Mathematics in Animation

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Presentation transcript:

Mathematics in Animation NOVEMBER 29 2010

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

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

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

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

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

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

Realistic Parabolic Arc

Exaggerated Arc

Exaggerated Arcs

Quaternions and Games Ps3 and 360 Runtime rigs Procedural Animation Blending

The Euler Problem Infinity Cubed Times Six Gimbal Lock Blending

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

Quaternion in Visual Space

Questions?