CSUDH Computer Science Department

CSC461 Computer Graphics I

Midterm Examination 2

(Fall 2005)

1. (20 points, 4 points each) Briefly answer the following questions.

1) What is homogeneous coordinate representation?

2) What is instance transformation?

3) What is the main difference between orthogonal projection, parallel projection, and perspective projection

4) What are the two categories of hidden-surface removal algorithms?

5) What are the three terms in the Phong reflection model?

2. (20 points, 4 points each) OpenGL

1) What is the default setting of viewing and projection in OpenGL?

2) Describe the two ways to position the camera in OpenGL.

3) Explain the two functions and their differences for perspective projection in OpenGL.

4) Explain the projection matrix and model view matrix in OpenGL.

5) Explain the following OpenGL functions: glTranslate(1, 1, 1), glScale(2, 3, 4), and glRotate(45, 1, 1, 1).

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

1) w = p + u - 2v

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(2, 6, 3, 5, 1, 5).

1) Describe the two steps to normalize the projection

2) Find the final projection matrix

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