Sorry for the late answer, yes the polyhedra are convex

Sorry for the late answer, yes the polyhedra are convex

Then it's much easier: there are libraries that convert between vertex representations and hyperplane representations (and back), you just need to convert both polyhedra to hyperplane (just planes actually in 3d), take the union of these sets planes and convert it to vertex representation.

If you want a more direct approach, in 3d, you can take one polyhedron, and for each triangle, generate a plane using the triangle normal and one of it's vertices. Take these planes, and intersect it with the other polyhedron, keeping only the inside half space. Specifically, throw away all triangles whose vertices are all in the outside half space, and keep all the triangles, whose vertices are in the inside half space. Then for all the triangles that cross the plane, clip them to the inside half space. The new vertices that result from the clipped edges will now form a convex polygon embedded within the the intersection plane. Triangulate this. Repeat this for each triangle/plane of the first polyhedron, and you're done!

Thanks for the reply - I will try to implement your algorithm

Hello Crowley99,
do you have some links that can help us implement one of the two given algorithms?
Regards,
Dimitris

Hello Dimitris

If the volumes are convex, it's possible to use the Séparating Axis Theorem (SAT) method. (http://en.wikipedia.org/wiki/Hyperplane_separation_theorem)
This method is well documented. I can give you my implementation "as an example" if you wish (for what it's worth of course )

What's more with this method you can get the penetration depth if you need it.

Nico

If it was calculating the intersection volume you meant (I'm not clear whether you meant this or just how far they 'poke' each other) it is probably best to google for CSG of convex hulls.

http://en.wikipedia.org/wiki/Constructive_solid_geometry

'QHull' is a library that may have an implementation to look at I believe, and also probably there is one in Dave Eberly's Geometric Tools http://www.geometrictools.com/ (he's a great egghead and has got libraries for everything lol, he wrote the NDL / gamebryo stuff).

In games the convex hulls are often known as 'brushes' and are widely used in quake derived stuff and unreal, if you have a look at dealing with their maps, or gtkradiant source you might get some ideas.

If you can valmorphanize your polygon representation into a set of planes defining the sides of a brush, you can then add planes (or their opposites) from one brush to another to split it up and do CSG jiggery pokery. Then you can use a routine to rebuild the brush from a set of planes back into a set of polygons (using e.g. the intersection of 3 planes to form a vertex) and chuck out any irrelevant planes / polys that have been clipped out by inserted planes. That's how I did it anyway.