Procedural Animation

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
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
s C P k (C P) V/V t sqrt( s2
k2 ) If ( t lt radius ), penetration of bounding
sphere occurs on current path
V
t
C
k
s
radius
P
Test for Collision with Bounding Sphere
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Collision Avoidance
V
r2 s2 t2 k sqrt( C P2 r2 ) k2 s2
(C-P - t)2 k2 r2 t2 (C-P - t)2 k2 r2
t2 C-P2 2C-Pt t2 t (k2 r2 -
C-P2)/(-2C-P) s sqrt(r2 t2)
B
r
C
r
s
k
t
Solve for t
P
substitute

• Right triangles (hypotenuse last)
• s, t, r
• k, r, C-P
• (C-P-t),s,k

Expand
10
New Trajectory
V
t (k2 r2 - C-P2)/(-2C-P) s sqrt(r2
t2) U (C P)/ (C P) W ((UxV) x U)/
(UxV) x U
B
U
r
C
r
W
s
k
t
P
B P (C-P -t)U sW
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Environment

• Physics/gravity
• Obstacles
• Constrained spawning area

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Extras

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