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Computer Animation Algorithms and Techniques

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Runge Kutta Integration: 2nd order. Aka Midpoint Method. For unknown function, f(t); known f '(t) ... Runge Kutta Integration: 4th order. For unknown function, ... – PowerPoint PPT presentation

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Title: Computer Animation Algorithms and Techniques


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