Computer Graphics (CMU 15-462/662)
CMU 15-462/662, Fall 2017
Date/Time: Mon/Wed 1:30-2:50pm
Location: GHC 4215
Instructor: Keenan Crane
Course Description

This course provides a comprehensive introduction to computer graphics. Focuses on fundamental concepts and techniques, and their cross-cutting relationship to multiple problem domains in graphics (rendering, animation, geometry, imaging). Topics include: sampling, aliasing, interpolation, rasterization, geometric transformations, parameterization, visibility, compositing, filtering, convolution, curves & surfaces, geometric data structures, subdivision, meshing, spatial hierarchies, ray tracing, radiometry, reflectance, light fields, geometric optics, Monte Carlo rendering, importance sampling, camera models, high-performance ray tracing, differential equations, time integration, numerical differentiation, physically-based animation, optimization, numerical linear algebra, inverse kinematics, Fourier methods, data fitting, example-based synthesis.

Smith Hall 215
Office hours: Wednesdays 5‐6pm
217 Smith Hall
Your fun and helpful TAs:
Nick Sharp
Office hours:
Thursdays 4–5pm
Location: Smith Hall
2nd floor lounge
Joel Loo
Office hours:
Mondays 4:30–5:30pm
Gates 5th floor Gates
Citadel Commons
Connor Lin
Office hours:
Fridays 3–4pm
Gates 5th floor Gates
Citadel Commons

Course prerequisites are (15-213, 21-259, and 21-240) or (15-213, 21-259, and 21-241) or (18-213 and 18-202). Basic vector calculus and linear algebra will be an important component of this course. Previous exposure to basic C/C++ programming is very helpful as course programming assignments will involve significant implementation effort.


There is no required textbook for 15-462, though a variety of books may provide good supplementary material:

Pete Shirley and Steve Marschner with Michael Ashikhmin, Michael Gleicher, Naty Hoffman, Garrett Johnson, Tamara Munzner, Erik Reinhard, Kelvin Sung, William B. Thompson, Peter Willemsen, and Bryan Wyvill
Fundamentals of Computer Graphics. A K Peters, 2009
[ On Amazon ]

John F. Hughes, Andries van Dam, Morgan McGuire, David F. Sklar, James D. Foley, Steven K. Feiner, and Kurt Akeley
Computer Graphics: Principles and Practice
[ On Amazon ]

Matt Pharr and Greg Humphreys
Physically Based Rendering: From Theory to Implementation
[ On Amazon ]
This book (PBRT) is the book for learning about modern ray tracing techniques. It has a great website with full source code online for an advanced physically-based ray tracer. It even won an oscar for its impact on the film industry!

Discussion Boards

We will be using Piazza for announcements. The 15-462/662 Piazza page is located here.


(5%) Written Assignment. Students will be given a written assignment to test their understanding of mathematical concepts that are core to computer graphics.

(60%) Programming Assignments. Students will complete four programming assignments; each assignment will be worth 25% of the programming component of the course, or 15% of the overall course grade. Most assignments will be done individually; some will have the option to work with a partner.

(7%) Take Home Quizzes. Following each lecture, students will complete a short take-home quiz that reinforces the most essential concepts from the lecture. To make sure you're getting some feedback on your understanding, these quizzes will be graded on quantized scale:

  • 100% — correct idea, details are correct
  • 85% — correct idea, minor details are wrong
  • 75% — rough idea, missing some major pieces
  • 60% — good faith attempt, but clearly wrong
  • 35% — “I don't know, and here's what I didn't understand.”
  • 25% — “I don't know.”
  • 0% — nothing handed in / too sloppy to read
Quizzes must be turned in by the student, at the beginning of the next lecture. To mitigate potential absences (sick days, etc.), students can omit up to six quizzes without penalty. Students are encouraged to discuss concepts with their peers, but final quiz answers must be written independently and individually.

(25%) Midterm / Final. There will be a midterm and a final, each worth 12.5% of the overall course grade. Both exams will cover the cumulative material seen in the course so far.

(3%) Class Participation. At the discretion of the instructors, based on consistent attempts at in-class comments, website comments, and other contributions to the class.

Late hand-in policy. Each student is allotted a total of five late-day points for the semester. Late-day points are for use on the first four programming assignments only. Late-day points work as follows:

  • A student can extend a programming assignment deadline by one day using one point.
  • If a student does not have remaining late day points, late hand-ins will incur a 10% penalty per day (10% of max points on the assignment).
  • No assignments will be accepted more than three days after the deadline. This is true whether or not the student has late-day points remaining.

The dates on the front page are the official due dates. If you find conflicting information elsewhere (e.g., on Piazza, in-class, talking to a TA...), you should always assume that the assignment is actually due on the date stated on the front page of the course web site. (But please let us know if something seems totally wrong! ;-))

Collaboration Policy

Students in 15-462 are absolutely encouraged to talk to each other, to the TAs, to the instructors, or to anyone else about course assignments. Any assistance, though, must be limited to discussion of the problems and sketching general approaches to a solution. Each student should write their own code and produce their own writeup. Consulting another student's solution is prohibited and submitted solutions may not be copied from any source. These and any other form of collaboration on assignments constitute cheating. If you have any question about whether some activity would constitute cheating, just be cautious and ask the instructors before proceeding!

You may not supply code, assignment writeups, or exams you complete during 15-462/662 to other students in future instances of this course or make these items available (e.g., on the web) for use in future instances of this course (just as you may not use work completed by students who've taken the course previously). Make sure to make repositories private if you use public source control hosts like github.