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Computer Animation Algorithms and Techniques

Explore physics simulations in animation, including rigid body dynamics, particle systems, and cloth simulations. Learn about forces, motion equations, collision detection, and response algorithms. Implement advanced techniques like constrained dynamics and energy minimization for realistic animations.

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Computer Animation Algorithms and Techniques

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  1. Computer AnimationAlgorithms and Techniques Physically Based Animation

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

  3. Physics Review: Gravity

  4. Physics Review: Spring-damper

  5. Physics Review: Momentum conservation of momentum (mv)

  6. Physics Review: Linear v. angular Linear postion velocity acceleration mass force momentum Angular rotation rotational velocity rotational acceleration moment of inertia torque angular momentum

  7. Spring-mass-damper system Topological springs: each edge of object Cross springs: keep stable Angular springs: maintain angle Virtual springs (‘soft’ constraints) Proportional derivative controllers (PDCs)

  8. Useful in modeling: Flexible objects Cloth, flags, clothes Enforcing ‘soft’ constraints while reacting to outside forces, try to maintain a distance or keep in contact

  9. Spring-mass-damper system

  10. Spring-mass-damper system

  11. Spring-mass-damper system

  12. Angular spring

  13. Particle systems http://www.vecpix.com/tutorials/3dstudio/sm003.php

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

  15. Particle system

  16. Particle system implementation add new particles assign attributes to particles deallocate any dead particles animate existing particles, modify attributes render particles

  17. Particle systems http://www.videotutorialsrock.com/opengl_tutorial/particle_system/home.php

  18. Particle systems http://www.cs.sun.ac.za/~lvzijl/courses/rw778/grafika/OpenGLtuts/Big/graphicsnotes018.html

  19. Rigid body simulation Bodies in free fall and under collisions Orientation and rotational movement Collision detection & impulse force of collision Collision response Numerical approximation Equations of motion Center of mass & Mass distribution Forces & torques Momentum & Inertia Tensor

  20. Rigid body simulation

  21. Integration

  22. Gravity

  23. (Explicit/Forward) Euler integration

  24. Step size explicit Euler integration dx = 0.2 dx = 5.0

  25. Step size explicit Euler integration dx = 2.0 midpoint method dx = 2.0

  26. Rotational velocity identical rotational velocity a) on-axis b) off-axis also has (instantaneous) linear velocity

  27. Axis of rotation

  28. Collision detection Particle-plane collision Testing polyhedra Collision response kinematic response penalty method Impulse force of collision Constant contact Friction Resting Contact Handling contact

  29. Collision detection: point-plane

  30. Collision response: kinematic

  31. Collision response: damped

  32. Collision response: penalty

  33. Collision response: penalty

  34. Collision detection: polyhedra

  35. Collision detection: swept volume

  36. Collision detection: time of impact

  37. Coefficient of restitution

  38. Impulse response

  39. Friction

  40. Resting contact

  41. Constrained dynamics Forces applied to linked appendages external forces forces applied at joints Forward dynamics apply (linear or rotational) force at joints propagate force (and reaction to it) throughout linkage Inverse dynamics from desired motion, determine joint forces

  42. Reaction to external force component reacts to force applied force from component outward, re-establish distance constraints

  43. Dynamics of Linked Hierarchies Constrained dynamics The Featherstone equations propagate forces along linkages

  44. Forward dynamics Torque at ui

  45. Cloth http://cg.in.tu-clausthal.de/publications.shtml From flags to curtains to clothes Flexible, thin material Self collisions as well as collisions with environment

  46. Cloth High-level: model folds directly catenary curve between support points Low-level: thin sheet of geometry collision detection & response Lower-level: model internal structure warp and weft threads

  47. Cloth - model physics Sheet of geometric elements (triangles) mass-spring-damper system finite element method Collision detection and response Method of numerical integration: accuracy v. efficiency Super-elasticity: how ‘stretchy’

  48. Cloth Baraff, D. and Witkin, A. 1998. Large steps in cloth simulation. In Proceedings of the 25th Annual Conference on Computer Graphics and interactive Techniques SIGGRAPH '98. ACM, New York, NY, 43-54.

  49. Cloth Huamin Wang, Ravi Ramamoorthi, James O'Brien Data-Driven Elastic Models for Cloth: Modeling and Measurement SIGGRAPH 2011

  50. Enforcing Soft and Hard Constraints Energy minimization Space-time constraints

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