Rendering a cube in perspective
Given:
-the center of view C
-the closest vertex V
-one edge coming out of V and ending on a vertex W
-the horizon line L of one of the planes of the cube containing this edge
-the focal distance d (the distance from your eye to the plane of projection; this can be a segment in the picture whose length is the focal distance)
1. Using C and d, mark the zenith Z of L along the perpendicular to L through C.
2. Mark P, the intersection of L and the line VW.
3. Draw the segment WZ.
4. Draw the segment VZ.
5. Draw the segment PZ.
6. Draw the perpendicular line to PZ through C.
7. Mark Q, its intersection with L.
8. Draw the segment WQ.
9. Draw the segment VQ.
10.Draw a perpendicular to L through C.
11.Mark a point on this perpendicular that casts a right (90 degree) angle to P and Q.
12.Draw this angle's bisector (a ray dividing it into two 45 degree angles).
13.Mark D, the bisector's intersection with PQ.
14.Draw the segment DV.
15.Mark A, the intersection of DV and QW.
16.Draw the line PA.
17.Mark B, the intersection of PA with QV.
Steps 18-25 are the same as steps 10-17, with L (which is PQ) replaced with QZ (and VW replaced with VB). Actually, these steps might be easier to do without labelling them.
26.Draw the line from P to the last marked vertex (the "second" B).
27.Mark E, its intersection with WZ.
The cube has visible vertices V, W, A, B, the "second" A, the "second" B, and E.