BSP Tree Construct a BSP tree of the following scene, WITH L7 as root.

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1 BSP Tree Construct a BSP tree of the following scene, WITH L7 as root.
Mark “free” or “solid” at the leaf nodes [10%] Write the equation of each line below[14%] Use your tree to do in/out test on (a) and (b) (mark the tree traversal path) [6%] p0 p1 p3 p2 p4 p5 p6 a b P0 P1 P2 P3 P4 P5 P6 (-8,-8) (8,-8) (8,8) (-8,8) (-3,-3) (-3,3) (3,3) L1 L2 L3 L4 L5 L6 L7 (eqn) P0P1 P1P2 P2P3 P3P0 P4P5 P5P6 P6P4 Note: right child > 0; all normals(+) of edges point to free space

2 Socket Programming 班級座號 姓名 Exam: Project = _________ : __________
班級座號 姓名 Exam: Project = _________ : __________ Suppose you want to send a short integer of value 385, from client to server. Short integer has ______ bytes [2%]. Decimal digit 385 is 0x________ in hex[2%]. Windows uses little endian. Hence, data in the memory of client’s computer is ordered as ____ ____ [2%] (MSB) (LSB) Network uses big endian. After “htons”, data becomes ____ ____ [2%]. The actual packets got sent in the network is _____ ______[2%]. Assume the server uses big endian. The following lines receives packets from the network The packets received are ____ _____. [2%] The data after ntohs are _____ _____.[2%] It is ______ in decimal (big endian).[2%]

3 Gradient values (from unit circle)
Perlin Noise (1,2) (2,2) (1.2,1.7) (1,1) (2,1) Find the following noise values [18%] N(1.2, 1.7) N(1.0, 1.0) N(1.3, 1) p Interpolant

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5 Finite State Diagram Draw a finite-state diagram for the non-ghost players. Including the states of 停止 &逃跑 [15%] 紅綠燈遊戲 由一人當鬼，其他人逃跑。 鬼可以抓人，被抓到的人就換他當鬼。 逃跑的人可以喊「紅燈」，進入停止狀態。 其他逃跑的人可以碰觸停止狀態的人，說「救」，將人救回逃跑狀態。 如果所有人都進入停止狀態，鬼就獲勝，重新選鬼，但有時是讓最後一個進入停止狀態的人當鬼。

6 Rotation Representations
x y z 1. Sketch the pose (as demonstrated right) after Euler angles ZYZ (90, 90, 90) [4%] 2. Find the equivalent 3x3 rotation matrix[4%] 3. Find the equivalent quaternion[4%], and axis-angle representation.[4%] 4. Find the coordinates after rotation of point (1,2,-1) using the Rodrigue’s formula [5%]