This page contains a number of resources to review or learn some of the mathematical skills that are useful for this course. This page will be updated throughout the semester and is organized roughly in chronological order. If you have anything to suggestions or requests, please post on Piazza!
Basic linear algebra concepts are extensively used throughout computer graphics, so it will be quite helpful to (re)familiarize yourself with the topics in this document. For each topic, we include a link to a short video (~3-15 minutes) that you may find helpful, courtesy of Professor J. Zico Kolter.
Linear Algebra Conceptual Organization: Outline
Linear algebra is useful for compactly representing sets of linear equations: Introduction
Basic Linear Algebra Notation: Notation
We frequently represent points and directions in 3D space as vectors, and transformations that act on these points as matrices. Computing the resulting transformed points or directions typically involves matrix-vector and matrix-matrix multiplication.
Solving Linear Systems:
Common graphics tasks such as computing parameters for curves that interpolate a given set of points or figuring out what values to show on a display to produce a response on the viewer’s retina can be expressed as the solution of a set of linear equations. It will be helpful to be familiar with setting up and solving systems of linear equations in matrix form.
- Inverses and Solving Linear Systems
- Putting Equations into Matrix Form 1
- Putting Equations into Matrix Form 2
- Putting Equations into Matrix Form 3
The effects of transformations used in graphics can be interpreted and characterized using functions of the respective transformation matrices, so it’s helpful to be familiar with basic functions such as norms, determinant, and transpose.