Abstract
This chapter presents step-by-step methods of drawing an ellipse from part of a cone, a parabola from part of a cone, and a rectangular hyperbola from part of a cone. Various objects are formed by a collection of geometrical shapes such as cubes, cones, spheres, cylinders, prisms, and pyramids and when any two of these shapes meet, a curve of intersection or interpenetration is produced. It is necessary to be able to draw these curves to complete drawings in orthographic projection or to draw patterns and developments. This chapter also presents some illustrations to show some of the most commonly found examples of interpenetration. When two cylinders, or a cone and a cylinder, or two cones intersect each other at any angle, and the curved surfaces of both solids enclose the same sphere, then the outline of the intersection in each case is an ellipse.
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