1. Procedural Animation

2. Broad Class Particle Systems (Reeves ‘83) Behavioral Animation (Reynolds ‘87) Intelligent Systems (game/strategy/AI) Physically Based Modeling (water, gravity) Input Driven (face animation) Algorithmic (e.g. Plant growth)

3. Particle/Behavior Examples Explosions, fireworks Waterfall, river, spray off waves Special effects e.g. lawnmower man Moving models: grass, hair Group behavior e.g. school of fish

4. Proc. Animation Types Type# of Elements Physics/ interaction Intelligence ParticlesmanyWith environment none FlockssomeEnvironment & members limited Autonomous Behavior fewlittlehigh

5. Input-Driven Speech phonemes drive facial animation (Kakumanu,2001) “Pizzerias are convenient for a quick lunch” Procedural Animation Type?

6. Properties of Particles Lifespan (birth/death) Position Velocity Shape Color Transparency

7. Particle Systems Assumptions: particles –Do not collide with each other –Do not cast shadows on other particles, just on environment –Do not reflect light; modeled as point light sources

8. Collision Avoidance Test for Collision with Bounding Sphere C P t V k s s = | C – P | k = (C – P) V/|V| t = sqrt( s 2 – k 2 ) If ( t < radius ), penetration of bounding sphere occurs on current path radius

9. Collision Avoidance C P V B r r t s k r 2 = s 2 + t 2 k = sqrt( |C – P| 2 – r 2 ) k 2 = s 2 + (|C-P| - t) 2 k 2 = r 2 – t 2 + (|C-P| - t) 2 k 2 = r 2 – t 2 + |C-P| 2 – 2|C-P|t + t 2 t = (k 2 – r 2 - |C-P| 2 )/(-2|C-P|) s = sqrt(r 2 – t 2 ) Right triangles (hypotenuse last): 1. s, t, r 2. k, r, |C-P| 3. (|C-P|-t),s,k Solve for t substitute Expand

10. New Trajectory C P V B r r t s k t = (k 2 – r 2 - |C-P| 2 )/(-2|C-P|) s = sqrt(r 2 – t 2 ) U = (C – P)/ (|C – P|) W = ((UxV) x U)/ |(UxV) x U| U W B = P + (|C-P| -t)U + sW

11. Environment Physics/gravity Obstacles Constrained spawning area

12. Extras Particle-particle interaction Spawning new generations (e.g. 2nd stage fireworks)