## Circle, Cone and Cylinder Tutorial

**The Circle**

Begin by drawing a single square in perspective. Connect the corners diagonally to locate the center point. Now project a line from each vanishing point through the center of the face to find the center of each edge. These four points mark the precise tangents where the circle comes in contact with the original square. We also know the direction, or vector of the circle at these four locations. Beginning at each location, draw a short length of line which is oriented toward the correct vanishing point. Gradually extend the length of each line and bend inward until the lines meet each other smoothly. Build up lines slowly until the curvature of the circle appears elliptical.

More reference points may be located by further subdividing the square. After dividing the square into sixteen squares connect the diagonals as indicated to locate eight additional points along the circle. While more accurate, this process tends to be slower and more time consuming. It is better to develop your eye for circles and use this process only when necessary.

**The Cone**

Begin with the same procedure as for the circle. From the center line of the circle, project upward to the point which you determine to be the apex. Connect the four tangent points of the original circle to the apex (lines A,B,C,D). Also connect the outermost edges of the circle to the apex. Again, this is the basic information to describe the cone however it's probably not enough to convey a strong sense of volume. Begin by marking a point anywhere on the center axis line. Using the vanishing points as a guide, project lines through this point which cross the original lines you extended from the tangents to the apex. This will give you another set of four points from which to construct a circle.

**The Cylinder**

Use the same procedure as above, except beginning with multiple squares. Make sure all squares are in correct alignment, one above the other.