Math for TDs - Table of contents
v7, 11/6/09

Week 4: Geometry [for Modeling TDs]

4.1 Geometric primitives

4.1.1 Basic measurements

4.1.2 Tile patterns

4.1.3 Curves

4.1.4 Surfaces

4.1.5 Volumes

4.2 Spatial queries

4.2.1 Containment

4.2.2 Closest point

4.2.3 Ray intersection

4.3 Spatial interpolation

4.3.1 Triangle-based

4.3.2 Pixel-based

4.3.3 Cube-based

4.3.4 Scattered

4.4 Space partitioning

4.4.1 Point-based approaches

4.4.2 Plane-based techniques

4.4.3 Hierarchical schemes

Week 5: Lighting, Shading [for Rendering/Lighting TDs]

5.1 Parameter interpolation

5.1.1 Linear interpolation

5.1.2 Nonlinear interpolation

5.1.3 Multi-sample interpolation

5.1.4 Weighted interpolation

5.1.5 Rotation interpolation

5.2 Lighting and shading calculations

5.2.1 The standard lighting equation

5.2.2 Lighting-related vectors

5.2.3 Falloff

5.2.4 Anisotropic shading

5.3 Noise

5.3.1 fBM

5.3.2 Perlin noise

5.3.3 Cell noise

5.3.4 Wavelet noise

5.3.5 Curl noise

5.4 Misc. shading topics

5.4.1 Random numbers - spatial distributions

5.4.2 Low discrepancy sequences

5.4.3 Tiled shading

5.4.4 Spherical harmonics

5.4.5 Mapping

Week 6: Dynamics [for FX/CFX TDs]

6.1 Implicit surfaces

6.1.1 Isosurfaces

6.1.2 Level sets

6.1.3 Alpha shapes

6.2 Vector calculus

6.2.1 Vector-valued functions

6.2.2 div, grad, curl (and all that!)

6.2.3 line, surface and volume integrals

6.3 Differential equations, solvers

6.3.1 Recurrence relations

6.3.2 Difference equations

6.3.3 ODE

6.3.4 PDE

6.3.5 Special techniques

6.4 Misc. FX topics

6.4.1 Particle systems

6.4.2 Procedural patterns and shapes

6.4.3 Signal processing

6.4.4 Fracturing

6.4.5 Strands

6.4.6 Collision detection