A General Physical-topological Framework using Rule-based Language for Physical Simulation

Salah, F. Ben; Belhaouari, Hakim; Arnould, Agnès; Meseure, Philippe

doi:10.5220/0006119802200227

Cited by 1 publication

(1 citation statement)

References 9 publications

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“…Currently, it supports some physics models such as massspring, finite element method, or mass-tensors among several meshes (triangle, quad, tetrahedron, hexagon). Rules help developers correctly design the location of force interactions [9], while runtime verification helps them write correct computations when designing new forces.…”

Section: Topological Extensionmentioning

confidence: 99%

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: Topological Extensionmentioning

confidence: 99%