1. Procedural Animation

2. Keyframe animation Start values End values time t Interpolation
Values at time t

3. Types of Keyframe Animation
curve interpolation
path following
forward and inverse kinematics
blend shapes
motion capture

4. Procedural animation
Initial conditions
starting values
start time
Model
constraints
rules
Increment
Updated values

5. Categories of Procedural Animation
gravity
springs
collision detection & response
rotational dynamics
physically based animation
flocking behavior
crowd behavior
prey-preditor model
walking
grasping and reaching
speech
personality
behavioral animation

6. Basic physcially based animation
state of the world
position
velocity
forces
acceleration
new velocity
f =Sum(fi)
new position

7. Gravity (earth)
a = -9.8 m/s
v = v + a*dt
p = p + v*dt

8. Gravitational Fields
f = G(m1*m2)/d2

9. Simple Spring
spring
let D = (P-Q)
L = |D|
P (moveable)
with mass m
f = ks * (L - Lrest)D/L
Q (fixed)
a = f/m
v = v + a*dt
p = p + v*dt

10. Works against velocity
Viscosity or Damping
Works against velocity
Velocity V
Damping force
f = - kd * V

11. V is rate of change of Length of spring
Simple Spring-Damper
spring
let D = (P-Q)
L = |D|
P (moveable)
with mass m
V is rate of change of Length of spring
Q (fixed)
f = (ks * (L - Lrest) - kd*V)*(D/L)

12. Simple Spring-Damper
spring
P (moveable)
with mass MP
Q (moveable)
with mass MQ
fP = - fQ

13. Simple collision response
kinematic response: negate horizontal component of velocity

14. Friction
static friction
f = kf*fn
dynamic friction
velocity ff g

15. Inclined ramp
velocity ff g