# CIRCLES AND CURVED SURFACES

When circles and curves are drawn in plan, you may use compasses, templates, and other mechanical devices to ensure accuracy. When drawn in perspective views, you must approximate circles and other curved forms from reference points based on straight lines and from angles that can be measured accurately.

When drawing a curve, it is ultimately necessary to sense its shape in much the same manner that you sense a curve when driving a car, for example. Even mathematicians must come to terms with this uncertainty; and, like them, you can narrow the range of uncertainty by increasing the number of reference points. The accuracy of circles and curves in perspective is relative. What is “good enough” or “close enough” depends on the requirements of the project.

## CIRCLES

Like squares, circles are the basis for a variety of more complex forms, such as cones, cylinders, spheres, and their derivatives. Being able to see the circles within these various forms is an indispensable aid to reproducing them.

For quick representations, it is often adequate to simplify perspective circles into regular ellipses, as illustrated above. However, a regular ellipse violates the principle that a closer object will appear larger than a distant one of the same size.

Forms Based ...

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