As a basis for treating geometrical similarities of 3-D objects, an idea of a new data structure called "two layer structure with convex components" for representing polyhedra is presented. The two layer structure, which can be constructed uniquely for a polyhedron, consists of convex components separated into two layers, i.e., the first layer includes only positive convex components to be added and the second layer represents negative convex components to be subtracted from positive ones. The procedure for constructing the two layer structure consists of the following two processes. (1) Forward process: A concave polyhedron is decomposed and represented as a hierarchical tree structure with convex components. (2) Backward process: Components belonging to leaf nodes of the tree structure are put into the two layer structure according to the level of the node. The components are removed from the original polyhedron after processing each leaf node of the tree structure. These procedures are repeated to the modified object until the processes reach to the root node. The two layer structure can be applied for extracting features of polyhedra such as protrusions, holes and pockets, and comparing 3-D objects.
