Guest Artist: Russell Black on Drawing the Cube – Getting Rid of Linear Perspective
Guest Artist: Russell Black on Drawing the Cube – Getting Rid of Linear Perspective
As artists, we have to deal with a lot of visual information. Our job is to take what we see and then recreate the three dimensional scene onto the flat, two dimensional surface of our paper or canvas. In effect, we lie. There is no possible way to draw three dimensions onto two. It’s just not possible. That being said, we have over the centuries developed ways in which we can create the illusion. One of these is called Linear Perspective.
Developed during the Renaissance, linear perspective is a mathematical way to project a three dimensional world onto a flat, two dimensional plane surface (like our paper or canvas). It’s not how we actually see or experience the world, but it is a mathematical construct to “imitate” what we see. It is a distortion and an illusion, and I want you to keep that in mind.
How we see the world is very different than how a camera sees the world, or how linear perspective constructs the image. Our eye is curved, both in the front lens and the rear retina. A camera, on the other hand, has a flat back screen on which the image is projected, as shown above. A light ray has to travel farther in a camera than it does within our eye, so the image captured by the film, or digital back of a camera is distorted. This is the same issue with the construction of linear perspective. The scene is mathematically projected onto the flat surface of our paper or canvas, similar to the way a camera captures an image.
Add to that is the issue of our binocular or stereoscopic vision. We see the world with two eyes. Each eye has its own POV (point of view), which are slightly different from each other. The two images are combined within the brain to create the illusion of our three dimensional world (note: even what we see is therefore an illusion as well). The two pictures above show what each eye sees independently, and we can even recreate the illusion with a device called a “View-Master,” a toy that was popular in the 1950’s and 60’s.
A camera and a linear perspective drawing uses only a single POV. So, what we draw using linear perspective is not in any way what we actually see with our own eyes. Unfortunately, too many artists think that linear perspective is the end all, be all of drawing skills. It’s not. Far from it. It also has some very important faults that can create some rather bad situations, and these are often overlooked by those who have a limited understanding about linear perspective. In my experience, most artists know just enough about linear perspective to always get it wrong, but never enough to ever get it right.
Above is an illustration from the book, “Graphics for Architecture” by Kevin Forseth. This is how the linear perspective construction functions. What we see is the subject, a large rectangular block, being viewed by an observer (at the SP or station point), with a single POV. The resulting drawing is the constructed projection of the viewed block onto the flat picture plane (PP). A horizon line (HL) is arbitrarily established and two vanishing points (VPL & VPR in this case), which are then used to construct the projection. Remember, all of this is a fiction. None of this is reality.
There are two major issues when constructing a linear perspective drawing, both of which cause massive problems.
The first problem is the establishment of the vanishing points. This is where we can create massive distortions in our drawing. If the VP’s are too close together, we get a distortion that is very similar to a fish-eye camera lens. The amount of distortion can be reduced by pushing the VP’s farther out along the HL. In a practical application, if the drawing area is approximately one foot in size, then the VP’s need to be pushed out to a distance of ten feet on either side of the drawing. You would therefore need a table that is twenty feet in length to reduce the distortion to proper levels. I don’t know about you, but I don’t have a table that long, and certainly not one that could fit in my pocket if I go out on location to sketch. From this standpoint alone, linear perspective is useless to me as a plein aire sketcher.
The second problem with constructing a linear perspective drawing is that we can draw something that we can’t physically see. Above is a possible drawing of a cube, but there is something radically wrong with this. Can you see what it is? It is physically impossible for us to see in two different directions at the same time. We cannot see the roof of a building and the base of the building at the same time. The POV would have to be changed in order for us to visually see each one. When I look up, I cannot at the same time look down. However, I can incorrectly draw this idea using linear perspective (and I can photograph this effect using a fish-eye lens). Now, just because I can draw it this way does not mean that this type of drawing is correct. It is a product of the mathematical construction, not how we visually see the object. We can look only in one direction at a time. We can look out and up, or out and down, but not both at the same time. So, linear perspective can construct an image that we cannot actually see. That to me is a problem.
What I need is a correct and useful way to draw a cube (above), that doesn’t rely on a complicated, mathematical construction with all of the inherent faults and problems that can pop up. Is there a simple way to do this so we can get rid of the linear perspective nightmare?
Let’s begin with some simple observations. Many artists try to draw a cube based on what they know to be true, that a cube has square sides – “A” above. This is the truth about how a cube is constructed, but it’s faulty logic to begin a drawing of a cube with a square. As you can see above, if we begin to draw a cube by starting with a square, we’ll end up with what’s called an isometric projection. It’s another type of mathematical or mechanical construction and is properly used by engineers and machine parts manufactures. However, it’s not the way we see a cube is it? So, the first thing we can deduce is that we cannot draw a cube by drawing a square. “B” above is what we see. Let me prove it to you.
If we look at a photograph of a cube, here a simple Kleenex box, we can see what a basic cube looks like. I’ve used a longer lens to reduce the distortion, so it’s close to what we actually see. If we check the edges, we can see that none of them are parallel (which we’ll get to more in-depth in a moment). If we can only see a square, then notice that we cannot see any of the other sides. This makes the drawing “A” incorrect, doesn’t it? When we can see more than one side of the cube, what we actually see are called projected planes, which diminish in size as they recede into space.
When we look closely at the cube, we can see several important points, and these will become the rules for how we draw a cube correctly.
Rule #1: Geometric shapes appear flat
Any use of geometric shapes (circle, square, rectangle, triangles), will destroy the illusion of depth within a drawing or painting. Avoid using these shapes if you want to maintain the sense of deep space.
Notice how the use of the square in the face of the cube is incorrect. Using geometric shapes will create an isometric projection, not a linear perspective drawing.
Rule #2: Projected planes create depth
Visually, this is the idea of diminishing size. An object when viewed close up will appear larger than the same object when viewed from farther away. It doesn’t matter what the distance is (an inch, a foot, or a mile), any surface will diminish as it moves farther away from the viewer.
Notice, our 6′ tall man gets visually smaller as he gets farther away from us. This is the relationship of diminishing size. Remember, things appear to get visually smaller the further away they are from the viewer.
The correctly drawn box would look like this, and if you compare this box with the one above, you will immediately see the difference.
This box visually looks correct. If you measure the cube carefully, you will see that no squares were used at all. If you measure the front vertical edge of the cube, you will see that it is longer than the other two vertical edges. Since the front vertical edge is closer, it has to be longer than the edges further away.
Rule #3: Point of View (POV)
You can only look in one direction. You cannot look in two directions at the same time. Here is where most beginners make their mistakes when setting up a linear perspective drawing or painting. Although a camera can distort the image, allowing us to see “up” and “down” simultaneously, our eyes cannot. We can only see in a single direction. Try it for yourself. If you look down at your feet, you cannot see the sky. If you look up at the sky, then you cannot see your feet. When drawing or painting, you must establish a POV and stick with it throughout the composition.
Here is where the books make a huge mistake when they show you how to set up a linear perspective drawing.
When you set up the horizon (eye) line (in red), and create a linear perspective drawing, you cannot place the object (in this case, the cube), both above and below the horizon line.
This creates a problematic POV. You cannot look up at the top of the cube and then down at the base of the cube at the same time. If this were a building, then you could not look up at the roof and down at the foundation at the same time. It’s just not possible to “see” this.
Yes, we can draw this and we can photograph this (using certain lenses), but our eyes cannot actually see this way in reality. This is what becomes confusing to the viewer when they look at this type of setup in a drawing or painting. We must, therefore, limit our POV to one of two options: A) either look out and up, or B) out and down. Once you establish the POV, keep everything consistent to that POV.
Usually, this problem pops up when working with buildings and architecture. How you “see” the box determines how you need to draw the box.
When you see a building from this angle, you are generally standing above the building, looking down on the building’s roof. Do not confuse this POV with standing on the ground looking level or up at a building just because you can see the roof. They are not the same.
The key to getting this right is the “arrow” of the near edge of the building. Look carefully. If the arrow points down, then you are looking down on the building. If the arrow points up (which is most of the time), then you are looking up at the building.
Above is a building that is below the horizon line (the base of the mountains), so we are looking “down” on the scene.
Above is a building that is above our eye line, so we are looking “up” on the scene. Also, check out the doors and windows as they are not squares or rectangles, they’re projected planes. They also obey rule #2.
The problem we encounter out on location is that we are usually standing up when we sketch, and that places our eye line, or the horizon, at about 5′ – 3″ above the ground. This POV allows us to see dominantly “up,” with just a little bit of “down” thrown in to confuse us. To make matters worse, we constantly turn our heads to view the details of the scene, creating more problems.
When looking at the scene, establish the POV first (out and down, or out and up), and then watch your angles carefully and keep things consistent. This holds true for everything we see, draw, or paint. Unless we are working in an abstract approach, these three basic rules can be applied to any scene that we are working on.
- Rule #1) Geometric shapes appear flat. Avoid using them.
- Rule #2) Projected planes create depth. This is the issue of diminishing size.
- Rule #3) Point of View (POV). You can only look in one direction at a time.
These three rules, if properly applied, will keep you from making those embarrassing errors of linear perspective and will keep your drawings and paintings looking professional.
To see how this is done, please watch my video, How to Draw a Cube on YouTube or click the play button below.