Re: [Algorithms] Kinematic Collision

[<Pau...@sc...>]

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> ...but you are talking about a physics engine here. I was only talking 
about
> an old-style "character controller", a.k.a. collide-and-slide, à la Paul
> Nettle / Quake / etc. Typical "modern" physics engines certainly need
> penetration vectors. Character controllers, not necessarily - you can go 
a
> long way without.

Ahhh, yes, you might get away with a lot more with a simple character 
controller. As long as nothing is allowed to 'push' the character into the 
ground or weigh it down, that is! :)

> Can you give more details here? I think you can find "a" penetration
> vector -in the direction of motion-, yes, but it is vastly different 
from
> "the" penetration vector, a.k.a. MTD, which can be in a completely 
different
> direction. I don't think I know a way to compute both with the same 
piece of
> code.

Ok, so if we're talking about a generic convex linear cast here, we can do 
the ray intersection (where the ray is the delta velocity vector of the 
two objects) against the minkowski difference of the two shapes (which is 
now static) iteratively as long as we have a utility function that will 
give us the closest point on the MD and the normal at that point. This 
information is actually already giving us penetration info if we start 
initially penetrated. 

Basically, you iterate (starting with the ray start position) asking the 
system for the closest point on the MD to the current ray pos and the 
normal. Then you intersect the ray with that normal and carry on. It 
usually converges very quickly, especially for poly objects and you get 
the TOI and the penetration info in one, should there be a TOI of 0. You 
can even use this to handle objects that rotate as well with slight 
modification of the algorithm.

This is gino van den bergen's algorithm btw, where he uses GJK for the 
utility function - but we don't have to use GJK, we can use any custom 
written algorithm. So for two spheres, you just need closest point on 
sphere to given point, which is easy to write, or for triangle vs sphere 
you just need a distance to triangle function...

Cheers, Paul.
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