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

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

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

Particle Structure UNC Chapel Hill M. C. Lin

Solver Interface UNC Chapel Hill M. C. Lin

Particle Systems UNC Chapel Hill M. C. Lin

Overall Setup UNC Chapel Hill M. C. Lin

Derivatives Evaluation Loop UNC Chapel Hill M. C. Lin

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

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

Type of Forces UNC Chapel Hill M. C. Lin

Gravity UNC Chapel Hill M. C. Lin

Force Fields Magnetic Fields Vortex (an approximation) Tornado 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 Q = magnitude/Rtightness 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 UNC Chapel Hill M. C. Lin

Viscous Drag UNC Chapel Hill M. C. Lin

Spring Forces 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) UNC Chapel Hill M. C. Lin

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

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

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

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

Condition for Contact UNC Chapel Hill M. C. Lin

Contact Forces Fc = - FN = - (N•F)F Friction: Ff = -kf (-N•F) vt UNC Chapel Hill M. C. Lin