UNB/ CS/ David Bremner/ teaching/ cs4735/ milestones/ Class test 1

Important information

Practice questions

1. transforms


Give an example in 2D that shows that scaling and rotations are not always commutative.



Give a transformation matrix that maps the black triangle to the gray one. You may leave your answer as a product of matrices, with rotations given symbolically as e.g. Rz(45) meaning rotate CCW 45 degrees about the z axis.

2. Camera Coordinates


Explain how to compute the view matrix give the eye position, the up vector, and the point center being looked at.

3. Projection matrices

Example projection/depth transform matrix

Consider the matrix

P =

1 0 0 0
0 1 0 0
0 0 3 -2
0 0 1 0

  1. Describe the effect of the matrix, both geometrically and in the context of a rendering pipeline.

  2. Describe the effect of applying this transformation twice.

Perspective projection matrix

Give a matrix that implements the following perspective transformation (D is the distance to the near clipping plane). Explain your answer.

   [x,y,z,w]ᵀ → [Dx/z, Dy/z, D]

4. Clipping

Give robust inequlities to clip a homogeneous point [x,y,z,w]ᵀ against the standard cube [-1,1]×[-1,1]×[-1,1]. Are there any special cases? If so, explain.