Introduction to simulation.

Thoughts

• Went over various integration schemes; forward/implicit/symplectic Euler, Verlet, Runge-Kutta. Symplectic and Verlet are surprisingly simple and cheap, and I believe these are most commonly used in physics simulation for games. RK4 sounds very possible and more accurate if your derivative evaluation is cheap enough, though.
• Rigid bodies: actually just like particles, but with a rotation and angular momentum term as well as position and linear momentum. Still easy to take derivative of rotation with quaternions.
• Constraint based systems seem like the current vogue; the concept is very simple - when your step violates a constraint, project your state back into the valid configuration space. This means just moving out of collisions, moving to preserve length constraints, etc. I believe this makes an appearance in the paper I’ll be presenting next week.
• Cloth simulation can go for either integration of spring systems or length constraint based. The constraint based example was quite interesting, actually, as it seemed extremely stable. However, it lacked some friction and folding ability.
• Unified dynamics by making everything a set of particles was very smart, I will delve into this more when making my paper presentation.