a. Figure 2-8 shows the proper layout of a circle drawn in perspective.

The first step in the layout is to draw a circle with the dimensions

desired. Fit a square around the circle as shown in the second step and add

the diagonals, center lines, and vertical lines shown in step two.

The

points at which the circle and square division lines intersect will give you

eight checkpoints for drawing the circle in perspective. The third step is

to draw the square in perspective including diagonal lines, center lines,

and vertical lines. The points at which the circle lines cross the diagonal

and other division lines in the perspective square are the points through

which the curve of the ellipse is drawn.

b. When drawing ellipses it is often best to rough them in freehand and

get the general shape desired, then relate the square in proper perspective

superimposed on the freehand ellipse. This procedure is down in Figure 2-9.

When the square is proportionally correct, cross the center with two

diagonal lines and cross these with a vertical line through the intersection

of the diagonal lines.

Draw a horizontal line through the center to

determine the perspective center.

Use the vanishing point to have the

direction of the receding lines correct.

Figure 2-9.

Drawing the circle in perspective

c. Figure

2-10

shows

a

circular

cylinder

constructed

in

two-point

perspective.

d. Figure 2-11 shows some of the applications of the circle in

perspective when it is associated with the right circular cylinder. At the

eye level the circular section line appears as a straight line. Above and

below the eye level the circular sections appear as ellipses that become

progressively more open as their distance above and below the eye level

increases. The proportion of the ellipses, the proportion of short to long

diameters, also depends upon the distance of the cylinder from the eye. The

nearer the eye, the more open the ellipse; the farther the eye, the thinner

the ellipse.

When seen at a considerable distance the ellipses appear as

nearly straight lines.