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Preserving consistency in geometric modeling with graph transformations

Published online by Cambridge University Press:  18 October 2022

Agnès Arnould ,
Hakim Belhaouari ,
Thomas Bellet ,
Pascale Le Gall  and
Romain Pascual Open the ORCID record for Romain Pascual [Opens in a new window]
Agnès Arnould
Affiliation:
Laboratory XLIM UMR CNRS 7252, Poitiers University, Poitiers, France
Hakim Belhaouari
Affiliation:
Laboratory XLIM UMR CNRS 7252, Poitiers University, Poitiers, France
Thomas Bellet
Affiliation:
Laboratory MICS, CentraleSupélec, Paris-Saclay University, Gif-sur-Yvette, France
Pascale Le Gall
Affiliation:
Laboratory MICS, CentraleSupélec, Paris-Saclay University, Gif-sur-Yvette, France
Romain Pascual*
Affiliation:
Laboratory MICS, CentraleSupélec, Paris-Saclay University, Gif-sur-Yvette, France
*
*Corresponding author. Email: [email protected]
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Abstract

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.

Keywords

DPO graph transformationtopology-based geometric modelinggraph transformation with variablesgeneralized mapsconsistency preservationstatic analysis
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 32 , Issue 3 , March 2022 , pp. 300 - 347
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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