课程名称︰ 计算机图形 课程性质︰ 选修 课程教师︰ 欧阳明 开课学院： 电资学院 开课系所︰ 资工所 考试日期（年月日）︰ 2010/12/6 考试时限（分钟）： 180 是否需发放奖励金： 是 （如未明确表示，则不予发放） 试题 : 1. (15%) Surface Normal (a) (3%) What is the normal vector? (in geometry) (b) (4%) What relationship do the normal and tangent vector have? (c) (8%) If we apply a transform matrix M on an object, can M be used to transform the object's normal vectors? If not, how to tackle this problem 2. (10%) Curves and Surfaces (a) (7%) If we have four control points for the Bezier curve, P1(1, 2, 5), P2(5, 8, 3), P3(7, 6 5), and P4(9, 2, 3). In order to draw the curve, we split it by half. What are the new control points of the two split curves? (Please give exact numbers). (b) (3%) Make a brief comparison between Bezier curve and B-spline. 3. (10%) In your homework 2, you realize pixel-based Phong shading utilizing vertex and fragment shaders. However, Phong shading can still be realized without shaders. Please describe what should be done in the OpenGL implementation. (For example, how to find pixels and their normals which will be rendered on the screen? In your homework 2, those are covered by the fragment shader.) 4. (10%) Illumination Model (a) (5%) The Blinn-Phong lighting model uses the half-vector h = (v + l) / |v + l| and the expression (n ˙　h)^k in its specular term. Describe the motivation behind the use if the half-vector in this lighting model. (b) (5%) Using the rendering equation, can you explain what's wrong with in Phong shading model for a scene with many objects. 5. (15%) Visible Surface Determination In general polygon rendering, the Z-buffer technique is used for visible surface determination. Some modified techniques can be applided to reduce the rendering time in implementation. (i) Using depth sort + Z-buffer (always display the nearest polygon first) (ii) Only using Z-buffer (a) (10%) Let the screen width = W, height = H, and there are N polygons in the building model. Based on yours experience, using the teapot model and CSIE department building model, how will you describe the improvement (speedup) using (i) over (ii)? (b) (5%) Compare the computational complexity of the two methods above, in terms of worst case and average case. 6. (10%) Shadow Generation (a) (5%) How can shadows be generated in the ray tracing algorithm? (b) (5%) Besides ray tracing, could you provide another way to simulate shadow in an OpenGL implementation? (describe the ideas first, then OpenGL implementation) 7. (10%) Microsoft XBox 369 just announced its KINECT depth camera (each pixel has a depth from 1 to 10000, at 30 FPS), and has gained more popularity than its competitor such as Sony Playstation 3. Please give your explanations on this fact. Why? 8. (15%) BSP Tree (a) (10%) Construct the binary space partitioning tree of the model in Figure 1 (use polygon 1 as the root, and always use the smaller polygon as the next node) (b) (5%) From the BSP tree in (a), derive the correct display sequence in terms of the viewing position (eye). 2 ╴╴╴╴╴╴╴╴╴╴╴╴╴╴╴ ︳ ↓ ↖ eye ︳ ︳ ⊙ ︳ ︳ 4 ↑ ︳ 3 ︳ ╴╴╴╴╴╴╴╴╴╴ ︳1 ︳ ︳ ︳ ︳ ︳ ︳→ ︳ ︳ ︳ ← ︳5 ← ︳ ︳ ↑ ︳ ︳ ︳ ╴╴╴╴╴╴╴╴╴╴╴╴ ︳　 Figure 1 6 9. (5%) What is your term project for this semester? What are the technical difficulties involved in the project? (You can refer to the project list). --

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