Past Midterm and Exam Questions (PDF) - Student.cs.uwaterloo.ca ...

54 CS488/688 Introduction to Computer Graphics
18.2 Bilinear Patches [Last Used: Spring 1992 Final]
A bilinear patch is given by
(1 − α)(1 − β)P 00 + (1 − α)βP 01 + α(1 − β)P 10 + αβP 11
If the patch is subdivided at α = 1/2 and β = 1/2, the four resulting patches involve control points
Q 00 , Q 01 , Q 02 , Q 10 , Q 11 , Q 12 , Q 20 , Q 21 , and Q 22 Give formulas for the Q’s in terms of the P ’s.
18.3 The de Casteljau Algorithm [Last Used: Winter 1996 Final]
1. Show the de Casteljau construction on the Bézier curve shown below at t = 0.5 (assume the
curve is parameterized over [0,1]).
2. In the figure above, draw the tangent to the curve at the point t = 0.5.
18.4 The de Casteljau Algorithm [Last Used: Fall 1997 Final]
In the figure below are the control points for a cubic Bézier curve P , defined over the interval [0, 1]
by the control points P 0 , P 1 , P 2 , and P 3 .
P P 2
1
P
0
P 3
Suppose we want to join another cubic Bézier curve segment Q (defined over the interval [1, 2]) with
control points Q 0 , Q 1 , Q 2 , and Q 3 , and we wish P and Q to meet with C 1 continuity at parameter
value 1 (i.e., the first derivatives should be equal at t = 1).