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18 CS488/688 Introduction to Computer Graphics (d) Explain how to modify the algorithm so as to completely compute the image at one pixel before proceeding to the next. In what circumstances would this be a desirable thing to do? (e) Indicate how to modify the algorithm of (c) so as to handle concave polygons. 8.6 Z Buffer vs. Watkins, Ray Tracing [Last Used: Fall 1986 Final] (a) Define the term depth buffer (z buffer) and explain how a depth buffer can be used to solve the hidden surface problem without explicitly computing polygon intersections. (b) Does the depth buffer algorithm take advantage of scan line coherence? Explain your answer. (c) Compare the depth buffer algorithm with Watkin’s algorithm for hidden surface elimination. Under what circumstances would one algorithm be preferable over the other? Relative criteria for judgement include time and space requirements, ability to incorporate transparency and anti-aliasing, and ease of programming. Justify your answer. (d) Keeping in mind what you wrote for part (c), what are the advantages/disadvantages of naive ray tracing as introduced by Turner Whitted in 1979? (e) Distributed ray tracing was first introduced in 1984 by Cook, Porter & Carpenter from Lucasfilm. How does it differ from the naive ray tracing algorithm? Explain. (f) Keeping in mind what you wrote for parts (c), (d) and (e), what are the advantages/disadvantages of distributed ray tracing? 8.7 Z Buffer and Translucency [Last Used: Spring 2000 Final] The standard z-buffer algorithm in the raster subsystem of most workstations goes like this: for each draw-object request { for each pixel covered by the object { if (the object z is greater than the stored z) { replace the color by the object color; replace the stored z by the object z; } } } This assumes that objects are opaque. If objects are translucent, then the color of a pixel should be, recursively, factor * front-object-color + (1 - factor) * color-resulting-from-all-further-objects where factor is a number between 0 and 1 related to the light transmission properties of the front object. Why can’t we handle this with the the z-buffer algorithm? Are there any modifications of the z-buffer algorithm that you can think of for handling transparency? If so, describe them briefly. If not, can you say what the insurmountable difficulty with the algorithm is? An interesting picture to look at while you are thinking is the following:
CS488/688 Introduction to Computer Graphics 19 9 Hierarchy 9.1 Hierarchical Modeling: A3 and A4 [Last Used; Winter 2013 Final] You implemented hierarchical modeling in both assignment 3 and assignment 4. If done correctly, you could have used the puppet you modeled in assignment 3 as a model for your ray tracer in assignment 4. However, despite the hierarchies being the same, the code you wrote in the two assignments did very different things when traversing the hierarchies. Discuss these difference by outline the operations performed on the hierarchies by each assignment. 9.2 2D Hierarchical Modeling [Last Used: Winter 2004 Midterm] In this question, the following notation is used: I is the do-nothing identity transformation, T (x, y) is a 2D translation by vector (x, y), S(x, y) is a non-uniform scale with factors x and y, and R(θ) is a counter-clockwise rotation about the origin by angle θ (in degrees). We want to model the following 2D “checker board”: Draw a DAG to model the checker board, with a single root node and a single leaf node containing a unit square centered at the origin as shown below. You should draw your internal nodes as boxes with one of the transformations listed above. The boxes should be connected with arcs; you may use multiple arcs to/from any box. You may use no more than 6 transformations (i.e., you may have no more than 6 internal nodes).
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Past Midterm and Exam Questions (PDF) - Student.cs.uwaterloo.ca ...

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