Computer Graphics (CMU 15-462/662)
CMU 15-462/662, Fall 2022
Tuesday and Thursday, 1:25-2:45pm
BH A51
Instructor: Jim McCann
Course Description

This course provides a comprehensive introduction to computer graphics. It 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.

To get a sense of what you'll do in the class, check out some student creations from Fall 2020!
[jmccann at andrew]
Your fun and helpful TAs:
Daniel Zeng
[dlzeng at andrew]
Office hours:
Monday 4-6pm
Location: Smith Hall 2nd Floor
Alan Lee
[soohyun3 at andrew]
Office hours:
Friday 5:30-7:30pm
Location: Smith Hall 2nd Floor
Mia Tang
[xinrant at andrew]
Office hours:
Thursday 5:30-7:30pm
Location: Smith Hall 2nd Floor
Junyi Zhang
[junyizha at andrew]
Office hours:
Thursday 5:30-7:30pm
Location: Smith Hall 2nd Floor
Nathan Glover
[nsglover at andrew]
Office hours:
Monday 4-6pm
Location: Smith Hall 2nd Floor
Eve Liu
[yixuanl2 at andrew]
Office hours:
Friday 5:30-7:30pm
Location: Smith Hall 2nd Floor

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 programming in C/C++ or similar languages is very helpful as course programming assignments will involve significant implementation effort.


The TAs will hold several recitations throughout the semester, to help supplement lecture material and provide key information about assignments. Recitations will also be used to review solutions to the mini-homework. Please refer to Piazza for the recitation schedule and associated links/info.

Discussion Boards

There are several mechanisms for discussing course content and asking questions:

  • Course Web Page — Our course web page has a nice setup that lets you directly ask questions / make comments on course slides. These slides will appear before each lecture. Part of your course participation grade will be to leave one question/comment per lecture (see below for more info).
  • Piazza — We will be using Piazza for general class announcements, as well as homework questions/help and general discussion. The 15-462/662 Piazza page is located here.


(70%) Programming Assignments. The bulk of the coursework is centered around four major programming assignments (A1–A4); each assignment is worth 17% of the overall course grade. You will also have a set of math review exercises at the beginning of the semester (A0), worth 2% of your grade. Programming assignments should be completed independently by each student; any duplicated work will be considered cheating, independent of who copied whom.

(20%) Midterm / Final. There will be a midterm and a final, each worth 10% of the overall course grade. Both exams will cover the cumulative material seen in the course so far.

(10%) Class Participation. To earn the first 5% of your participation grade, you are required to ask two questions/comment on each set of lecture slides, via the 462 webpage. In order to receive credit, this comment must be made prior to the beginning of the next class period. The remaining 5% of the participation grade will be based on completing mini-hws and/or in-class exercises. These exercises are just a few short questions that reinforce the most essential concepts.

Late Policy

All programming assignments are due at 11:59:59pm Eastern time on the due date, as reported by Each student is allotted a total of six late-day points for the semester. Late-day points are for use on the four programming assignments only (A1–A4). 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).
  • Late-day points get used up for each checkpoint. So for instance, even if you already used one late point for A2.0, you would still have to use another late point if you wanted to turn in A2.1 a day late.
  • 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.
  • You may not use late days past the last day of the semester (i.e., the last day of the week before finals week).
  • Late-day points are also meant to help cover incidents like sick days, interviews, family emergencies, etc. You do not need to ask special permission to use late-day points, nor will we allocate additional late-day points due to such events. For instance, we won't give you extra late days just because you have a bunch of interviews—please plan accordingly. The whole point of this “no questions asked” mechanism is to streamline the process for everyone.

The dates on the course schedule 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!

If you are caught cheating, you will get a zero for the entire course (not just the assignment). Also, if two identical assignments are handed in, both students will be accountable for cheating (no questions asked). So please be careful to ensure that nobody is copying your work!

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.



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!