This content introduces the fundamental concept of three-dimensional space through the use of three primary axes (X, Y, and Z) as a system for understanding and representing objects and environments in drawing and visual art.
Mind Map
Click to expand
Click to explore the full interactive mind map • Zoom, pan, and navigate
You're traveling into imaginary space.
The same three dimensions you've known since you were born.
A wondrous illusion created by the placement and combination of only three
lines.
We'll call them X, Y, and Z.
Perspective lines take us into imaginary space.
Before we learn to navigate and measure in there, we need to know the three
guiding lines.
They're called axes, plural for axis.
It just means a line, usually one you can't actually see.
An imaginary line can help us foreshorten.
The long axis shortens when it points toward us.
Pretty much every object has a long axis.
Unless it doesn't.
So we need a system that works for all forms, including environments, which can
get complicated.
But here's one way to solve it.
Rather than start with a whole scene, we can start with placement lines.
Big jump.
From placement lines to city street.
But placement lines give a base from which to jump.
We can imagine three sets of lines and those three line systems position the
whole scene.
Three line directions.
Let us find other lines.
Now, let's see where we are.
We learned about angles and protractors.
That was the flat surface out of perspective.
You put a good deal of work into getting an eye for those angles, but that was
only a start.
It wasn't yet space.
Then orthos, orthos say this flat surface means something more, a thing that is not
flat.
But now we move into the really hard views that slant into space.
Prepare yourself here.
Three-quarter views, oblique views, tipped, tilted, slant, at an angle.
That changes everything.
How could we ever predict it?
I got an idea.
Tilt it back behind a window, look at the window and measure the angles on the
window with a protractor.
That is how perspective works and we could take the time to label those
angles, but would we?
If we do, it names angles but it wouldn't help much with learning to draw besides
noticing angles and labeling them.
Not enough.
You could get old doing that and not learn how to draw in perspective.
We are about to learn something simpler and more useful.
The simplest and most useful angle of all.
The right angle.
Two lines.
Oh, I'm sorry.
Three lines.
One I forgot.
Right here where the two lines meet.
Can you guess it?
If you're thinking a 45 degree angle comes out of there, you're learning the
protractor.
Good.
But that's not a right angle and that's not where we're going.
There's another right angle facing toward us.
We're looking right at it.
It's pointing at us.
Let me show you.
It's a right angle to vertical if we look at it from one direction.
And it's a right angle to horizontal if we look at it from another.
This is how we coordinate space.
This three-dimensional compass of XYZ arranges the three poles of space each at
right angles to both of the others.
Let's think about that.
A compass rose shows north and south, up and down on the map.
It shows east and west, right and left on the map.
But it doesn't show a third dimension unless we give it an axis that's upward,
not northward.
With three axes in an oblique view, we have the most simplified arrangement
possible to navigate space.
Naming the axes.
Why do we use letters?
We could say up and down, left and right, close and far.
But, spin this and what was up is now left.
What was left is now far.
So, we can't always name a line by its position or where it points because that
may change.
X, Y, Z lets us place objects so that even in different positions their names
stay the same and it still makes sense if they spin or tumble.
How about environments?
They don't spin into different positions.
Ah, but we do.
In environments, we use letters for axes in case our viewpoint changes.
But you can call the axes anything as long as they don't get confused with
their directions on the surface.
This is not about the surface, this is about the world in there.
If we move around in that world, every angle on the surface changes.
How can we keep track?
Remember that a setting, like a form, has its own set of axes.
Sometimes axes have vanishing points, sometimes not.
Sometimes the vanishing points are close, sometimes distant.
The thing that stays constant is the name of each set of lines from the orthos.
By the way, some systems swap out the Y and the Z. No biggie, different names,
same thing.
Let's review the names that we'll use in this course.
X is width of the object, not its direction on the paper.
Y is height of the object, as we named it in the ortho.
X and Y represent width and height of an object.
X and Y could still be flat dimensions if they are flat designs, but Z
Requires us to acknowledge depth and usually introduces a vanishing point.
But our concern here is only that three sets of parallel lines cover all three
dimensions.
Those are the axes.
They will apply to very complex objects as you advance.
Let's prepare with a literal assignment.
Your assignment is simple.
You literally assign one of three letters, X, Y, or Z, or any system you're
used to, to each set of lines in these images.
If you go to proko.com/perspective you'll find these 3D models which you can use to
do this assignment.
We've made a number of them available for free.
You can also find them on the Zolli app with even more options to choose from.
That's at proko.com/zolli for the motherlode.
Then sketch from each image.
Sketch the object.
Sketch the scene.
Don't get fussy.
Doing several a little loosely is better than doing only one very precisely.
Find the three line systems.
Label them to recognize which line system this line belongs to.
Naming these lines should be easy.
Everything here is lined up.
This is the easiest level, you may get through it fast.
Here's the next level.
Here things are not lined up.
That means that this could be X or Z. You can decide which is width, which is
depth.
The important thing is that once you decide, stay consistent as you work
through the object to rehearse your awareness.
Remember the letters you choose don't change their names when an object changes
position.
Y does not turn into X when it lays horizontal.
When it lies horizontal.
Lose horizontal.
Whatever it does.
We label per object so that when objects tumble, we know which direction is which.
If this still seems too easy, try the next level.
It includes...
Bevels.
Diagonal lines.
That means they move on two axes.
Scary?
Perhaps that some of these lines move in two directions at once?
But we can deal with it.
We label them not as belonging exclusively to one of these three
directions.
We name two axes on which the lines move.
XZ.
That's width and depth.
Or ZY.
That's depth and height.
or XY that's width and height if you are cutting these boxes you move the cutting
blade out and back or up and back or in and up two axes combined two letters
assigned
If you want the hardest of all, try lines that move on all the three axes.
Say out loud the directions in which each line moves.
This lets you know that more than three axes exist.
So why only three letters?
If you want more, here's where to find them.
Spherical coordinates.
Axes that could melt your brain.
This simple labeling gets your brain ready to handle that heat.
The secret is not to learn all of those lines in between.
It's to learn primary lines which give you the lines in between.
It's something like color.
Three primary colors yield lots of others.
Three primary axes give us enough to deduce the spatial structure of the
globe.
Notice the primary lines, three to begin.
This will expand your awareness of spatial dimensions.
X, Y and Z and the parts in between.
If you need help, I'll demo in premium, explain sections, and show you how to
position objects in space using three-dimensional arrows.
You'll learn how every straight line relates to X, Y, and Z. I think there's a
song about it.
You can study many lines or you can study three.
Everything spatial is X, Y, Z. Okay, label and sketch.
In the next free episode, we'll see how grids can help us in guessing
proportions.
Click on any text or timestamp to jump to that moment in the video
Share:
Most transcripts ready in under 5 seconds
One-Click Copy125+ LanguagesSearch ContentJump to Timestamps
Paste YouTube URL
Enter any YouTube video link to get the full transcript
Transcript Extraction Form
Most transcripts ready in under 5 seconds
Get Our Chrome Extension
Get transcripts instantly without leaving YouTube. Install our Chrome extension for one-click access to any video's transcript directly on the watch page.
