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︰资工系 考试日期（年月日）︰2008.11.24 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 : Interactive Computer Graphics Midterm Exam 11/24, 2008 1.Shadow generation:(10%) (a)(5%)Why there will be shadows in a scene with Ray Tracing Algorithm? (b)(5%)Please describe briefly any method as to how to add fake shadows? (Hint: Visible-surface algorithm with some modifications is one possible solution. Maybe you can draw some pictures to show the ideas.) 2.Shading(10%) (a)(5%)Please describe the Gouraud Shading and Phong shading. Draw a triangle and state how the colors of interior pixels are interpolated. (b)(5%)What are the visual differences between Gouraud Shading and Phong Shading? Also, discuss the cffect on simple models and complex models. 3.(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.) 4.The Rendering Equation(20%) (a)(10%)What is "The Rendering Equation", please draw pictures and show the equations with short explanations. (b)(10%)Using the above equation to explain the weakness of Phong shading and ray tracing. 5.(15%)In two dimensions, we can specify a line by the equation y = mx + b. (a)(10%)Find an affine transformation to reflect two-dimensional points about this line. (b)(5%)Extend your results to reflection about a plane in three dimensions. 6.(10%)In 2D, please consider if a rotation transformation by angle A can be specified as a series of shear transformation matrices. Give these matrices, or it can't be done, prove it. 7.Illumination Models(20%) A popular illumination model is called Phong model, which is developed in 1975. The formula of this model for each color channel is(please refer to textbook): _ _ _ _ I = IakaOd + fattIp[kdOd(N‧L) + ks(R‧V)^n]. where L is light direction, V is viewing direction. (a)(6%)Could you give two examples of materials that definitely can not be approximated by the Phong model? And simply explain why. (b)(8%)A general depiction of illumination model is called bidirectional reflectance distribution function (BRDF) (bidirectional reflectivity): I = fBRDF(L,V). The idea of this function is that given a viewing and lighting(single light source) direction, the BRDF function returns its reflectance (or precisely, the retio between the incident flux and reflected intensity). Please design a platform to capture BRDF of materials. You will have the following equipments: 1.Spheres of different materials 2.A digital camera 3.A light source with a 1DOF rotational arm that allows you to move the light direction horizontally. (c)(6%)The function I, if stored as a database, can be quite big(much larger than 1.0 Giga bytes). This can be a problem for ordinary PC graphics card in real-time graphics. Can you think of a way to compress the data of function I? (Assume viewing and lighting direction is in division of one degree, say in spherical coordinate system, per sample in theta and phi direction.). 8.BSPtree(10%) i.(5%)Construct the Binary Space Partitioning(BSP) tree of the model in Fig 1. Please use the right part of node 3 as the root. Split any line segment as you wish, and mark them as a, b, c, d etc. ii.(5%)From the BSP tree in (a), derive the display sequence in terms of the viewing position "the eye". 2 ----------------------------- │ ↓ │ │6 │ │→ │ │ ←│1 │eye ↑3 │ │ ------------ │ 5│ │ │ │ ↑ │→ -------------│ Figure 1. │ │4 --

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