Physically Based Simulation - Constrained Dynamics & Contact Force Computation
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Physically Based Simulation - Constrained Dynamics & Contact Force Computation
- 1. KGDC 2003 1 Physically Based Simulation Physically Based Simulation Constrained Dynamics & Contact Force Computation 이웅수 peras@rigorware.com Rigorware Corp.
- 2. KGDC 2003 2 Physically Based Simulation The Elements of Simulator Broad Phase Collision Detection Narrow Phase Collision Detection Contact Determination Contact Analysis Collision Solver Time Control Motion Solver Constraint Solver Mass Property Analysis
- 3. KGDC 2003 3 Physically Based Simulation What Are Constraints? Inequality(≥) ConstraintEquality(=) Constraint
- 4. KGDC 2003 4 Physically Based Simulation General Constraints Prismatic Joint
- 5. KGDC 2003 5 Physically Based Simulation General Constraints Spherical Joint
- 6. KGDC 2003 6 Physically Based Simulation General Constraints Revolute Joint
- 7. KGDC 2003 7 Physically Based Simulation Contact
- 8. KGDC 2003 8 Physically Based Simulation Dynamic States T = IαF = ma힘 / 회전력Force / Torque αa가속도 / 각가속도acceleration L = IwP = mv운동량 / 각운동량momentum wv속도 / 각속도velocity Im질량 / 관성텐서mass / Inertia Tensor AngularLinear술어Terminology
- 9. KGDC 2003 9 Physically Based Simulation A Single Geometrically Constrained Particle [ ] 1. Implicit ( ) 0 2. Parametric cos ,sin 0 legal position 0 legal velocity 0 legal acceleration C r r C C C θ θ = − = = = = = q q q
- 10. KGDC 2003 10 Physically Based Simulation Point On Circle 1 ( ) ( 1) 0 2 0 ( ) 0 ( : Constraint Force) 0, C C C C m C m m ∧ ∧ ∧ ∧ = − = ∂ = = = ∂ = + = + = + = + = = − − q q q q q q q q q q q f f q f f f q q q f q f q q q
- 11. KGDC 2003 11 Physically Based Simulation The Principle of Virtual Work Translational Kinetic Energy , 2 0, | 0 m T T m m λ λ ∧ ∧ ∧ = = = + = ∀ = = − − = q q q q f q f q f q q q q f q f q q q q q
- 12. KGDC 2003 12 Physically Based Simulation Drift and Feedback Spring & Damping s dC k C k C= − −
- 13. KGDC 2003 13 Physically Based Simulation Avoiding Penetrations The normal distance function
- 14. KGDC 2003 14 Physically Based Simulation The Contact Force Total contact force = Normal force + Friction force The normal force The normal force is repulsive
- 15. KGDC 2003 15 Physically Based Simulation LCP
- 16. KGDC 2003 16 Physically Based Simulation LCP The complementary condition
- 17. KGDC 2003 17 Physically Based Simulation The Notation
- 18. KGDC 2003 18 Physically Based Simulation The Linear Dependence The contact point position The contact point velocity The contact point acceleration
- 19. KGDC 2003 19 Physically Based Simulation The Linear Dependence The angular momentum The angular velocity The angular acceleration
- 20. KGDC 2003 20 Physically Based Simulation The Linear Dependence
- 21. KGDC 2003 21 Physically Based Simulation The Linear Dependence
- 22. KGDC 2003 22 Physically Based Simulation The Linear Dependence
- 23. KGDC 2003 23 Physically Based Simulation The Linear Dependence and
- 24. KGDC 2003 24 Physically Based Simulation Appendix – Euler Angles Euler angles are Non-commutative
- 25. KGDC 2003 25 Physically Based Simulation Appendix Vertex, Edge, Face 6 cases
- 26. KGDC 2003 26 Physically Based Simulation Note