Let's say I have a upright capsule shape (swept sphere) that I would like to cast it along a velocity vector. I would like to be able to find the point of contact and a surface normal for any convex shapes it would intersect along this path. I would also like to find the distance the swept caspule traveled to the point of first contact. Heres a quick diagram of a capsule being casted against a large convex polyhedra (only one face is drawn) What kind of algorithm or process could do this? I assume it would be similar to a sphere-cast, but i can't find much on that either.