Creating the Perspective Projection Aspect Graph of Polyhedral Objects

Abstract

An algorithm is presented for constructing the perspective projection aspect graph of polyhedra. The first phase determines the set of surfaces involved in the parcellation of viewing space around the object. Three types of surfaces are involved: object planes, in which the faces of the object lie, auxiliary planes, defined by the visual interaction of edge-vertex pairs, and auxiliary quadric surfaces, defined by the visual interaction of edge triplets. Auxiliary planes and surfaces in a sense enumerate the potential self-occlusions of the object. A list is constructed for each type of surface. Next the algorithm constructs the geometric incidence lattice representing the arrangement of object planes, and distinguishes each 3-face (node) as representing either object or viewing space. The auxiliary planes and surfaces are then added to the lattice. Each 3-face (node) in the lattice has visibility attributes which identify the potentially visible object features from viewpoints within it. These attributes are updated throughout the process of building the lattice. Finally, the lattice is traversed to make a final update of the visibility attributes and merge neighboring 3-faces which have the same visible features. The resulting structure represents the perspective projection aspect graph.