Unformatted text preview: p T a 1 . In addition, prove that R T 3 x 3 = R-1 3 x 3 and R T 3 x 3 R 3 x 3 = I 3 where I 3 is a 3x3 identity matrix. It is known that n 2 x + n 2 y + n 2 z = o 2 x + o 2 y + o 2 z = a 2 x + a 2 y + a 2 z = 1, n T o = n T a = o T a = 0, and n × o = a . Problem 3 (10 Points) Determine a matrix T that represents a rotation of α angle about the OZ axis, followed by a translation of b units of distance along the old OY axis, followed by a rotation of φ angle about the new OX axis. Assume frame transforms. Problem 4 (10 Points) Prove that rotation is actually the result of combining scaling and skewing. Use the 3-D transfor-mations. Problem 5 (20 points) What is the shape of the image of a cylinder? Assume perspective projection. 1...
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This note was uploaded on 10/21/2011 for the course CSCI 5561 taught by Professor Papanikolopoulos,n during the Spring '08 term at Minnesota.
- Spring '08
- Computer Science