1. Mathematics in Animation
NOVEMBER

2. Introduction Simon Sherr Animation Director
Sr. Technical Animation Director
Games
EA Sports MMA
Madden NFL 09
NBA Street Homecourt
Marvel Nemesis
FIFA 2004/2005
Films
Lord of the Rings: Two Towers
Blade 2
Matrix 2/3
The One
Blue Crush
X-Men 2
Transformers
Jumper

3. Principals of Animation
Disney “Illusion of Life”
Squash and Stretch
Anticipation
Follow-through
Straight ahead and Pose to Pose
Slow in Slow out
Arcs
Secondary Action
Timing
Exaggeration
Solid Drawing
Appeal

4. Straight ahead and Pose to Pose
In Games:
Cycles
Linear Animation

5. Hierarchical State Machines
Visual Programming
Quick Iteration
No Syntax Errors
Quick Learning Curves
Less Technical
Operators and Functions
Input->output
Entry Conditions

6. Physics Principals Objects in Motion Stay in Motion Anticipation
Overlap and Follow-Through
Slow in Slow Out
Arcs
Secondary Action

7. The Math of Falling Movement is Constant Falling Parabolic Arcs
System of pendulums acting under physics
9.8 meters per second per second
Exaggeration
The physics of Bugs Bunny
Just a different parabola
Not 9.8

8. Realistic Parabolic Arc

9. Exaggerated Arc

10. Exaggerated Arcs

11. Quaternions and Games Ps3 and 360 Runtime rigs
Procedural Animation Blending

12. The Euler Problem
Infinity Cubed Times Six
Gimbal Lock
Blending

13. Quaternion Only 2 vector solutions
When displayed as deltas in Cartesian 3D space only 1 plausible solution
Procedural Blending Becomes Possible

14. Quaternion in Visual Space

15. Questions?