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Main points of this exam paper are: Trivial Rejection, Line Segment, Cohen-Sutherland, Line-Clipping Algorithm, Simultaneously Viewable, Colors, Not Invertible, Special Cases, Computing, Inverse Matrices
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When performing perspective projection, which sets of parallel lines will NOT have a banishing point?
Given a frame buffer system with 10 bit planes, and a 1024 entry look up table (palette), with 30 bits for each entry (10 for each red, green, blue) answer the following:
(a) [3 points] How many bits should we have for each DAC (red, green and blue)?
(b) [3 points] How many colors will be simultaneously viewable on the screen (assuming 1024 x 1024 resolution)?
(c) [3 points] How many colors can be displayed (not necessarily at once)?
Line clipping.
(a) [6 points] Describe two trivial rejection cases for the Liang-Barsky line-clipping algorithm.
(b) [6 points] Show one example of a line segment that is trivially rejected by Liang-Barsky, that is not trivially rejected by Cohen-Sutherland. Briefly explain.
(c) [6 points] Show one example of a line segment that is trivially rejected by Cohen-Sutherland that is not trivially rejected by Liang-Barsky.
Consider the basic dimensional modeling transformations (translation, rotation, and scale):
(a) [6 points] What are the inverses of these transformations? (Do not sue brute force.)
(b) [4 points] Are there any special cases that are not invertible? If so, what are they?
(c) [4 points] Do your methods for computing the inverse matrices generalize to 3D? If not, explain why not.
In class we discussed two ways of setting up a perspective projection matrix. The two matrices are given below:
(a) [6 points] One of these places the center of projection (COP) at z = 0 and the other places the projection plane (VP) at z = 0. Label the correct matrices with "COP = 0" and "VP = 0."
(b) [6 points] Is there a basic transformation that transforms one into the other? IF so, what is it?
Determine which are rotations. For the one(s) that are not rotations, what are they?