[ODE] collision matrix

[Jaap Stolk]

On 4/22/06, Bram Stolk <bram at sara.nl> wrote:
> >There is a formula for finding the smallest distance between the two
> >(center) lines (and the points on the lines where the shortest
> >distance is. (this can even be done for any N-dimensions) If the
> >distance is less than the sum of the radius of both cylinders, and the
> >closest points are within the length of each cylinder, it's a hit.
> >for a capsule, check the distance from the the center line to the end
> >of the other cylinder.
>
> No, this is not a correct test.
>
> Just draw some scenarios on paper, and you will see why.
> There are so many cases where this is not true.
>
> E.g. two cylinders stacked on top of eachother have dist 0
> between center lines. Heck, a cylinder floating directly
> above another, a million miles away has 0 dist between
> center lines.
> Even if you take dist between linesections it does not hold.
>
> capsule vs capsule is very easy. cyl vs cyl is very hard.
>
> Also the sum of radii is bogus: just take the case where
> a cylinder is resting with its curved surface onto the
> cap of anoter cylinder.

I'm no expert on math, but I think it should work:

- calculate the points on the center lines where the center lines are
closed together.

- depending on whether those points are within or outside the
endpoints of the cylinders, choose form the following:
- cylinder - cylinder collision (use sum of radii)
- cylinder - cap collision (compare nearest point of cylinder-plane
intersect within radius)
- cap collision - cylinder (same as above)
- cap - cap collision (plane-plane intersect (result is a line) find
closest point between this line and each of the two center lines, and
again compare the distance with the radius of the cylinder)