Title: Computer Animation Algorithms and Techniques
1Computer AnimationAlgorithms and Techniques
Integration
2Integration
Given acceleration, compute velocity position
by integrating over time
3Projectile
given initial velocity under gravity
4Euler integration
For arbitrary function, f(t)
5Integration derivative field
For arbitrary function, f(t)
6Step size
7Numeric Integration Methods
(explicit or forward) Euler Integration 2nd order
Runga Kutta Integration (Midpoint Method) 4th
order Runga Kutta Integration Implicit (backward)
Euler Integration Semi-implicit Euler Integration
8Runge Kutta Integration 2nd order Aka Midpoint
Method
For unknown function, f(t) known f (t)
9Step size
Euler Integration
Midpoint Method
10Runge Kutta Integration 4th order
For unknown function, f(t) known f (t)
11Implicit Euler Integration
For arbitrary function, f(t), find next point
whose derivative updates last value to this
value required numeric method (e.g.
Newton-Raphson)
12Differential equation, initial boundary problem
(implicit/backward) Euler method
(explicit/forward) Euler method
e.g. linearize f and use Newton-Raphson
13Semi-Implicit Euler Integration
14Methods specific to update position from
acceleration
Heun Method Verlet Method Leapfrog Method
15Heun Method
16Verlet Method
17Leapfrog Method