课程名称︰游戏设计 课程性质︰系选修 课程教师︰陈炳宇 开课学院：管院 开课系所︰资管所 考试日期（年月日）︰11/07-11/16 考试时限（分钟）：带回家写 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : Game Programming Mid-term Exam. Date:2011/11/16 1. Please describe the root-base system used for biped characters. 2. Please describe the importance of system analysis in game development. 3. Please describe the three major techniques of character models (the actor in The Fly) used in real-time 3D games and compare their pros and cons. 4. Consider curves in a two dimensional space defined by figure construction. In the following questions, assume that four points P0, P1, P2, and P3 are all different and any three points of them are not on a line. Answer the following question. a. Consider three control points P0, P1, P2, and line segments connecting them as in the right figure. Let t be a real number satisfying 0<=t<=1. Let P0' divide line segment P0P1 in the ratio t:t-1, and, likewise, P1' divide line segment P1P2 in the ratio t:t-1. Further, let P divide line segment P0'P1' in the ratio t:t-1. Show that P is expressed as: P(t) = (1-t)^2P0 + 2(1-t)t P1 + t^2 P2. b. By moving t from 0 to 1, the point P forms a quadric curve. Is this curve a part of ellipse, a hyperbola, or a parabola? c. Add one more control point P3, and determine P in the same way as the above question a., that is, by repeating interior divisions between beighboring points (see right figure). Express P(t) as the sum of Pi's each multiplied by a polynomial of t, as in the above question a. d. Consider approximating a quarter of circle of radius r by a cubic curve with four control points as is obtained in the above question c. Points are arranged as in the right figure. Determine P1 and P2 so that P(1/2) = (r cos(π/4), r sin(π/4)), is satisfied. e. Divide the cubic curve in the above question d. into two parts at t = 1/2. Determine the positions of the two sets of control points that determine the left and the right curves, so that the divided curves are exactly the same as the original curve. You may as well determine them by construction of figures. 5. For the Barycentric coordinate system of a 3D triangle with vertices, p0(x0,y0,z0), p1(x1,y1,z1), and p(x,y,z), on the plane formed by the triangle being inside the triangle or not? 6. In separating axis algorithm, how can we project the vertices of each object on the axix/plane that is perpendicular to axis/plane we are going to find? --

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