課程名稱︰計算機圖形 課程性質︰選修 課程教師：歐陽明 開課學院：電資學院 開課系所︰資工所、網媒所 考試日期（年月日）︰2012.11.21 考試時限（分鐘）： 試題 : Interactive Computer Graphics Midterm Exam Nov 21, 2012 1. (20%) Shading (a) (10%) Indicate the strength and weakness of flat shading, Gouraud shading, and Phong shading. (b) (5%) Simply using these illumination methods to render a 3D scene with multiple objects and single light source, what is missing with regard to the rendering equation? (c) (5%) How can you solve the problem in question(b)? 2. (10%) Ray-Tracing is time-consuming because of numerous and independent ray calculations. Please propose at least 3 methods to speed up Ray-Tracing algorithm. 3. (10%) Graphic Pipeline Figure: http://i.imgur.com/kfvPvpC.png It is a simplified computer graphic pipeline. Please describe the functions of each stage. (Do not regard it as a specific CG API such as OpenGL, please describe the general reason why we need these stages in computer graphic) 4. (10%) Curves and Surfaces Figure: http://i.imgur.com/Fr5oB8S.png (a) Please give a brief comparison (advantages) between Bezier curve and B-spline. (b) Given a 4-point Bezier curve B(t) with points P0(8,1,0), P1(6,9,0), P2(14,9,0), P3(16,1,0), please calculate the value of new control points if the Bezier curve is split into two Bezier curves at the middle point. (c) Using the values you have obtained from (b). Please sketch the Bezier curve B(t), starting from P0 and ending at P3. 5. (10%) Visibility Figure 1: http://i.imgur.com/YG8Cj40.png (a) Construct the BSP tree of the model in Figure 1 below. (use polygon 1 as root, and always use smaller number polygon to the left of the tree) (b) From the BSP tree in (a), derive the correct display sequence in terms of viewing position (eye). 6. (5%) Clipping & Transformation A line can be clipped by Cohen-Sutherland algorithm in your homework. Now you are asked to do polygon clipping (i.e., a clipped primitive is still a polygon): Please write a pseudo code for clipping a triangle. Note: Assuming the clipping box (cuboid) is enclosed by: x = -1, x = 1, y = -1, y = 1, z = -1, z = 1. And the vertices of the triangle are: ((x0, y0, z0), (x1, y1, z1), (x2, y2, z2)) 7. (20%) Denote R_x(θ), R_y(θ), R_z(θ) as functions to rotate an object about angle θ along three principle axis of your camera. Note: Assuming camera is aligned in world system. (i.e. It is located at the origin, targets along z direction, and be up along y direction) (a) Denote O_x, O_y, O_z as principle axis of an object O, and its center is located on (x_c, y_c, z_c). Please design an algorithm for self-rotation alone three principle axis of the object respectively in terms of R_x, R_y, R_z and x_c, y_c, z_c. You can define other matrices for your convenience (b) An extension on (a). Please design a self-rotation along x axis of the object and simultaneously orbital rotation along z axis of camera (similar to the fig. below). Figure: http://i.imgur.com/Xnec6sJ.jpg 8. (5%) What is your term project for this semester? What are the technical difficulties involved in the project? (You can refer to the project listing). 9. (10%) In 2D, a rotation transformation by angle can be specified as a series of shear transformation matrices. Give these matrices, or if it can't be done, prove it. --

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