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# Computer Animation Algorithms and Techniques - PowerPoint PPT Presentation

Computer Animation Algorithms and Techniques. Integration. Integration. Given acceleration, compute velocity & position by integrating over time. Projectile. given initial velocity under gravity. Euler integration. For arbitrary function, f(t). Integration – derivative field.

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## PowerPoint Slideshow about 'Computer Animation Algorithms and Techniques' - habib

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Computer AnimationAlgorithms and Techniques

Integration

Given acceleration, compute velocity & position by integrating over time

given initial velocity under gravity

For arbitrary function, f(t)

For arbitrary function, f(t)

(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

Runge Kutta Integration: 2nd order

Aka Midpoint Method

For unknown function, f(t); known f ’(t)

Euler Integration

Midpoint Method

Runge Kutta Integration: 4th order

For unknown function, f(t); known f ’(t)

For arbitrary function, f(t), find next point whose derivative updates last value to this value: required numeric method (e.g. Newton-Raphson)

Search for point such that negative of tangent points back at original point

(implicit/backward)

Euler method

(explicit/forward)

Euler method

e.g. linearize f’ and use Newton-Raphson

Heun Method

Verlet Method

Leapfrog Method