Topological consistency preservation with graph transformation schemes

Pascual, Romain; Gall, Pascale Le; Arnould, Agnès; Belhaouari, Hakim

doi:10.1016/j.scico.2021.102728

Cited by 3 publications

(3 citation statements)

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“…Some syntactic conditions on the rule schemes were also given to ensure that instantiated rules satisfy the conditions of Theorem 1. These variables have been revisited with a functorial approach exploiting a product-based construction in [46]. Here we aim to discuss geometric operations, meaning that the embedding consistency is the issue tackled.…”

Section: Basic Topological Transformationsmentioning

confidence: 99%

“…As topological structures can be represented as a particular class of graphs, the use of graph transformations to define modeling operations has already been studied [57,50,58,46]. Derived from string and tree rewriting techniques, this rule-based approach offers a natural way to describe complex transformations intuitively.…”

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confidence: 99%

“…The context of topological-based geometric modeling is then presented in Section 4. We focus on the topological model of generalized maps [38] and give conditions from [50,46] to preserve the model consistency. Section 5 then similarly presents our embedded version of generalized maps and conditions under which graph transformations preserve the embedding consistency.…”

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confidence: 99%

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Preserving consistency in geometric modeling with graph transformations

Arnould

Belhaouari

Bellet

et al. 2022

Math. Struct. Comp. Sci.

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Labeled graphs are particularly well adapted to represent objects in the context of topology-based geometric modeling. Thus, graph transformation theory is used to implement modeling operations and check their consistency. This article defines a class of graph transformation rules dedicated to embedding computations. Objects are here defined as a particular subclass of labeled graphs in which arc labels encode their topological structure (i.e., cell subdivision: vertex, edge, face) and node labels encode their embedding (i.e., relevant data: vertex positions, face colors, volume density). Object consistency is defined by labeling constraints which must be preserved by modeling operations that modify topology and/or embedding. 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.

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Section: Basic Topological Transformationsmentioning

confidence: 99%

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confidence: 99%

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