Query-replace operations for topologically controlled 3D mesh editing

Abstract

We propose a generic framework to describe modifications on 3D objects (surfaces and volumes) based on a query and replace mechanism. These modifications are described in terms of rewriting rules: a set of patterns is provided, each one defining a possible replacement. The patterns are expressed using 3D combinatorial maps, ensuring the global topological validity of the transformed mesh. At the core of the framework, we use topological signatures to efficiently query and match patterns on the input. Our formalism can generically describe many different transformations like subdivision, smoothing, topological correction, or remeshing. Its interest is twofold. It provides an easy implementation for such operations, especially when many cases arise: we provide an example with over 300 cases. It is also able to detect corner cases that were not provided and are required to ensure the topological correctness of the output.