Synthesis of Solid Models of Polyhedra from their Orthogonal Views using Logical Representations

In this paper a representational language of a logical kind which is expressive enough to model concepts of descriptive geometry is presented. The language is employed to produce solid models of polyhedra from representations of their orthogonal projections. The synthetic process has as its input well-formed expressions representing the geometrical entities and relations of bidimensional orthogonal views and employs expressions representing drafting concepts of descriptive geometry to produce expressions denoting the 3D objects contituting the final polyhedra. The production of 3D models of solid objects from their orthogonal views has a significant history within computer graphics and CAD. Most previous approaches are based on numerical algorithms modeling geometrical and topological constraints of the problem domain in a quantitative fashion. However, in this approach, geometrical objects are referred to through expressions of a declarative language, and the final object is produced through symbolic inference.