CS 318: Homework #2
Assigned: Tuesday March 2, 2004
Due: Tuesday March 9, 2004
This homework is intended to help you prepare for the midterm exam. The majority of the questions on
here are from past exams. You should hand in this assignment at the end of class on Tuesday, March 9.
Please be organized when writing your answers to these questions. Make sure that all solutions are
clearly indicated and labelled with the question they are answering. Remember to write clearly and legibly.
Unreadable answers will receive 0 credit.
1. We want to define a new spline type with control points p0,p3,r1,r2. The curve should interpolate its
endpoints p0,p3and should have tangents r1,r2at u=1
/
2and u=3
/
4, respectively. Given that our
standard matrix-form for this cubic splines will be
p(u) = 1u u2u3M
p0
p3
r1
r2
derive the 4×4 basis matrix Mfor this class of splines.
2. Suppose that you are given the following shape:
(−1, −1)
(1, 1)
For each of the following figures, describe how to transform the initial shape above into the given result.
You may only use combinations of the following three transformations:
T: translate by [1 1] S: scale by [2 1] R: rotate (counter-clockwise) by 45◦
NOTE: Your answers should consist of products of these 3 fundamental matrices. Make sure to put
them in the correct order.
