# 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