Procedural Animation

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)

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

Proc. Animation Types

Type # of Elements

Physics/interaction

Intelligence

Particles many Withenvironment

none

Flocks some Environment & members

limited

Autonomous Behavior

few little high

Input-DrivenSpeech phonemes drive facial animation (Kakumanu,2001)

“Pizzerias are convenient for a quick lunch”

Procedural Animation Type?

Properties of Particles

• Lifespan (birth/death)

• Position

• Velocity

• Shape• Color• Transparency

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

Collision Avoidance

Test for Collision with Bounding Sphere

C

P

t

V

k

s

s = | C – P |

k = (C – P) V/|V|

t = sqrt( s2 – k2 )

If ( t < radius ), penetration of bounding sphere occurs on current path

radius

Collision Avoidance

C

P

V

B

rr

tsk

r2 = s2 + t2

k = sqrt( |C – P|2 – r2 )

k2 = s2 + (|C-P| - t)2

k2 = r2 – t2 + (|C-P| - t)2

k2 = r2 – t2 + |C-P|2 – 2|C-P|t + t2

t = (k2 – r2 - |C-P|2)/(-2|C-P|)

s = sqrt(r2 – t2)

Right triangles (hypotenuse last):

1. s, t, r

2. k, r, |C-P|

3. (|C-P|-t),s,k

Solve for tsubstitute

Expand

New Trajectory

C

P

V

B

rr

tsk

t = (k2 – r2 - |C-P|2)/(-2|C-P|)

s = sqrt(r2 – t2)

U = (C – P)/ (|C – P|)

W = ((UxV) x U)/ |(UxV) x U|

U

W

B = P + (|C-P| -t)U + sW

Environment

• Physics/gravity

• Obstacles

• Constrained spawning area

Extras

• Particle-particle interaction

• Spawning new generations (e.g. 2nd stage fireworks)