Week 6: Dynamics [for FX/CFX TDs]

6.1 Implicit surfaces

6.1.1 Isosurfaces

blobby functions

 - Blinn, Wyvill etc.

blobbies based on lines

Marching Cubes

6.1.2 Level sets

SD fns

Surface generation

6.1.3 Alpha shapes

Polygons as generators

* extns to polys (what about polyhedra!?)

6.2 Vector calculus

6.2.1 Vector-valued functions

* fns
* fields

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

div

grad

curl

6.2.3 line, surface and volume integrals

LIC

Discrete integration over a surface

DDG

??

6.3 Differential equations, solvers

6.3.1 Recurrence relations

Fibonacci sequence

Chaos iterations

6.3.2 Difference equations

central, fwd, backward differences

FDM/FDE

6.3.3 ODE

Basics

come from physical systems, eg. oscillations of a mass-spring system.., ie SHM

Numerical solution

Verlet integration

6.3.4 PDE

Basics

Numerical solution

6.3.5 Special techniques

implicit vs explicit solvers

Stam - large steps

CGM (conj gradient)

6.4 Misc. FX topics

6.4.1 Particle systems

classical particle systems

SPH

6.4.2 Procedural patterns and shapes

Patterns from randomness

* rotate slightly a field of rand #s, to get a pattern
* Truchet, tern. Truchet!

Non-linear dynamics

strange attractors

Iterated Function Systems (IFS)

collage theorem, ferns, conn. to L-systems
Again, repeat a generation rule.. 
Great for image compression too (Barnsley's stuff)..

Generative modeling

* L-systems
* phyllotaxis

1D CA

2D CA

Close packing

* circle packing (start w/ Apollonius and Farey fractals)
* sphere packing - FCC, BCC, more

Link to put up:http://www.rdmag.com/News/2009/08/General-Sciences-Princeton-pair-sets-world-record-in-packing-puzzle/

Crowd systems

boids :) [see Shiffman, Craig's cwr writeup ppr etc]

6.4.3 Signal processing

1D FFT

2D FFT

* incl. ocean waves

6.4.4 Fracturing

Mention fracture-fx.com :)

CSG for fracture

* esp. intersection, difference
* 3D CA for hollow Vor polyhedra..

Voronoi-based techniques

* edge cracking
* stamping patterns

Surface-cutting based on fields

Volumetric fracture

* tet-based

6.4.5 Strands

Featherstone algorithm

* also look up Sunil's and Fedkiw's work.. [possibly more h4 subcategs]

6.4.6 Collision detection

Canny-Lin

GJK algorithm