Graph transformation: a tool for designing geometric modeling operations

APR Seminar at LIP6 (Sorbonne Université).

Abstract: Domain-specific languages allow abstracting over the actual code (i.e., instructions written in a generic programming language) based on a particular application domain. I will present a language based on graph rewriting that formalizes topology-based geometric modeling operations. In this context, nD objects are represented via a combinatorial structure, called a generalized map (Gmap), that encodes the decomposition of an object into topological cells (vertices, edges, faces, volumes …). The topological structure of a Gmap is represented as a graph and is extended with data called embeddings. These embeddings describe the geometric information added to the cells. In the first part, I will present the assets of the language in terms of genericity and correctness analysis. Then, I will present a mechanism to infer operations from examples and discuss practical concerns of the approach in JerboaStudio. In particular, we will see that the inference mechanism highly simplifies the process of conceiving new operations while relying on a formal language, ensuring the well-formedness of the operations through statical analysis of the rules.