hw1-F09-sol

hw1-F09-sol - CS685 - Homework 1 Due date: September 23 Be...

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CS685 - Homework 1 Due date: September 23 Be as concise as possible . 1. (5) Consider rigid body transformations in the plane. Draw a right triangle defined by three points A = ( 2 , 1 ) , B = ( 4 , 1 ) , C = ( 4 , 6 ) . Consider a rotation matrix T 1 = ± cos θ - sin θ sin θ cos θ ² a. What is the determinant of the matrix ? Consider transformation matrix T 2 = ± sin θ cos θ cos θ - sin θ ² a. Is the matrix orthonormal ? What is the determinant of the matrix ? Matrix is orthonormal when the determinant is + / - 1 . The determinant of the above matrix is - 1 . c. Is T 2 rigid body transformation ? What is the difference between T 1 and T 2 , how are the results different? T 2 is not a rigid body transformation, since it is not orientation preserving. Rigig body transformations must have deteminant of the rotation matrix +1. By apply- ing T 2 in addition to rotation we also get a mirror image of the original triangle. There is no way how to get from initial to the final position by translation and rotation around origin only. 2. (5) Point
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This note was uploaded on 10/24/2009 for the course CS 685 taught by Professor Luke,s during the Spring '08 term at George Mason.

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hw1-F09-sol - CS685 - Homework 1 Due date: September 23 Be...

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