CSC 461: Computer Graphics I (Fall 2006)

Sample solution to Assignment 1

1. Briefly explain:
1. Angle of view and depth of field
2. Disadvantages of the pinhole camera model
3. How the synthetic camera model overcomes the disadvantages of the pinhole camera model
4. Graphics pipeline

Sample solution:

a. Angle of view: the largest angle that the camera can image objects on its film plane. Depth of field: the length of the range that the camera can see.

b. Two disadvantages of the pinhole model: the single pin hole (too small) and the fixed angle of view.

c. Allow the film plane to be put anywhere and the center of projection to be adjusted.

d. Vertex à Vertex processing à Clipper and primitive assemble à rasterization à fragment processing à pixels in frame buffer

2. The focal length of a camera lens is the distance from the center of the lens to the point at which parallel rays of light will all be focused. For a pinhole camera, the focal length is the distance from the pinhole to the film plane. The dimensions of a frame of 35-mm file are about 24mm x 36mm. Assume that the human visual system has an angle of view of 90 degrees, what focal length should we use with 35-mm film to achieve a natural view? (Refer to Figure 1.16)

Sample solution:

We can apply the formula for the angle of view from page 18, q=2tan^-1(h/(2f)), where we have replaced the length of the camera d with the focal length of the lens f. Solving for f, we have f=(h/2)cot(q/2). We can use the diagonal of the 24mm×36mm file for h and q=90. Thus, we find f=6 sqrt(13) cot(45)=21.6mm.

3. Movies are generally produced on 35-mm film that has a resolution of approximately 2000x3000 pixels. What implication does this resolution have for producing animated images for television as compared with film?

Sample solution:

Each frame for a 480x640 pixel video display contains only about 300k pixels whereas the 2000x3000 pixel movie frame has 6M pixels, or about 18 times as many as the video display. Thus, it can take 18 times as much time as to render each frame if there are a lot of pixel-level calculations.

4. It is possible to design a color CRT that uses a single electron gun and does not have a shadow mask. The single beam is turned on and off at the appropriate times to excite the desired phosphors. Why might such a CRT be more difficult to design, as compared to the shadow-mask CRT?

Sample solution:

There are single beam-CRTs. One scheme is to arrange the phosphors in vertical strips (red, green, blue, red, green, …). The major difficulty is that the beam must change very rapidly, approximately three times as fast as each beam in a three beam system. The electronics is such a system that electronic components must also be much faster (and more expensive).