BU CLA CS 480: Introduction to Computer Graphics

Spring 1995

Homework Assignment 2---due Friday, March 24

1. We want to scale a 3-D object by a factor S along an axis given by the unit vector U . Derive the 3 by 3 transform matrix, using vectors, not trigonometric functions.

2. Show what happens when an object behind the center of projection is perspective projected and then clipped. Your answer should demonstrate why, in general, we cannot project and then clip.

3. Give the viewing parameters for top, front, and a side view of the house of Figure 6.18 in the text. Put the view reference point (VRP) in the middle of the viewing window. Must the projection reference point (PRP) be different for each of the views? Explain your answer.

4. Stereo pairs are two views of the same scene made from slightly different centers of projection, but with the same view plane. Let d be the stereo separation --- that is, the distance between your eyes. Let P be the point midway between your eyes. Given P, d, VRP, VPN, and VUP, derive expressions for the two projection reference points.