## Mathematics in computer animation## Saty Raghavachary, DreamWorks Feature Animation |

- Introduction
- A variety of examples

It is *all* math!!

- camera motion/scene setup - layout
- shape generation - modeling
- material assignment - surfacing
- motion - animation
- phenomena simulation - fx
- image synthesis - lighting/rendering

From tiling patterns to topology to differential geometry to integral calculus, practically every branch of math is useful in some aspect of computer graphics/animation

Let us start looking at examples - we'll use Youtube clips, trailers and clips from DW's movies, wikipedia entries, research papers etc. to illustrate the ubiquitous use of math in CG.

Random numbers are used to set particle count, velocity, direction etc. in a 'particle system'.

Perlin noise is a workhorse function that can replicate the look/motion of fluids, smoke, wood, marble, banana peel spots.. Animating it (over time) is a great way to replicate ocean waves.

Spline curves and surfaces offer an intuitive, controllable way to model smooth curves and surfaces.

A deceptively simple, recursive, polygon (quad)-splitting algorithm creates smooth 'limit' surfaces out of low-resolution polygonal models.

Monte Carlo techniques are used to sparsely *sample* a scene's environment while rendering. This is useful for producing soft shadows, color bleeding across surfaces, etc.

The most common technique to sim cloth uses a connected springs model. Here is more detail.

What if we could 'warp' the volume that a character (or part of it) is embedded in?

Needless to say, this makes for a *GREAT* career! To help you explore, here are some links..

CG sites (academic, hobbyist, studios..):

- Ron Fedkiw (Stanford)
- Robert Bridson (UBC)
- Peter Schroder(Caltech)
- cgtalk (forums)
- DreamWorks
- Pixar
- Disney
- Blue Sky

Online learning:

CG software:

Programming:

- Processing
- HTML5
- ...

Gallery/fun: