Lesson Objectives

Students will be able to:

• Use construction techniques to find the center of rectangles in perspective, and to divide rectangle regions in half.
• Draw a circle in perspective, given a bounding box.
• Construct cylinders, cones, pyramids in perspective, given a bounding box.

Vocabulary

• Circle
• Ellipse
• Cylinder
• Cone
• Pyramid
• Bisect
• Bounding Box

The Circle, Squared

Consider the square drawn about a circle so that the circle fits perfectly inside of it. The circle touches the square in exactly 4 places.

If I took this square and I rotated it, the circle still touches the edge of the square at just exactly 4 places.

The Circle In Perspective

When the circle is turned in space, the way it appears to us is always an ellipse.

Note About Ellipses

• Ellipses are symmetric horizontally and vertically.
• The widest and shortest widths of the ellipse are always perpendicular to each other.

Drawing the Circle Inside the Perspective Box: The Wrong Way

With all that we have discussed before, we see that these three problems are the same.

• How can we draw the circle in perspective correctly?
• How can we draw the ellipse, so that it touches the box in just 4 places?
• How can I find the midpoints of the edges of the square in perspective?

Should it be done like this?

## No! This will not work! The ellipse that touches all 4 points will fail to stay inside the bounding box. # Drawing the Circle Inside the Perspective Box: The Correct Way Consider the following construction. Suppose I have a rectangle (or a square), if I draw an X by connecting opposite corners, the place where the diagonals cross will mark the center. Even if the card rotates, the X still indicates the center of the card.