CS216 Spring 2010Practice Final

To study for the final I would suggest you: (1) Know how to do (by heart) all the practice problems. (2) Go over your notes at least three times. Second and third time try to see how much you can remember from the first time. (3) Go over the homework problems. (4) Try to create your own problems similar to the ones I have given and solve them. (5) Skim the relevant sections from the book. (6) If you want to study in groups, at this point you are ready to quiz each other. The practice final is below. Here are some facts about the actual final: (a) It is comprehensive (b) It is closed book, closed notes. Nothing will be permitted on your desk except your pen (pencil) and test. (c) You should bring photo ID. (d) There will be more than one version of the test. Each version will be of comparable difficulty. (e) It is 10 problems, 6 problems will be on material since the lecture before the midterm, four problems will come from the topics covered prior to the midterm. (f) Two problems will be exactly (less typos) off of the practice final, and one will be off of practice midterm.

1. Draw an example of a 3D figure whose medial axis representations has at least one sheet, seam, and junction.

2. Suppose we have a CSG space of objects that consists of the 2D rectangles as linear halfspaces as base objects and derives the space of object by using closure under regular operations. Explain how in out testing could be done in this case for at least two regular operations.

3. Briefly explain our algorithm from class for converting from a B-rep to a CSG representation.

4. Give an algorithm for determining the bounding box of a general, linear polyhedra.

5. Let T be the right triangle with vertices (0,0), (0,3), (4, 0). Use the barycentric coordinate test to determine if the point (3,2) is in this triangle.

6. Describe BSP visible surface algorithm given in class.

7. Draw a box with three overlapping figures in it. Describe how the Warnock visible surface determination algorithm would work for your picture.

8. Show a Delauney graph of a set of points need not be a triangulation.

9. Define the following terms: geodesic curvature, Frenet Frame, parallel transport.

10. What is the discrete geodesic problem? Briefly give an algorithm to solve it.