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）︰2011.11.21 考試時限（分鐘）： 試題 : Interactive Computer Graphics Midterm Exam 2011/11/21 1. GLSL (20%) (a) In vertex shader, what is gl_NormalMatrix used for? What is the relationship between gl_ModelViewMatrix and gl_NormalMatrix? (b) Without using functions glShadeModel(GL_FLAT) and glShadeModel(GL_SMOOTH), how to use vertex shader and fragment shader to implement Flat shading and Gouraud shading? Please describe what is done in the vertex and fragment shader. 2. Rendering equation and ray tracing (20%) (a) Describe the strength and weakness of Ray Tracing model, using the theory of "The Rendering Equation". (b) In addition to the bounding box (sphere) method, please propose three more methods to speed up the ray tracing algorithm. 3. BSP Tree (15%) Figure: http://i.imgur.com/jvafwo3.png (a) Construct the Binary Space Partitioning (BSP) tree of the model in Fig.3 below. Please use the node "a" as the root. Split any line segment as you wish, and mark them as b.1, b.2, b.3, b.4, etc. Please choose smaller numbers/alphabets as the sub-tree root node. (b) From the BSP tree in (a), derive the display sequence in terms of the given viewing position in this figure. 4. Coordinate (5%) (a) Why does OpenGL use homogeneous coordinates (x, y, z, 1) instead of Cartesian coordinates (x, y, z)? 5. Curves and Surfaces (10%) Figure: http://i.imgur.com/8Ha337p.png If we have five control points for the new 5-point Bezier curve, P1(16, 4, 48), P2(8, 8, 16), P3(24, 28, 32), P4(32, 16, 8), P5(48, 12, 32). The definition of this new curve is the same as the regular 4-point Bezier curve. In order to draw the curve, we split it by half: (1) If the 4-point Bezier curve has degree 3 in terms of t parameter, i.e., (1, t, t*t, t*t*t), what's the degree of this 5-point Bezier curve? (2) Similar to the methods used in 4-point Bezier curve, what will be the new control points of the two split curves? (You need to give exact numbers for the first 5 control points only). 6. Head Pose Estimation (15%) Figure: http://i.imgur.com/SaWaed1.png Head pose information is useful in many human computer interaction systems. Assuming that human head can be approximated by a bounding box with six planes, and the orientation of the box is the pose of the head, we would like to estimate the head pose via this box. Given that you have already estimated the normal vector N(上面加向右箭頭) = (a, b, -1) of the frontal plane, how would you use this normal vector to drive a head model in OpenGL programming? (Note that the normal model faces to negative z-axis and positive y-axis is its up vector. ) 7. (5%) What is the topic of your term project? What will be the major problems to be solved in this project? 8. Geometry Objects and Transformation. (10%) The following are two code segments of an OpenGL program. Figure 1 is the display of the program using function A as its display callback function. If we replace function A by function B, what figure will be displayed on the screen? Please draw your answer. (Note: The width of the big rectangle is 80, and the height is 120. The width of the small rectangle is 60, and the height is 30. The width of the triangle is 60, and the height is 40) function A: function B: ══════════════════ ══════════════════ void display(){ void display(){ glClear(GL_COLOR_BUFFER_BIT); glClear(GL_COLOR_BUFFER_BIT); gluLookAt(0,0,1,0,0,0,0,1,0); gluLookAt(0,0,1,0,0,0,0,1,0); drawXAxis(); drawXAxis(); drawYAxis(); drawYAxis(); drawBigRectangle(); glRotatef(45,0,0,1); drawSmallRectangle(); glTranslatef(200,0,0); drawTriangle(); glPushMatrix(); glutSwapBuffers(); glTranslatef(0,100,0); } drawTriangle(); ══════════════════ glPopMatrix(); glPushMatrix(); Display: glTranslatef(-100,0,0); glRotatef(45,0,0,1); Figure 1: drawSmallRectangle(); http://i.imgur.com/r2tRkL4.png glPopMatrix(); drawBigRectangle(); glutSwapBuffers(); } ══════════════════ --

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