by Robert Gardiner, the University of British Columbia, Vancouver, Canada

Perspective - the simplified basics

If you stand in the middle of a long straight street and look down it, the sides of the street appear to get closer together as they get farther away. This phenomenon is a consequence of our visual apparatus - a creature with 100 eyes spread over a square mile would percieve the street in a different way.

We use "perspective drawing" to represent on paper the way we perceive 3-dimensional objects in space. It's possible to construct a geometric model that includes an observer, and plot the way that observer will perceive an object in 3 - space. This geometry is called "single plane" or "perspective" projection. One can do this using mechanical drafting, by hand or computer, but it's important to be able to sketch freehand perspective as well.

The fundamental rules of freehand perspective drawing are relatively simple

- objects, lines, or surfaces appear to diminish in size as they become more distant from the observer. This means that....
- parallel lines or objects appear to converge as they become more distant from the observer
- the point at which such lines would seem to meet if they were infinitely extended is called a "vanishing point"
- in a front view (the one we most commonly see), vanishing points are located on the "horizon" which is normally perceived by the observer to be at her eye level (even when not actually visible).
 Above is a group of shapes seen in simple perspective, illustrating the basic "rules." The more complex view of the same objects (below) gives you an idea of their actual shape. Notice that in this example we are well above the objects. Also notice that these objects were drawn using the computer. The objects in the two pictures are the same virtual models: in the picture above they are viewed from the front, and in the picture below the view has been tilted and rotated.

The simple rules about "vanishing to the horizon" describe much of what we see. In the example below, two vanishing points have been found by extending lines on the photograph - lines that we can assume are parallel on the actual building. These two vanishing points establish the viewer's horizon. Notice that in the photo - as in the first picture above - vertical lines appear to be approximately 90 degrees to the horizon. This represents what we most commonly percieve, but is never strictly true. Notice also that the lines of the sidewalk and street don't seem to converge to the same horizon. The building is on a hill, so those lines aren't square to the viewer's vertical and aren't useful for finding the horizon.

If you understand the basic idea, you can sketch objects in perspective by first drawing a "bounding box" (a simple box that will just contain the object). The (parallel) lines of the edges of the bounding box must appear to converge when extended, and the line that connects the points where they converge is the "horizon," which should be at your eye level.

Put a cardboard box about 10 feet away from you on the floor, and sketch it while seated. Extend the lines of the edges, following the example. Notice that the percieved convergence of "vanishing" lines is often very slight, with an implied vanishing point somewhere "off the page" to the left or right. Now try extending these lines with a straightedge until they do converge (off the page, probably), connect the two points with a "horizon" line. That horizon line ought to be "flat" - parallel to the top and bottom edges of the paper. If it isn't - redo your perspective until it is.

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