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Computer Animation Algorithms and Techniques

Computer Animation Algorithms and Techniques. Physically Based Animation. a. f. v’. a. Physics Review: force, mass, acceleration velocity, position. m. v. v ave. Physics Review: Gravity. Static friction. Kinetic friction. Viscosity for small objects No turbulence. For sphere.

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Computer Animation Algorithms and Techniques

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  1. Computer AnimationAlgorithms and Techniques Physically Based Animation

  2. a f v’ a Physics Review: force, mass, acceleration velocity, position m v vave

  3. Physics Review: Gravity

  4. Static friction Kinetic friction Viscosity for small objects No turbulence For sphere Physics Review: Other forces

  5. Physics Review: Spring-damper Hooke’s Law

  6. Physics Review: Momentum conservation of momentum (mv) In a closed system, momentum is conserved After collision has same momentum as before collision

  7. Elastic Collisions No energy lost (e.g. deformations, heat)

  8. Elastic Collisions & Kinetic Energy As in all collisions: momentum is conserved In elastic collisions, kinetic energy is also conserved Solve for velocities

  9. Inelastic Collisions Kinetic energy is NOT conserved

  10. Inelastic Collisions Kinetic energy lost to deformation and heat Momentum is conserved Coefficient of restitution ratio of velocities before and after collision

  11. Center of Mass

  12. Physics Review Linear v. angular terms Angular Rotation, orientation rotational (angular) velocity rotational (angular) acceleration Inertia tensor Torque Angular momentum Linear postion velocity acceleration mass Force momentum

  13. Change in point due to rotation - Angular velocity On-axis or off axis rotation Angular velocity is the same

  14. Delta-orientation due to rotation

  15. Change to a point on rotating object

  16. Physics Review: Angular Stuff r F r

  17. Angular Momentum

  18. Inertia Tensor Aka Angular mass

  19. Inertia Tensor of particles Discrete version For particle collection

  20. Standard Inertia Tensors Symmetric wrt axes Cuboid Sphere

  21. Inertia Tensor transformations

  22. The Equations F r Object attributes M, Iobject-1 If using rotation matrix, will need to orthonormalize updated rotation matrix

  23. Springs Flexible objects Cloth Virtual springs Proportional derivative controllers (PDCs)

  24. Spring-mass-damper system f -f

  25. Spring-mass system V3 E23 E31 V2 V1 E12 Force

  26. “Virtual” edge springs system

  27. Angular springs Linear spring between vertices Dihedral angular spring

  28. Spring mesh Each vertex is a point mass Each edge is a spring-damper Diagonal springs for rigidity Angular springs connect every other mass point Global forces: gravity, wind

  29. Virtual springs – soft constraints

  30. Proportional (Derivative) Controllers e.g., particle reacts to other forces while trying to maintain position on curve – virtual spring

  31. Particle systems Lots of small particles - local rules of behavior Create ‘emergent’ element Particles: Do collide with the environment Do not collide with other partcles Do not cast shadows on other particles Might cast shadows on environment Do not reflect light - usually emit it

  32. Particle system Collides with environment but not other particles Particle’s midlife with modified color and shading Particle’s demise, based on constrained and randomized life span Particle’s birth: constrained and time with initial color and shading (also randomized) source

  33. Particle system implementation • STEPS • for each particle • if dead, reallocate and assign new attributes • animate particle, modify attributes • render particles Use constrained randomization to keep control of the simulation while adding interest to the visuals

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