Aspect graph generation for non-convex polyhedra from perspective projection view

Abstract

The aspect graph is basically a multiple-view representation of the designated three-dimensional (3D) object. In this paper, a complete algorithm is presented for constructing the aspect graph of general polyhedral objects from the perspective point of view. The aspect graph generation is based on a so-called visual event. These visual events will completely capture the way the appearance of an edge or a face can be occluded by other faces and edges in the model. All the visual events can be found for polyhedra as facial, EE, and EEE events. The facial event indicates the visibility transition of the faces, the EE event indicates the possible visibility variation of the occlusion of two edges, and the EEE event represents another visibility change, the consecutive occlusion among three edges. The system consists of the following five stages: (1) find the viewing cell for each planar face, EE event, and EEE event and then create the “parcellation graph”; (2) employ the parcellation graph to create a “face-level enumeration array” and “edge-level enumeration array”; (3) generate test points; (4) examine plausible cells that enclose a volume of viewing space; and (5) generate an explicit aspect graph structure. Finally, nine non-convex polyhedra are obtained in the experiments. The aspect graphs of these non-regular shaped objects can be easily generated by this system.