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The Linear Basics

Linear perspective has a few broad and all encompassing rules with many specific and exacting applications. By learning these rules along with a few of the specific applications, an artist can pick and choose just how exacting a flat image will appear in depth and scale.

To understand these rules, we will first need to highlight and explain some basic concepts. Many of these will seem obvious, while others may appear contrived for the sake of discussion and measurement.

For opening concepts we will need to deal with the concepts of diminution, convergence, and foreshortening. Each of these ideas intersects the other in part of their meaning, so it is probably simplest to lump them al together.

Diminution is the concept that the farther something is from us, the smaller it appears. It is quite obvious when we look for it, but our brains are so good at interpreting our visual experiences, that we hardly notice he effect unless we dwell on it. Mountains far away appear smaller than rocks up close, and the same person who appears six feet tall when standing right next to us might appear only six inches tall when standing on the other side of a large room. Our ability to interpret our environment sometimes gets in the way of our understanding, but as an artist we must always be aware that true size is not always the same as perceived size.

Convergence is the idea that although parallel lines never actually meet, they will appear to meet converge at a point that is far away from us. We will later call the place where they seem to meet a vanishing point. This is actually a sort of corollary to the principle of diminution. Eventually parallel lines can get far enough away from us that the space between them becomes to small to see. What linear perspective does with this is actually quite simple: it assumes that the rate of shrinkage due to distance is constant and measurable. It is the particular angle measurements that can get confusing.

Foreshortening is the basic idea that as objects rotate in space, different parts of them become closer to and farther from the observer. Therefore, the concepts of diminution and convergence will apply not only to individual shapes, but to different parts of the same basic shape. This is perceived as warpage of an image as it is seen at different angles. Our brains, powerful as they are, allow for this on a constant basis so we do not have to constantly concentrate on reinterpreting our surroundings every time we or it moves.

Some Examples

Meet Candy and Spike. They will be helping us illustrate the nuances of our concepts.

In the above image, both Candy and Spike appear to be of a similar height. Even though they are just cartoon outline people, we make certain visual assumptions about them automatically. The main thing that our brain registers about them visually is that they are about the same size and therefore the same distance from us.

Now the image of Candy has been shrunk. Since we assume that most people should be of a similar size, she appears farther away from us than Spike does. The fact that her head is at the same level as Spike's and that her feet are not also enhances this illusion. Candy is a victim of diminution. Because her image is roughly half the height of Spike's, we understand that she is about twice as far from us than he. If Spike were ten feet from us, Candy would have to be about twenty.

Here the image of Spike has been enlarged slightly, making him a step or two closer to us. Notice how the hand that he waves in our direction appears enlarged, making it look even closer still. Candy, is likewise protruding her hands toward us, but hers do not appear oversized. If we now assume that Spike is about eight feet from us and that his reach is around three feet, that places his hand about five feet away (8-3=5) from us. His hand is about 38% closer to us and has been enlarged accordingly. If Candy is still twenty feet away, her hands then are only 15% closer to us, and the size change is relatively small.

Cameras can seem to bring us closer to a subject by enlarging the perceived image, but they cannot allow for relative ranges of diminution. This is the key reason why photographs, especially long range ones, tend to flatten perspective.

When objects become so diminutive that we can no longer see them, they vanish. Since the rate at which objects shrink in relation to distance is constant, we can describe their rate of diminution with straight lines across the flat visual field. These lines are known as lines of perspective and they meet where we would cease to be able to see an object if it continued all the way into the distance. This concept is less obvious than diminution because we assume that parallel lines will never meet. By definition they will never meet, but visually they do converge at a distant point.

ForeshorteningSimple objects like cubes and cylinders are rather easy to draw using the basic rule of convergence. More complex and compound shapes may cause some difficulty, but even with relatively flat drawings a feeling of depth can be created if we remember that lines of perspective show a rate of diminution by showing where parallel lines converge.

With or without strict linear perspective, the actual two dimensional shape of perceived objects will change as the angle of the object changes to us. Foreshortened squares become rectangles and diamonds, while circles become ovals or ellipses. The more complex the original shape, the wilder the change. The key element here is that our brains are specifically geared to figuring out actual three dimensional shapes from foreshortened two dimensional images. When possible, it is important to observe actual objects closely from intended angles in order to allow for this change in shape. Images that do not allow for foreshortening will appear flat or just plain wrong even when diminution and convergence seem to be working.

Linear Perspective is the geometric study of how objects foreshorten, diminuate and ultimately converge in two dimensions in order to appear as if they exist in three. Ultimately, any three dimensional shape can be reduced to a point where the laws of linear perspective can be applied. In practice, however, real world objects are often so complex that applying these principles to each foreshortened facet is time and effort prohibitive. Therefore, most artists use simpler geometric shapes that they employ as frameworks or "wireframes" which are later embellished with details. The key idea is that if a simple object can be drawn with proper perspective, the completed drawing will inherit this feeling of depth from the formative stages.

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