# Outline

• Introduction

• A variety of examples

# Introduction

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

# Examples

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 - particle systems

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

# Navier-Stokes equations - fluid simulation

N-S equations are a staple in fluid calculations..

# Voronoi polygons/polyhedra - fracturing

The Voronoi diagram is a very important and useful spatial data structure..

# Perlin noise - water etc.

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.

# Splines - smooth geometry

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

# Subdivision surfaces - easy models

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

# Monte Carlo integration: global illumination

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.

# Cloth simulation - numerical integration

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

# Char setup (rigging) - animation

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

# References

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