What's the basic ideas of *continuous physic simulation* like box2d/bullet3d?

Question

Traditional physics simulation in games or graphics industry was basically discrete. But engines nowadays such as box2d or bullet3d implement continuous physics simulation. I know basic principles of discrete simulation, but I have no idea about continuous simulation. That's magical to me, and using magic is hard and dangerous. So I want to make the magic into tools by understanding them.

So I want to know: (1) What are the basic ideas and implementation principles of these continuous physics simulations? (2) Could the idea be generalized to other kind of discrete simulation? Please let me understand this!

Subgenus

Answer 1

I know only what I've read in this document, which certainly has better information and better references than are worth simply repeating here.

Nonetheless, it sounds like the collision detection is what's continuous. Consider a bullet (coincidence?). If you simulate it with ∆t = 1/30 s, there's a pretty high probability that it'll be 5m in front of you at one timestep and 5m behind you at the next. From what I understand, a continuous physics engine would treat the bullet as a ray which intersects me precisely at the time that I die. It sounds like this method solves directly for when and where collisions will occur. I suspect the algebra for rotating and translating bodies gets complex, but if you really want to explore that, there seem to be some PhD theses referenced.

I hope that's not too obvious and condescending, but the document looks to have the relevant references. Good luck!

Yard