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Computer Animation Algorithms and Techniques

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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Computer Animation Algorithms and Techniques

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

  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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