# CS 426 Exercises   Hidden Surface Removal

1. Write the equation for determining whether a polygon is back-facing with respect to a viewer.
2. For each of the following algorithms, how does it insure that the pixels resulting from rendering the front-most polygons are in the frame buffer: a) depth-sort, b) z-buffer, c) ray casting, d) Warnock's area subdivision, e) scan-line?
3. What is image-space precision? object-space precision? Specify whether the following algorithms operate with object-space or image-space (pixels) precision: a) back-face culling, b) depth-sort, c) z-buffer, d) ray casting, e) Warnock's area subdivision, f) scan-line.
4. For each of the following hidden surface removal methods, a) back-face culling, b) depth-sort, c) z-buffer, d) scan-line, specify in which stage of the rendering pipeline it executes: DB traversal, modeling transform, trivial reject, lighting, viewing transform, clipping, projection, rasterization, or display.
5. If writing pixels into the frame buffer is hypothetically the performance bottleneck in the rendering pipeline, rank the following algorithms from fastest to slowest: a) depth-sort, b) z-buffer, c) ray casting, d) Warnock's area subdivision, e) scan-line?
6. Which hidden surface removal algorithms perform more slowly for frame buffers with higher resolution?
7. What is depth-complexity? Which hidden surface removal algorithms perform more slowly for scenes with high depth-complexity?
8. Z-buffers have become ubiquitous in hardware on most PC graphics accelerators. What are the disadvantages of the z-buffer algorithm?
9. The z-buffer method requires a z-value to be stored for every pixel in the entire screen. In some situations, this memory requirement is prohibitive. Propose a method in which the z-buffer approach is used, but memory is allocated for only part of the screen. What additional problems arise?