
I'm gonna square it out.
So I'll go ahead and draw out my first shape, just to make it a real shape.
Real quick. And I'll go ahead and make it transparent.
So I'm showing my back work too, oops.
Alright, that's my back
corner. Come up with my vertical for my back corner.
We got my first box. And I'll make that clear with a
line. Okay. Let's just say that basically represents our first box.
I'll make the ground line a little darker.
And then we'll continue. So now we could say this box is
one and a half deep
by one and a half deep to the right
by one high by one deep to the left. So the
box is as wide as it is high on the
left plane and it is one and half times its height
on the right plane. Okay.
just by visual guessing. As you know what we did was we simply
said that would be an invisible kinda of idea of a square. That would be two, that's about one and a
half. Okay. So let's go ahead and double
that. How do we know how to do that? Well, we can still X the
face of the box here.
And make it clear
that's the halfway point. And I'll cast that in to here.
Space. So there's our halfway thing. We'll bring our
front top corner again
to the back plane, halfway point.
Cast through, like we did before,
now we're doing it with the rectangle. And that is our second space.
I'll go ahead and draw the vertical for that
And I'll close out that shape as a cube now - or not a cube but a rectangular
box because we're gonna immediately make
these three dimensional. There's the back row there. I'll go ahead
and make it transparent a little bit. Lighter with those ideas.
So there's the back of our second.
let's be clear and thicker with the line for our two. So now
this gave us our second box.
Now we can repeat. Now if we want the middle of the second
box, we simply have to go across here until
we hit our middle line. This is our middle line coming back, right there, so
we could find it and come back and do what we did before if we want to do
a light indication in blue. Just to be clear form our last diagram.
And there's our first, that's how
we'd half that. Quarters.
Quarters. Now, so we've got two boxes now drawn out.
I'll do a third obviously, taking front
top corner new box, second box, drawn through the halfway point.
On the rear plane, vertical, coming
Going into space, into space, where that
marks there, that gives me my back vertical. I'll take the pencil and the T square to do that
Alright. I'll go ahead and
draw my box out.
Just like these go out here. We want to be clear, to the left VP
of course. Alright.
So, now I've got a third box
and I thought again I wanna come through the diagonal the opposite way
for convenience. I'll strike that middle line and that's the middle again. So I can take my blue
and once again
get half of my rectangle, side to side.
Oops, blue. Okay.
And we'll repeat one more time.
Front top corner of new rectangle box
through the halfway to the back plane here.
Driving it through,
gives me a fourth
back of my fourth box.
There it is.
Go ahead and draw that out.
To the left side VP.
I'll lightly put in the interior, I just don't want to get
interfering too much with our
idea of our
information, so I'm doing it lighter. Okay.
So I'll make it really clear with thicker lines real fast.
Our four standing boxes that are not squares, they're one and
a half deep for every one high, for every one
crossed to the left. One, two, three, four, we've just repeated.
Again we could X off the last one again with a diagonal against the
center line once again to find our half way points with the blue. I'll go
ahead and just lay this down here. Okay.
And again, same
information for our facing plane to the left. We can
X that off.
We can find the center
if we need to. And we can draw
that plane's center back like this as well
to get its
halfway point as well, horizontally.
And we could again
double this over easily, by taking this corner
to here now, that's our halfway line.
Driving through. This is very close
this is gonna look like a tangent but bear with me.
It's just a little bit on that line and we come out to here, strike right here.
There. To get our second plane.
Or square in this case, because remember the end of the box on that side is
a square. So we can draw it over there. There. There's a second
one. Now we can draw it back and say okay, we're gonna have a second row.
Go back. Close that off.
I'm not gonna draw a lot of interior space, it'll become too confusing.
But we do have the seams going back to say top of another box
Going four back again. I'll put a little bit of the transparent
interior, but not much. I don't wanna get too confusing here,
That moves across, yeah. Okay. There we have that. So we've just
double those over. And let's say
we kind of wanted to create a step, so we're gonna -
we're gonna double up
the boxes on this second plane over here to the
left. We're gonna double them up twice as high. So we're gonna have a
little stack. So there'd be one row of four boxes, the second row of four boxes, and then one
more stacked on top of the second row to the left there gonna be another four
boxes on top of that. So I wanna make sure I X off
my left plane box. Get my middle point.
Now I'm gonna drive my middle point up
and make it in blue.
Just like we always do, make our middle plane in blue. Then I'm gonna
drive that one up higher. And I'm also gonna drive
up the sides, the vertical sides, of that particular
second standing box.
to the left. So
let me make that clear. I'm driving up these verticals up.
And I'm gonna go ahead and drive that vertical
up as well, longer than I need.
And I'm gonna use the same method, but now I'm gonna come from just this bottom
front corner of the second box end
and come through here, my halfway point that divides the plane in half.
Coming up. And doing so will give
me, if I'm careful,
my second height of boxes. So what that does
right there should give me my second
height. So I'll draw that height back to the vanishing
point to the left. Okay.
So now I've got the front face
of the first stack of the box there on the second left. But it's easy now, we can just draw it out.
We have the seams going back and we have the depth of the second row of boxes.
So now all we have to do is literally
Remember we're coming up just for the second row, it's like a step.
And we're gonna meet that there. Okay.
We're also gonna meet each scene, going back.
So those boxes are lined up on the second row there.
So where they cross -
where each new box is because the plane of the top of the first row of boxes
is meet the side plane of the second row that's on top of it at the same place.
We're gonna also then draw the top of our box planes for the
second row on top there to the left. So I'm gonna overextend that line.
I'm gonna draw that toward the left. Oops.
And I'm also gonna take these
seams and draw them across to the left vanishing point carefully.
My pencil's not the sharpest in the world.
Always keep your pencil sharp. Oops.
There. So other than that, let me get my eraser, that is
most irritating isn't it. Alright, so I'll go ahead and get rid of a little of that
and clean it up a little. Okay.
I'll go ahead and draw in the back corner, just freehand.
Say okay that corner is gonna be around there
Okay. And the idea of these seams are around here.
Just draw those in freehand actually. Just
show you that it's not all (indistinct) but ya know. We're trying to get the
idea of these boxes.
Got the idea.
And I'll really make the
seam a little more clear. So there's
that second row seam. Add a little thicker to make it clear.
Alright so now we what we have is we
had - we started with our first shapes, so I'll go ahead and tone that in in
blue and I think that will be helpful. Very lightly though. We started with our first
box, that's one and a half deep compared to being
one unit high and one unit deep to the left. So
one and a half units to the right,
one unit high, one unit to the left.
Then transparently we got the idea of the rest of the boxes. So we took the first
rectangular box, repeated, repeated,
repeated, made our first row. Then added a second row by simply drawing
out the face of this one, going back, meeting the seams, and making a second row.
Then we decided to add the third row by taking this face
plane and just doubling it up here by Xing, halving,
driving it up, creating the next one, then just by driving back and following the seam
we got our back depth and all our crossings to create a third row
of boxes stacked on the back row. So we essentially have a step
and of course the step is right here.
A little step. But we can do it all by just doubling and halving and all that, you know,
we could keep going and going with this idea.
The thing is too, we could also do it in one point. So let's do a little work up here again like we're underneath
a floating sculpture or something.
So what I'll do is I'm gonna set an
rectangular box facing us, just going into space. So
let's see, I'll put it about right here.
And I'll put the top line about there.
I believe that's still in our frame, I hope.
Be close. But I'll go ahead -
I'm using the one point vanishing point now. We use
for this entire construction down here we used the two points. Now
we go back and use that one point vanishing point in the middle of our picture to make a random
square facing us. And remember, any time
I need a square I just take my 45
and say okay, that's the height I want it. I'm gonna come down.
45 degrees and strike a square right there. I'll put in my
Here I go.
So we have a facing box toward us.
we're gonna make this box facing us so it's gonna go down like this.
And we're gonna show the back corners too. That's gonna be very close to our 45 but not
quite so I won't show it going down like that. Okay, so that's the back.
So that other pencil line coming near to the red one, of course, is the back scene.
We're gonna play that down though as we go. Okay.
Then I'm gonna make a guesstimation again. I could do it from the side or here, since we did it
before from here I could say well, yeah, what do I think would be one
square's depth. Okay, I'm just gonna guess and say alright,
I believe, you know, foreshortened, that could be
where there - alright. So I'll put one in there.
Alright. So that's my first square, just as a measurement.
I'm gonna put that in blue because I'm gonna double that. And I'm gonna say
because I want - I want this floating box that's facing us as a square to be
twice as long now as it is high and wide.
So we know a square is the same width as it is high. But I want the box receding into space
to be twice as long as it is high and wide.
So that equals one square that I started here in depth. So I'll shade in my
first depth guess at a square.
Right there in blue. And I'm gonna then double it. How do I do that? Let me
sharpen up my pencil here and we'll be on our way.
Okay. So now
I'm gonna X the box
I can X it in front and then come down but I can also X
this plane real carefully. Let me get my head out of the way, hello.
I'm gonna X that and I'm gonna then take the exact
corner of that, oops.
Excuse me. I forgot to shade in a hair of the
corner of the box. Alright.
the square so I'm gonna make that clear. Come back with a second, right here.
Say that's the center. And I'm gonna drive the center back
of the X. Okay.
What that does -
excuse me, we'll do this up here - is we've just found the center
to be driven back from here. Which also should be
the center of the box that way. Make a mark. We're just dealing with
the bottom plane. Then how do I double it?
Remember I take - I can take this far corner and come
to the half way point of the back wall here, with middle line we just drove back
strikes the back wall from the kitty corner over here.
And driving through that, carefully, should give us our second
box. This is a bit foreshortened. I'll go ahead and have
faith in it. And it hits right
there. So I'm gonna go ahead and draw that through.
And that goes on into space
and it hits right there for that second square.
So I'll go ahead and draw that back. And that gives
me my depth as being twice as deep as
it is wide and tall. So I'll carefully draw that in
So there's that second plane that I needed.
to add on. And I'll put that one into red, saying okay there's my second half
to make it twice as deep
as it is wide or tall, which I know from the square. And I'll go
ahead and draw that - close that shape off
by the side. And I'm not gonna bother doing the halving work on this
plane or this plane. We just did it underneath, which is a little more foreshortened but it shows you
that if you're precise and have your tools relatively in order
you can get what you want. So let me highlight the box now.
Total rectangle box we wanted to make. And I'll kinda just draw
that through a little thicker so it's more obvious.
So now we have a floating box that we
first got the face of by creating a square. Then we cast it back
to the one point vanishing point because this box is obviously facing us straight on
so it has to be going, being at 90, you know, being an object that
has 90 degree corners. It has to be facing the one point vanishing point, which secretly holds our
center of vision underneath. We then took that
box, cast it back, and we guesstimated
the first blue depth. That was a guesstimate of that blue line for the first
depth. Once we had that we simply doubled it and said, I wanted a box.
Again that was twice as deep in perspective than it is wide and high.
And that's what we got. So that's that box. What I'll do is I'll
shade the depth of the box
real simple that we got here.
Eventually, but that was the last move we made, remember, is the side of the box.
Coming up like that from the depth we got underneath. Okay.
So again that was just another example of Xing, halving and doubling. Okay
that's about it. So again let's review. We originally started
with this corner and said I'm
gonna create a plane that I feel is one and a half as deep as it
is high and wide this way. So we got - we basically created this
box. Then we put our diagonal string and got our halfway
plane and drove it back. Also got our halfway plane, drove it back later for this one.
But we effectively created this whole original rectangle first, we even drew through a little
bit transparently in the back. We then, by using the halving and doubling method,
we created the second, the third, and the fourth box, as we've been doing
with the squares. And we also got the the tops of all those.
We then decided to take this plane and go ahead and add a second row of boxes
behind the original, the first. So the second row came to the left. We created all those
not really doing much interior work to get confusing. Then we decided to really
X this off, find the half way plane, not only
casting back to the vanishing point, but straight up in blue. That gave us the ability to
double, by taking this corner through the halfway point of the top
plane and by striking the back plane, we got our
second, standing square, which then I cast to be square boxes
to these others already on the ground. So now we have a third row of boxes and
by the way they're stacked, they actually make a little stair step.
Just a whole little grouping we did by pure reference. Just guessing at the depths
of a one and a half square, by one, by one. So one high,
one deep to the left, one and a half to the right. And all those squares have that
same proportion correctly in perspective because we went ahead and did the Xing
and halving and doubling method using that. Then we took the one point vanishing point
and just created a real face of a real square, cast it back
on the side planes, in a perpendicular manner back to the one point vanishing point, which secretly
holds our center of vision underneath. Then I created my first
real square of depth I wished to face from that box, just as a guesstimation
where the blue line is, then did the doubling method through the half way plane I put in,
got the second square. Then I could draw my side plane in, but this is not
a - remember it's very critical here, in perspective - let me put the blue
line in it'll actually help, this is not the depth of the square, it's a
the depth of two squares. So let me make that clear and write that down actually, I think that's
important. So I have to remember that
right here is the point where my second
square comes in. So I gotta make that clear. There's that division.
Okay. That's the
first square's depth and the red is the second. So we've got one, two,
deep. So remember, this square in the front, this width
and this height is doubled in perspective space. That's how fast
foreshortening happens is that we've got two lengths of a square, not one,
for the depth. Whereas we have one and one here. So that's a good lesson how fast and
steep foreshortening can be. Okay.
So that's just another idea of how we can use the
Xing, the halving and the doubling. Both with rectangles and the little double square
up there, going to the one point vanishing point, where these were of course done to the two point vanishing point.
Started with that, started with that. Okay, now we're
to the next.
to do a doubling method with, considering a
space in between evenly. So we're gonna take some box cars, for instance, on a train,
or something like that where we have a rectangular box by a
particular space between the next rectangular box. And then those same
boxes and spaces are repeated over and over again with a quick reference
point method as well as using the Xing and halving and doubling method. So it's both
using the physical reference point on the face of the objects
with a line as well as halving and doubling with Xing.
Okay, so let's give it a try here. We're gonna do the flat space idea of it.
So I'm just gonna represent here
the space in which my line of
objects will go. And I'm gonna just
pretend here that we have
random space here.
It's gonna be like a box car, about that long.
Then there's gonna be a little space in between like this.
And I'll go ahead with my kneaded eraser and actually lighten
up the space in between so we get the idea
that's gonna be a space in between.
We're gonna consider
the box car and the space in between as one
total length of the shape. So I'm gonna
go ahead and make an X. Remember, I'm not Xing the box
only, I'm Xing the entire shape created by the box and it's
space to the next box.
That's also the same way, as you'd just by Xing the box, give me
a halfway point now. So look at that
and drive my - down the middle like that.
Okay so as a reminder I've gotten this
by Xing off the total of the shape of the box, or the box
car and the space in between to the next wall of the next box car. I've considered that my entire
shape. And then I've Xed that off to get the center.
What I'm gonna take note of here
in red is where this X shape hits
the side plane of the back of my box.
I'm gonna call that a reference point. And I'm gonna drive a red line
to take note of that space.
like that. Alright.
Then I'm gonna continue because I want to
create another space of this box car plus its
counter point, or counterpart I should say, space. Box,
space, next box, next space. So I'm gonna again, I'm considering
the box and the space as a whole shape. So
therefore I'm gonna put my
Xing point here so that when I take
this entire box from here and this entire negative space
and come through here I'm gonna create, again, this
space from the box and the space here again, for the box and the
space again. So I'll carefully go through there
So that red mark represents both the space and the
box. So I'm gonna make a horizontal now for the ending of that combined space.
So technically that would be beginning
of the third car, which we'll keep drawing out if we have to.
And now I'm gonna still put a diagonal through
the space that now represents this entire space at the bottom
end of space. Very carefully put down the X
I already have my center here of that entire space, like I did here, now.
Because I already had the middle line and I went diagonally. The other point of interest is in the
same way this diagonal in the first box struck
the side of the back of the box car the first time, continuing
on its way here for the entire shape, I'm gonna make a note of that.
I'm gonna make a note of it again there.
Right there. And that gives me
the back of the second box car
followed by the space, which makes the
total of the second shape. So again, I'm considering the box
car and the negative space between it and the next box car a total shape.
So there's my box car. And
again. And I'll take my kneaded eraser again to remind us
that this is a little lighter because it's a negative
space between the boxes. I'll go ahead and then take my T square
and create a third box car.
And lengthen this.
And do the same thing again. I'm gonna consider the entire length
of the second box car and the space in between
as a shape. Therefore, I'm gonna put my
as a shape. Therefore, I'm gonna put my
mark here on the plane to get - so I'm gonna come back from the
beginning of that second shape, including the box car and the space,
I'm gonna come back from the beginning, go through there to get a
third marcation of another box car and another space.
Woops, let me make that a little longer so I can put an arrow on it.
I should have done that the last time, I apologize for not being thorough.
Okay, and this of course
would have done the same for...
Okay. Let me just make sure I clean that up. Okay.
Making sure everything's tidy here. Notice these are parallel. Okay, so I've taken
the second shape, the start of the second shape, which is actually the box car and the negative space.
I've taken that and considered it from front top corner over to the left
through the half way point, coming down, makes another
complete shape, which includes the next box car and its negative space
for the fourth box car.
I'll go ahead, mark that off.
And as I did before, I will go ahead and put
a diagonal from the top right to the bottom left.
Like I did here to get that mark, which is the halfway mark of the
total shape. But now
again, where that diagonal hits, the red line
I originally put in my original reference point from
I get my second, RP 2,
and again I get my RP 3.
Which becomes the end of my third box car
and its counter part, negative space to the fourth box car.
So I'll go ahead and lightly erase
that line again so we get the idea that oh, that's right. Those are actually
negative spaces. And we'd
continue the process to the next box car.
And repeat and repeat and repeat. We can do the same thing in perspective.
So three's all I need to show you. We have the original
box car, so we'll say, original,
box car, box car, box car,
So that's the total
shape. So what I'll do is I'll just remind you
that we considered
idea the space. So in blue I'll lightly
shade in our first idea, not to cover up our work, but just to remind us that
box car and its counterpart
space between it and the other space. So it's actually
this whole thing. Even though
the box car is darker. I'll kinda make a gradient like this,
back. So the idea we're taking the whole.
So again, I don't have much room up here, so I just want
to, you know, this is the entire shape.
We then X off that entire shape from here to
here, considering it the corner, so I'll put those in in blue
That's the entire first shape. Got the middle line,
drove it back, Xed it off, and where that second diagonal
hits the side of where I wanted the back of the first box car I made a reference
point. So I took that shape again
with the half point, came through here, through
the halfway point, doubled it, so now I have doubled that shape again,
I want to make it clear that from there to here is the
new space. Did the same thing, made the reference point when I struck back
the diagonal. I continued on, considered this entire thing again
the third actual shape. So when I drove
back again through the halfway creating the space, that diagonal again struck a third
reference point. Which is right here. So again, by repeating
this process over and over again, it's a pretty quick way, once you kinda understand the logic
without having to draw a ton of lines on the ground or a ton of reference points. It's actually
pretty easy. All you're doing is considering the rectangular
box and the negative space as one shape. As long as the shape
boxes or the car shapes or the objects that you create
kind of a rectangle plane around, they could even be standing, you know, columns or whatever.
This could represent the negative space of arched columns and its pillar.
Negative space, pillar, negative space, pillar. The idea is, any space that
works like this that you could reference with standing rectangles easily, or sitting for that matter,
the idea would be it's a fast way to reference
actual space and carry along its - automatically carry along its negative space.
Or in the case of arches it would be negative space, pillar,
negative space, pillar, negative space, pillar. In this case it's box car,
empty space, box car, empty space. As long as those objects
and the spaces between them are even, you can consider the space
and the object as one object. Then with a diagonal you simply make these
references. And each time you strike that reference you know where to draw
the end of the first shape, the second shape, the end of the third shape. So the object of the reference
point is to marcate this. Then when I do the whole shape again from here,
go across and double it,
put the diagonal through to the corner, to the corner, this diagonal, I strike here.
That gives me the end of the second car. And I do the same process again,
take the diagonal across, it strikes. Where it strikes
is where I got this line. So the reference point has to come first before you're able
to get the back of the second car. Before you're able -
actually that's not true, we created the first box car in the space. I should say, correctly,
in order then to double back the entire space, you'd
get the entire space first, then by putting the diagonal in and striking again the red line
the end of the second box car. And again, creating the third space,
considering the whole thing a third space, putting the diagonal in and where it strikes the red
line again, that diagonal is where the reference point is. The reference point
gives you the back of the third box car again. And that's the order.
So you have to practice this. It's a little confusing, but ultimately instead of
writing a dissertation on it, like you know, fifty pages, which if you had to try to send an email of this,
it would be a nightmare, right? The idea is by drawing it out slowly and repeating
the lecture and simply pausing, reversing, pausing, you'll get this. But it's a great
way, when you eventually get going on, you know, either empty space, pillar, empty
space, pillar, empty space, pillar. Or object, empty space, object, empty
space, object, empty space. Either way, it's a fast way to reference many, many
of those back in space. And after you've created the first shape that you think looks
correct, you can do a whole row of windows on a building this way,
you could, you know, a whole bunch of stuff that you don't have to actually measure it out or count it out and
hope you're kinda right. Or even using a measuring line and measuring the entire thing out.
I find this reference method fairly quick when you apply it in different situations.
Okay, so that's the flat work. So just to remind us again,
we consider the entire rectangle our shape and then cut in by a diagonal
to get to the box of the car. The first car was made up with the shape first. We have
to establish the first box and space first, then the second comes
with the reference point method, draw, third, by halving and doubling.
So we're still using the X method and doubling.
We did it here, through this space, to here. That's the entire first shape.
Then the diagonal cuts through and touches a reference line here.
So we'll call those reference points and this is our reference line. So let
me go ahead and make that clear actually. I'll continue that and make
sure we understand this is our reference line.
Okay. Now we're gonna do it in
space. In perspective I'll go ahead and make
box cars going this way. So I'll do this way.
Actually I'll lighten these up a bit.
There. That way we'll have a little depth left without getting too
out of the cone toward the vanishing point.
Just to imply
there's some over there. Okay.
Alright we're gonna do these boxes this way, from the flat work
down here. Sharpen my pencil a bit. Anyway, that's what we're gonna do.
So again, by considering the entire shape and its space,
take it to the second shape and its space, then to get to the
third space and its shape. So, let's go ahead and
figure out what we think this is in perspective. So if we think the box car is about that long, let's say
that's about right. Okay. There's our first
standing rectangular car. We'll draw that out.
Okay. Now I'll go ahead and draw that
out as an actual shape.
Okay. A little bit of transparency here, just real light and then disappear.
So we don't interfere. And then decide how much do we want the back? Okay, to about there.
Okay. That's our first box car if you wish to think
of it that way. And I will continue this line -
so I'll go all the way down. Okay. And we'll
draw a little bit of the transparent space in here. Kinda let it disappear, okay.
Alright. Now we want to create that second space
So I want that space to be about there, let's say. Okay.
So I've created the second space now, same method.
There's the beginning of the second box car. I'll go ahead
and lighten the lines here to make it a little easier with my kneaded eraser.
Just a little bit, leave a ghost. Okay.
That's still a whole shape. We'll go across.
a little bit to the vanishing point.
And I'll come back and connect, very lightly
back here so that I know I could come back
and do that kinda like that. And I'll get really light in the inside. I don't
wanna interfere with our referencing stuff. So there's the beginning of the second box car.
And I've got the back of the third - the first I'm sorry.
I'll get lighter as we go down. Okay. There's
the idea. First box car, beginning of second box car. Alright. So we consider
this entire thing the first shape. So we'll do the same exact moves
we did considering from here to here,
and to here and to here, the first shape. So I'll
lightly X that off.
Because I need to get my middle line. This isn't our middle line yet, that's just the back, bottom scene
of the box car. So what I'll do is I'm gonna X this off
and find my middle spot. It is very close to that one, but it's not quite the same
thing. Ours is a hair lower than that. So I'm gonna make that clear by a darker
halfway point line, there. There.
And it goes all the way back into space. It's very close, that's a coincidence only.
So slightly lower is the one we're looking for. Okay.
So now we know that to double this entire shape by the little
blue beads at the end, we need to go from this corner to
the halfway point on this to go into space and get an entire shape
that includes the next box car in its space.
Here we go. Through. Okay. So that's
foreshortening pretty quick. Remember
I'm drawing the beginning of the next box car
just for the heck of it.
But now I have to go back and make a reference point
how to do that. Okay. So here we go with our diagonal.
Let's get back to this and say where our diagonal comes across from when we Xed.
Right. It's critical we now look at where that diagonal
just like here crosses where we want the end of the box or we see
that it crosses the first time that we made this box in the space. We have to make
a reference point, right there. That's where that diagonal
strikes the first time, the box we already made
so we already made this first box and this space. That was a random decision so they've been
constructed together. They must be made first because you have to have an existing shape
and its negative space to consider it an entire shape on its own. Anyway,
very simply you make that, and we're gonna cast that back into space
toward our vanishing point. Bingo. Right there.
I'll draw it a little more and it'll go into space like that. That's our reference line again
Okay. And that's our RP.
That's how we knew how to get to this reference line,
by the way, was because we take note of the RP. So the
reference point comes first, then that is cast back. We didn't know where to put
the red line back to VP on the right until we had our reference point from this
diagonal going kitty corner for this whole shape.
That struck that plane that we drew for our original box. So
it's a simple kind of on object reference point as we like to call it. Anywhoo.
Okay. Now we've got the entire length of the second box
and its space like this. So I'll go ahead and circle that very lightly in blue, again,
so we just make sure we understand that. When I take a diagonal now
through my second total shape
make sure that's correct. I take note again
where that diagonal strikes the red line. That becomes our second
RP. And I simply draw down
where I know the end of that second box car is, because of the reference point.
It's fairly simple when you start and it's real clean. So a lot less than
putting a whole bunch of references on the ground for doing this method and then going
to the horizon line. That creates about three times the work. So I just prefer this kind of stuff for
windows and all that stuff. So there's my second box car.
I'll take my kneaded eraser, like I've done before, tap out the middle space
just a bit. I'm gonna draw the corners of my
back car a little bit until they come back like this.
Like that. Draw my second car over to here.
Come down a little bit, just a little bit, let it disappear.
Front corner come here, because that's the back corner of the
first box like that. There's the second box.
Just wanna make sure that's nice and dark and obvious. That's the end of the second
box. That's the beginning of the third box. So let me go ahead and accent the
these a little bit - it's a little confusing - to make it clear.
I'll just make my outside shapes darker, not the interior, so it becomes
very clear what are exterior shape is.
A little heavier line weight.
Okay, get outta the way of the camera here. Alright.
Those are my actual boxes.
So we still have a little bit of ghosted lines in between.
There's my second, my third box idea. We'll get to
that in a second, just wanted to accent this to make it a little less confusing.
Ooh, make sure these are a little heavier too.
There's my third box, starting there, so I'll lightly go over across to there
and imply that those come together in that