hw1-F09-sol

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online