What are the main ideas * of continuous physical modeling *, for example box2d / bullet3d?

Question

Traditional physical simulation in games or the graphics industry was mostly discrete. But now engines, such as box2d or bullet3d, implement continuous physical simulation. I know the basic principles of discrete modeling, but I have no idea about continuous modeling. It is magical to me and using magic is difficult and dangerous. Therefore, I want to make magic tools by understanding them.

So, I want to know: (1) What are the main ideas and principles for implementing these continuous physical simulations? (2) Is it possible to generalize the idea to another type of discrete modeling? Please let me know this!

Answer 1

I only know what I read in this document , which certainly has better information and better links than just repeating here.

However, it seems that collision detection is continuous. Consider a bullet (coincidence?). If you simulate it with Δt = 1/30 s, there is a rather high probability that it will be 5 meters ahead of you one time out and 5 meters ahead of you next time. As far as I understand, a continuous physics engine will consider a bullet as a beam that crosses me exactly at the time when I die. This method appears to directly decide when and where the collision will occur. I suspect that algebra for rotating and translation bodies is becoming complicated, but if you really want to study it, then, apparently, there are some candidate dissertations that are referenced.

I hope this is not too obvious and condescending, but there are relevant links in the document. Good luck