Based on loop chain

a fast algorithm is presented for decomposing arbitrary polyhedron into convex polyhedrons without adding new vertexes

in which the final number of convex polyhedrons is close to the least. A loop is consist of several vertices that start from one vertex go to next adjacent vertex can come back this vertex

all vertices in a loop is consist of a partition plane. The least perimeter loop chain is selected from all the loops consisted of edges and diagonal edges of the polyhedron

and decomposes the polyhedron with a series of planes consisted of all edges of the loop. Experiments show that this method can decomposing arbitrary polyhedron into the least number convex polyhedrons without adding new vertexes

can process most kinds of polyhedrons (e.g. a polyhedron with a inner hole)

and has low cost in calculation. The algorithm of convex decomposing 3D objects has been a research direction of computer geometry for a period and is widely used in fields of pattern identifying

animation and CAD.