Computer Animation Algorithms and Techniques

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