1. UNC Chapel Hill M. C. Lin Review Particle Dynamics (see transparencies in class)

2. UNC Chapel Hill M. C. Lin Disclaimer The following slides reuse materials from SIGGRAPH 2001 Course Notes on Physically-based Modeling (copyright  2001 by Andrew Witkin at Pixar).

3. UNC Chapel Hill M. C. Lin A Newtonian Particle

4. UNC Chapel Hill M. C. Lin Second Order Equations As discussed in the last lecture, we can transform a second order equation into a couple of first order equations.    as shown here.

5. UNC Chapel Hill M. C. Lin Phase (State) Space

6. UNC Chapel Hill M. C. Lin Particle Structure

7. UNC Chapel Hill M. C. Lin Solver Interface

8. UNC Chapel Hill M. C. Lin Particle Systems

9. UNC Chapel Hill M. C. Lin Overall Setup

10. UNC Chapel Hill M. C. Lin Derivatives Evaluation Loop

11. UNC Chapel Hill M. C. Lin Particle Systems with Forces

12. UNC Chapel Hill M. C. Lin Solving Particle System Dynamics

13. UNC Chapel Hill M. C. Lin Type of Forces

14. UNC Chapel Hill M. C. Lin Gravity

15. UNC Chapel Hill M. C. Lin Force Fields Magnetic Fields –the direction of the velocity, the direction of the magnetic field, and the resulting force are all perpendicular to each other. The charge of the particle determines the direction of the resulting force. Vortex (an approximation) –rotate around an axis of rotation  = magnitude/R tightness –need to specify center, magnitude, tightness –R is the distance from center of rotation Tornado –try a translation along the vortex axis that is also dependent on R, e.g. if Y is the axis of rotation, then

16. UNC Chapel Hill M. C. Lin Viscous Drag

17. UNC Chapel Hill M. C. Lin Spring Forces

18. UNC Chapel Hill M. C. Lin Collision and Response After applying forces, check for collisions or penetration If one has occurred, move particle to surface Apply resulting contact force (such as a bounce or dampened spring forces)

19. UNC Chapel Hill M. C. Lin Bouncing off the Wall

20. UNC Chapel Hill M. C. Lin Normal & Tangential Forces

21. UNC Chapel Hill M. C. Lin Collision Detection Collision!

22. UNC Chapel Hill M. C. Lin Collision Response (k r is the coefficient of restitution, 0  k r  1)

23. UNC Chapel Hill M. C. Lin Condition for Contact

24. UNC Chapel Hill M. C. Lin Contact Forces Friction: F f = -k f (-NF) v t F c = - F N = - (N F)F