"Trevor G Quayle" <Tin### [at] hotmailcom> wrote:
> "Lars R." <rou### [at] gmxnet> wrote:
> > I wrote a C++ program that generates the scene you see in the attached
> > image. (40k non-intersecting spheres)
> >
> > Now I'd like to change it to use many,many small cubes (randomly
> > rotated, of course), so I need an intersection formula for cubes.
> >
> > I tried something like this: If one of the 8 corners of a cube is inside
> > the other one than the cubes intersect:
> >
> > |  for corner = cubeA.corner0 … cubeA.corner7:
> > |     if( corner is_inside_of cubeB ) return true;
> > |
> > |  for corner = cubeB.corner0 … cubeB.corner7:
> > |     if( corner is_inside_of cubeA ) return true;
> >
> > But it is possible that 2 cubes intersects even if none of the corners
> > is inside of the other cube. :-(
> >
> > Has anyone a better formula for me?
> >
> >      Lars R.
>
> I don't have the maths for you but the general concept is this:
>
> When testing for the intersection of spheres, you are really testing if the
> centers of the spheres are at least 'x' distance from each other where 'x' = the
> sum of the two radii.  Now you can extend this to cubes, but the difficulty is
> deterning the 'x' value as it is not constant.
>
> You need to:
> 1) determine the direction vector between the two cubes
> 2) determine the local rotations of the cubes relative to the direction vector
> from 1)
> 3) determine the distances to the surfaces of the two cubes from their centers
> along that direction vector.
> 4) ensure the sum of these two lengths is less than the total distance between
> the centers.
>
> Yes it's that simple!
>
> -tgq

I have had some more thought to this, and it isn't entirely true.  I'll have to
put some more think into it.

(The simple comment was intended as a joke, but turns out even more so...)

-tgq

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