TITLE: How is math used in computer graphics?
QUESTION [6 upvotes]: I'm doing a research paper on the mathematics of computer graphics and animation (3D) and I do not know where to start. What mathematical equations and concepts are used for computer graphics and animation (3D)?

REPLY [5 votes]: Computer graphics is a broad field (and consequently the mathematics used), so I'm going to focus on the mathematics and techniques used in animation, specifically, special effects in movies to answer your question. Worth noting that while the focus of this answer is narrow, the domains mentioned are also used in other areas of computer graphics. 
The mathematics used in animation can be fairly simple. For example, after the release of the film Tron Legacy, Joshua T. Nimoy of Digital Domain wrote about the techniques he used on the film covering everything from basic linear algebra, geometry, physics-based calculus, topology and numerical methods.
While simple mathematics can be used to animate most real world objects, more advanced mathematics is required to animate things such as fabric, fire, fluids, fur and smoke in film. In particular, differential geometry and (partial) differential equations are used. Aleka McAdams, Stanley Osher and Joseph Teran wrote an excellent survey (pdf) on how these domains are used. More technical notes (pdf) from 2002 SIGGRAPH workshop on Level Set and PDE Methods for Computer Graphics is also worth a look.
The mathematics used are just part of the picture, additional tools used from computer science and software engineering (e.g., data structures, computational geometry, and optimization) are used to devise optimal algorithms to efficiently produce animations in the least amount of time with the greatest clarity.
Hopefully this gives you a better idea of the breadth of mathematics used in computer graphics for animation. If you want to learn more, you can pick a handful of papers from any one of the conference proceedings or journals below to get a better idea.

ACM SIGGRAPH 
ACM SIGGRAPH Symposium on Interactive 3D Graphicsand Games
Eurographics Workshop on Rendering
IEEE Computer Graphics and Applications
IEEE Transactions on Visualization and Computer Graphics
ACM Transactions on Graphics