Semi-algebraic solids in 3-space: a survey of modelling schemes and implications for view graphs

Abstract

The formal description of the bounding surfaces of a solid in 3-space represents the input formula for a view (or aspect) graph algorithm (VGA). The design of solids in 3-space and algorithms for computing formal descriptions of the boundaries of such solids are being studied within the field of computer aided (geometric) design (CA(G)D). In this survey, we introduce a specialization hierarchy for the major surface classes in CA(G)D and VGA research, in which the bounding surfaces of semi-algebraic solids represent the most general class. We state upper bounds for the nodes in the view graph for the surface classes in this hierarchy. We also describe possible interactions between symbolic CA(G)D algorithms (like conversion algorithms between parametric and implicit surface representations and boundary-representation algorithms) and symbolic VGAs and the consequences for the efficiency of VGAs.