Graph Transformation for Topology Modelling

Poudret, Mathieu; Arnould, Agnès; Comet, Jean‐Paul; Gall, Pascale Le

doi:10.1007/978-3-540-87405-8_11

Cited by 10 publications

(39 citation statements)

References 8 publications

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“…Topology has already been introduced in graph transformation in different kinds of contexts [16][17][18]. Work presented in [17] is far from our purpose since the concept of topology is used to ensure structural constraints on graphs being transformed.…”

Section: Resultsmentioning

confidence: 99%

“…MGS has also been extensively used in this context [4]. Since we focus in this paper on an application in topological modeling, our work can be compared to [18] where graph transformations have been applied to specify topological operations on G-maps. G-maps are a data structure used to encode cellular complexes corresponding to a specific class of topological objects called quasi-manifolds [20].…”

Section: Resultsmentioning

confidence: 99%

“…Because G-maps are a specific kind of cellular complexes, they can be handled by the approach presented here. Indeed, they have been implemented in MGS (see [10] for an elaboration) as well as many of the applications proposed in [18] (especially in biology). The formal approach developped in [18] is very specific and focuses on the correct handling of involutions in G-maps construction and deletion operations.…”

Section: Resultsmentioning

confidence: 99%

“…We propose to transform cellular complexes since the extension from graphs to complexes seems intuitive and relevant in a lot of application area [21]. Our mathematical description is not based on the usual graph morphisms and pushouts (like in [12,17,18]). Our objective was here to relate the notion of transformation to the very definition of topological collections in the context of a programming language.…”

Section: Resultsmentioning

confidence: 99%

See 3 more Smart Citations

Declarative Mesh Subdivision Using Topological Rewriting in MGS

Spicher

Michel

Giavitto

2010

Lecture Notes in Computer Science

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Abstract. Mesh subdivision algorithms are usually specified informally using graphical schemes defining local mesh refinements. These algorithms are then implemented efficiently in an imperative framework. The implementation is cumbersome and implies some tricky indices management. Smith et al. (2004) asks the question of the declarative programming of such algorithms in an index-free way. In this paper, we positively answer this question by presenting a rewriting framework where mesh refinements are described by simple rules. This framework is based on a notion of topological chain rewriting. Topological chains generalize the notion of labeled graph to higher dimensional objects. This framework has been implemented in the domain specific language MGS. The same generic approach has been used to implement Loop as well as Butterfly, Catmull-Clark and Kobbelt subdivision schemes.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Declarative Mesh Subdivision Using Topological Rewriting in MGS

Spicher

Michel

Giavitto

2010

Lecture Notes in Computer Science

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“…Generalized maps (g-maps) [44] and the cell-tuple structure [45] are capable of storing a large class of cell complexes, including orientable and unorientable manifold objects of arbitrary dimension, including objects with boundaries by Poudret et al [46]. They have been implemented in libraries and software, including Moka and Gocad.…”

Section: Storing a 4d Modelmentioning

confidence: 99%

Modeling a 3D City Model and Its Levels of Detail as a True 4D Model

Ohori

Ledoux

Biljecki

et al. 2015

IJGI

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The various levels of detail (LODs) of a 3D city model are often stored independently, without links between the representations of the same object, causing inconsistencies, as well as update and maintenance problems. One solution to this problem is to model the LOD as an extra geometric dimension perpendicular to the three spatial ones, resulting in a true 4D model in which a single 4D object (a polychoron) represents a 3D polyhedral object (e.g., a building) at all of its LODs and a multiple-LOD 3D city model is modeled as a 4D cell complex. While such an approach has been discussed before at a conceptual level, our objective in this paper is to describe how it can be realized by appropriately linking existing 3D models of the same object at different LODs. We first present our general methodology to construct such a 4D model, which consists of three steps: (1) finding corresponding 0D-3D cells; (2) creating 1D-4D cells connecting them; and (3) constructing the 4D model. Because of the complex relationships between the objects in different LODs, the creation of the connecting cells can become difficult. We therefore describe four different alternatives to do this, and we discuss the advantages and disadvantages of each in terms of their feasibility in practice and the properties that the resulting 4D model has. We show how the different linking schemes result in objects with different characteristics in several use cases. We also show how our linking method works in practice by implementing the linking of matching cells to construct a 4D model.

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