Combinatorial Laws for Physically Meaningful Computational Design

Vasu Ramaswamy and Vadim Shapiro

A typical computer representation of a design includes geometric and physical information organized in a suitable combinatorial data structure. Queries and transformations of these design representations are used to formulate most algorithms in computational design, including analysis, optimization, evolution, generation, and synthesis. Formal properties, and in particular problem-specific existence and validity of the computed solutions, should be assured and preserved by all such algorithms. Given a rich variety of representations and algorithms for computational design, there appears to be little reason to believe that most of them may be formulated within a single combinatorial framework. We argue that not only such a framework is possible, but it is formal because it is based on the tools from algebraic topology, practical because it arises naturally from computational considerations, and ubiquitous (Tonti 1975) because it spans most of the geometric and physical laws.
