Three dimensional surface representation by polygonal volume primitives

Abstract

A new representation method of three dimensional surface is proposed to represent general objects. The method is based on the cuberille model of three dimensional image space. We devised a small set of polygonal volume primitives (PVP) with regular shape based on a cuberille configuration of the surface. We classified 256 possible cuberille configurations into 21 cases and in order to represent them with a few number of primitive volumes, 5 basic PVPs are selected. One of the 5 basic PVPs with a pose is locared at each cuberille of a 3-D surface according to both the cube configuration and normal direction. After the surface is tiled with PVPs, the polygons description which came mainly from the primary face of PVPs is generated. In order to obtain the compact representation, a multiresolution surface modeling method based on the PVP modeling is proposed. One of the 5 basic PVPs posed distinctively is located with bintree structure hierarchically at each duberille of the surface according to the cube configuration and normal direction where the size of a PVP varies with the level of bintree. Several examples of geometrical objects, tomography data, and range images are shown.