c++ - Decomposing a concave mesh into a set of convex meshes

I'd like to be able to decompose a concave mesh into a set of convex meshes for 2 reasons:

1. Transparent rendering


2. Physics shapes

Is there an algorithm that takes a set of triangles (concave) as input and outputs a number of sets of triangles (convex)? I'd like it to not fill in the holes between parts of the original mesh.

I've already come across a small idea: find all the concave edges, and split the meshes along the edge loops. Am I on the right track? How could I implement this?