player vs player collision

ellipsoid - ellipsoid collision is difficult. For your players, you could use bounding boxes instead of ellipsoids. Of three spheres that roughly approximate your ellipsoid and do sphere-sphere collision.

That is trivial to do, and in fact, the code is already there in the paper. Vertex-sphere is basically equivalent to doing a sphere with zero radius against a sphere. It's not hard to extrapolate the code and write a sphere-sphere algorithm, which will give you the contact point and the normal of collision.

To simplify, when you test a player (player A) against another (player B), you can consider player B as static to detect the time of collision of A against B. However, when computing the collision response (how va and vb changes after the collision), the velocity you will have to consider will be (va - vb), and compute the change of momentums on the two players. afaik, that's what Quake 3 does.

thanks for the reply oliii.I know there are a lot of articles on the net about sphere-to-sphere collision, but the part that confuses me is changing vector spaces. In this article, all points (basePoint, velocity, and the 3 triangle points) are scaled by eSpace before the collisionPoint is detected. When I test against a sphere, do I have to scale the sphere's position and radius as well?

That's probably overkill. The transform is needed for the ellipsoid but not the sphere.