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acceleration algorithm Andrew Witkin angular velocity Apple Computer applied force approximation axis behavior block body space bounding boxes calculate Carnegie Mellon University center of mass colliding contact collision detection Computer Graphics constant constrained particle constraint force contact forces contact point damping define derivative describe di(to diagonal differential equation dst++ dydt dynamics energy function Euler step Euler's method evaluate expression external force Figure for(int force accumulator force acting force objects global gradient h(to Ibody implement implicit impulse inertia tensor inter-penetration interaction interval iteration ith particle mass point Michael Kass midpoint method numerical ODE solver pa(t pa(to particle system Pb(t Pb(to polyhedra position problem quadratic quadratic programming quaternion represent resting contact rigid body rotation matrix routine scalar separating plane SIGGRAPH simply simulation solve spring stepsize stretched energy term torque triple update variables vertex/face contacts world space y'th contact ydot++ zero