CS465 Fall 2003 -- Final exam solution -------------------------------------- Problem 1 --------- 1.1 too dark (2 pts) 1.2 more saturated (4 pts) Problem 2 --------- 2.1 It is a cylinder of radius r around the axis through c in the direction v. 2.2 (a) an axis-aligned ellipsoid with major radii 1 x 0.5 x 1 in x, y, and z respectively. (b) a cylinder of radius 2 around the y axis. 2.3 Here is a correct procedure: intersect(M, p, d): p' = M * p d' = M * d return intersectUnitSphere(p', d') It does work for both cases, even the singular one, because we never need to invert the matrix. Problem 3 --------- (3 pts per correspondence) 1 - b 2 - c 3 - a 4 - e 5 - d Problem 4 --------- (1 pt per bit) C0 C1 int Property: (a) (b) (c) Filter 1 Y Y Y Filter 2 Y N Y Filter 3 N N Y Filter 4 Y Y N Problem 5 --------- (4 pts each) 1. scale(2,3,4) 2. scale(2,1,3) 3. rotate-y(90) 4. translate(0, -1, 0) Problem 6 --------- 6.1 (3 pts -- one per answer) eye coords -> image coords -> pixel coords (0, -10, -20) (0, -1/2) (500, 250) (2, -10, -20) (1/10, -1/2) (550, 250) (0, -10, -30) (0, -1/3) (500, 333 1/3) 6.2 (3 pts -- one per answer) (work out beta, gamma, then deduce alpha from alpha + beta + gamma = const) al_x = -1/50; al_y = -1/(83 1/3) bt_x = 1/50; bt_y = 0 gm_x = 0 ; gm_y = 1/(83 1/3) 6.3 the texture coordinates will be interpolated. Their values are u v 1/2 3/5 1 3/5 1/2 4/5 (2 pts for getting this far) what is actually interpolated is u/w, v/w, 1/w: w u/w v/w 1/w -20 -1/40 -3/100 -1/20 -20 -1/20 -3/100 -1/20 -30 -1/60 -4/150 -1/30 (2 pts for getting the rest of the way) 6.4 Vertex stage: transform, lighting interpolate: texture coordinates, lighting factor (or color) Fragment stage: texture, hidden surface (4 pts -- 2 for interp, 2 for allocation of tasks) 6.5 Vertex stage: transform interpolate: texture coordinates, normal Fragment stage: lighting, texture, hidden surface (4 pts -- 2 for interp, 2 for allocation of tasks) Problem 7 --------- 7.1: (1 pt per bit) Hue Sat Lum (a) N Y Y (b) N N Y (c) N N Y (d) Y Y N 7.2: (2 pts per bit) (a) Y (b) Y (c) N