Variations in solids : a declarative treatment

Abstract: "Underlying the notions of variational geometry, design prototypes, features, and representation of assemblies seems to be a common concept of variations. This paper develops the core of a monontonically declarative system for variations on solids. It introduces a set of language constructs that are the basis for ASCEND, an object oriented equation solving language. It presents equations for representing certain spatial relationships between primitive geometric elements. Using plex grammar notation it develops a set of Euler operators that are monotonic in the strict sense required by the ASCEND language.These operators are collectively shown to generate representations for all plane models of 2-manifold objects and to generate only such representations. Finally it presents the core of a system for variations using the ASCEND language to implement both models and the new Euler operators."