# CSE Intro to Computer Graphics. ANSWER KEY: Midterm Examination. November 18, Instructor: Sam Buss, UC San Diego

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1 CSE Intro to Computer Graphics ANSWER KEY: Midterm Examination November 18, 2003 Instructor: Sam Buss, UC San Diego Write your name or initials on every page before beginning the exam. You have 75 minutes. There are eight problems. You may not use cheat sheets, calculators, notes, textbooks, or other materials during this exam. You must show your work in order to get credit. Good luck! Name: Student ID: Total

2 Name: 2 1. An affine transformation A(x) :R 2 R 2 maps the F -shape on the left to the F on the right. 0, 1 y 1, 1 1, 1 y 0,1 0, 0 1, 0 x = 2, 0 1, 0 0,0 x 0, 1 a. Give a 3 3 matrix that represents A over homogeneous coordinates. ANSWER: A = b. Give a 3 3 matrix that represents A 1 over homogeneous coordinates. ANSWER: A 1 = Consider the following sequence of OpenGL commands: glmatrixmode(gl MODELVIEW); glloadidentity(); glrotatef( 90.0, 0, 1, 0 ); glrotatef( 90.0, 0, 0, 1 ); glrotatef( -90.0, 0, 1, 0 ); // Watch out: negative sign! gltranslatef( 3, 4, 5 ); Show explicitly the contents of the 4 4 ModelView matrix after these commands have been executed. ANSWER: You must be careful here to note. that the gltranslatef comes after the glrotatef s.

3 Name: 3 3. An ellipsoid has 2 radii equal to 1 and one radius equal to 2. It can be viewed as a unit sphere which has been stretched to twice its usual width and streches from 0 = 0, 0, 0 to 4, 0, 0. The ellipsoid has circular crosssections when intersected with planes parallel to the yz-plane. The GLUT command glutsolidsphere(r, 10, 10); can used to generate a sphere of radius r. Using this command, plus other OpenGL commands, such as glmatrixmode, glloadidentity, glrotatef, glscalef, gltranslatef, write a code fragment that will generate the ellipsoid. ANSWER: glmatrixmode(gl MODELVIEW); glloadidentity(); gltranslatef( 2.0, 0.0, 0.0 ); glscalef(2.0, 1.0, 1.0); glutsolidsphere( 1.0, 10, 10 ); 4. What are the different kinds of light from point light sources in the Phong lighting model? Give a short descrition of each one (one sentence, and possibly a simple picture). ANSWER: Specular light Light that reflects primarily in the direction of perfect reflection (see figure III.3, on page 69.). Diffuse light Light that reflects with equal brightness in all directions (see figure III.2, on page 69). Ambient light This is not really from a point light source, but no points were taken off if it was mentioned, since the OpenGL implementation of Phong lighting does include ambient light from point light sources.

5 Name: 5 7. Let x = 2, 2 and y = 1, 1. (a) What is the point u 1 = Lerp(x, y, 1)? ANSWER: 1, 1. (b) What is the point u 2 = Lerp(x, y, 1 2 )? ANSWER: 1 2, 1 2. (c) What is the point u 3 = Lerp(x, y, 2)? ANSWER: 8, 8. (d) Let u 4 = 1, 1. Find the value of α such that Lerp(x, y,α)=u 4. ANSWER: α = Let x = 1, 0, 5 and y = 0, 5, 1 and z = 4, 1, 2 be the vertices of triangle. Consider barycentric coordinates relative to this triangle. (a) What point v 1 has barycentric coordinates 1 3, 1 3, 1 3? ANSWER: 1, 2, 2 3. (b) What point v 2 has barycentric coordinates 1, 0, 0? ANSWER: 1, 0, 5. (c) What point v 3 has barycentric coordinates 1 4, 1 4, 1 2? ANSWER: 7 4, 3 2, 0. (d) What point v 4 has barycentric coordinates 1 3, 2 3, 0? ANSWER: 1 3, 10 3, 1. (e) What are the barycentric coordinates of the point y? ANSWER: 0, 1, 0.

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