CSUDH Computer Science Department

CSC461 Computer Graphics I

(Fall 2004)

Midterm Examination 2

1. (40 points, 4 points each) Briefly explain

1) Vector space and affine space

2) Homogeneous coordinate representation

3) Model-view matrix and projection matrix

4) Projection pipeline

5) Axonometric Projections

6) Image-space algorithms for hidden-surface removal

7) The four steps of finding the oblique projection matrix

8) The default setting of viewing and projection in OpenGL

9) The two ways to position the camera in OpenGL

10) The two functions for perspective projection in OpenGL

2. (10 points) Show that the following sequences commute:

1) A rotation and a uniform scaling

2) Two translations

3. (15 points) Given two three-dimensional vectors u=(1, 2, 1)^T and v=(1, 1, 0)^T, and a point p=(3, 2, -1)^T, find

1) w = p + 2u - 3v

2) A frame with w as one of the basis vectors and p as the origin

3) The transformation matrix from the frame in step 2) to the default frame

4. (15 points) The OpenGL function glOrtho requires six parameters which are used to determine the projection matrix and the viewing volume. Assume the projection plane is the default plane z = 0). Consider the function call glOrtho(1, 5, 3, 9, 2, 6).

1) Describe the two steps to normalize the projection

2) Find the final projection matrix

3) Find the projection of the points (-1, 2, 2), (3, 6, 4), and (2, 5, 3).