Preserving consistency in geometric modeling with graph transformations

Abstract Labeled graphs are particularly well adapted to represent objects in the context of topology-based geometric modeling. Thus, graph transformation theory is used implement modeling operations and check their consistency. This article defines a class rules dedicated embedding computations. Objects here defined as particular subclass labeled which arc labels encode topological structure (i.e., cell subdivision: vertex, edge, face) node relevant data: vertex positions, face colors, volume density). Object consistency by labeling constraints must be preserved that modify topology and/or embedding. Dedicated variables allow us access existing from underlying (e.g., collecting all points order compute new using user-provided functions barycenter several points). To ensure safety operations, we provide syntactic conditions on preserve object constraints.