Subdivide and multiply the cube.


When drawn correctly, a cube may be subdivided or multiplied indefinitely. Draw diagonal lines connecting the corners of one face of the cube. This locates the center point, while correcting for perspectival foreshortening. Using the vanishing points as guides, project lines through the center of the face. This will effectively and accurately subdivide the cube.


Having subdivided the cube, you may now multiply it through extension. Extend the parallel edges of one face back toward a vanishing point. Extend a straight line from one corner of that face through the center-line of the opposite edge until it intersects one of the lines that you originally extended. (tough sentence, look at the illustration). This intersection identifies the edge of the next cube, again, corrected for perspectival foreshortening.

The Pyramid

Use the cube and scaffold system as the basis for more complex geometric forms.


Begin by drawing a single square in perspective. Connect the corners diagonally to locate the center point. Project upward from the center to a point you establish to be the apex. Draw lines from the corners of the square to the apex. This completes the basic outline of the pyramid, however it appears anemic and undeveloped. Add section lines as described above to suggest the surface and volume of the pyramid. Begin at any edge and then project according to vanishing points all around the pyramid.