Computer Graphics: Math to Code

Question

First, lets start out with my math background. I've taken calculus I - IV and Differential Equations. I've taken a first semester computer graphics course where we implemented pretty much our own graphics pipeline including shading using Phong without any graphics API.

I'm taking a graduate level Advanced Computer Graphics course this semester and when reading the math involved it loses me. This class is basically an image synthesize class. We'll build a ray-tracer in our first project and build on it from there on.

When reading up on advanced computer graphics, I'll usually get a bunch of math. I understand computer graphics is math heavy but I'm having problems when trying to figure out exactly how I'm suppose to implement the math into code. I'm really going to need to get the hang of this in order to excel in CG.

For instance, this article from GPU Gems: http://http.developer.nvidia.com/GPUGems/gpugems_ch01.html There's a bunch of math, but I have no clue where to start implementing the math if I want to.

So, is there something I'm missing? Am I suppose to look at the math and be able to derive the code? Are there tutorials/books out there that could help me understand what I'm needing to do?

Answer 1

Programming for the sort of math you see in the GPU gems article would generally fall under numerical analysis. The more applied side of numerical analysis would be treated in a course or book on numerical methods or scientific programming. I'd suggest starting from the wikipedia article on numerical analysis and looking at some of the specific linked articles. Once you know the names of some relevant methods, sample code is easy to find.

A tip: a big part of implementing derivatives and integrals is really just learning how to handle limits (in the mathematical sense) in your programs. Often, that's not explicitly stated.