Constraint-preserving labeled graph transformations for topology-based geometric modeling
Résumé
As labeled graphs are particularly well adapted to represent objects in the context of topology-based geometric modeling, graph transformation theory is an adequate framework to implement modeling operations and check their consistency. In this article, objects are defined as a particular subclass of labeled graphs in which arc labels encode their topological structure (i.e. cell subdivision: vertex, edge, face, etc.) and node labels encode their embedding (i.e. relevant data: vertex positions, face colors, volume density, etc.). Object consistency is therefore defined by labeling constraints which must be preserved along modeling operations that modify topology and/or embedding. In this article, we define a class of graph transformation rules dedicated to embedding computations. Dedicated graph transformation variables allow us to access the existing embedding from the underlying topological structure (e.g. collecting all the points of a face) in order to compute the new embedding using user-provided functions (e.g. compute the barycenter of several points). To ensure the safety of the defined operations, we provide syntactic conditions on rules that preserve the object consistency constraints.
Origine : Fichiers produits par l'(les) auteur(s)
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