Language of topologically valid bounding manifolds

Abstract

The kernel of a boundary-based modelling system, rooted in a formal graph language of topologically valid representations of rigid solids as connected 2-manifolds, is discussed. The representation grammar includes a syntax of face-based Euler operators and their embeddings in manifold models. Since inclusion of both elements provides necessary and sufficient conditions for solidity, topological validity of the representation scheme can be proven as follows. First the start graph is shown to be representative of a solid, then productions in the grammar are shown to be both complete and closed in the solids.