A generic query-modify framework for volumetric mesh processing

Abstract: We introduce a query-modify framework for automating volumetric mesh processing. Our method enables flexible and efficient modifications of geometric structures composed of multiple volumes with minimal user-implemented code. Modifications are provided as rules consisting of a query mesh and a target mesh representing structural information to be extracted and replaced. The rules enable both localized queries to be matched with a portion of an input mesh and targeted modifications on the matched portion of the input mesh. Our approach generalizes standard mesh manipulations and adapts to various applications, including geometric modeling, remeshing, and topology-aware transformations. We showcase our framework on several use cases, including the first complete implementation of a tetrahedral recombination method based on 171 cases, exhaustively classifying all possible recombinations. Our framework allows for arbitrarily connected collections of volumes as queries, enabling automated and application-driven mesh modifications.

Keywords: Combinatorial maps; Mesh processing; Query-modify framework; Tetrahedral recombination