Simplification of tetrahedral meshes

Trotts,; Hamann,; Joy,; Wiley,

doi:10.1109/visual.1998.745315

Cited by 36 publications

(32 citation statements)

References 16 publications

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“…Trotts et al [10] method for decimation of tetrahedral meshes is most similar to ours. Their algorithm computes a local error metric to assign priorities to tetrahedra.…”

Section: Volume Simplificationsupporting

confidence: 60%

Volume decimation of irregular tetrahedral grids

Gelder

Verma²,

Wilhelms³

1999

Proceedings Computer Graphics International CGI-99

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“…Trotts et al [10] method for decimation of tetrahedral meshes is most similar to ours. Their algorithm computes a local error metric to assign priorities to tetrahedra.…”

Section: Volume Simplificationsupporting

confidence: 60%

Volume decimation of irregular tetrahedral grids

Gelder

Verma²,

Wilhelms³

1999

Proceedings Computer Graphics International CGI-99

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“…These operations are used to simplify tetrahedral meshes. See [32] for a detailed description of the operation. We use bottom-up incidences for all algorithms, whereas for the subdivision algorithms we test different variants: With bottom-up incidences enabled and with only a subset of the bottom-up incidences enabled (those necessary for the computations).…”

Section: Computational Costsmentioning

confidence: 99%

OpenVolumeMesh – A Versatile Index-Based Data Structure for 3D Polytopal Complexes

Kremer

Bommes

Kobbelt

2013

Proceedings of the 21st International Meshing Roundtable

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Summary. We present a data structure which is able to represent heterogeneous 3-dimensional polytopal cell complexes and is general enough to also represent nonmanifolds without incurring undue overhead. Extending the idea of half-edge based data structures for two-manifold surface meshes, all faces, i.e. the two-dimensional entities of a mesh, are represented by a pair of oriented half-faces. The concept of using directed half-entities enables inducing an orientation to the meshes in an intuitive and easy to use manner.We pursue the idea of encoding connectivity by storing first-order top-down incidence relations per entity, i.e. for each entity of dimension d, a list of links to the respective incident entities of dimension d−1 is stored. For instance, each half-face as well as its orientation is uniquely determined by a tuple of links to its incident halfedges or each 3D cell by the set of incident half-faces. This representation allows for handling non-manifolds as well as mixed-dimensional mesh configurations. No entity is duplicated according to its valence, instead, it is shared by all incident entities in order to reduce memory consumption. Furthermore, an array-based storage layout is used in combination with direct index-based access. This guarantees constant access time to the entities of a mesh.Although bottom-up incidence relations are implied by the top-down incidences, our data structure provides the option to explicitly generate and cache them in a transparent manner. This allows for accelerated navigation in the local neighborhood of an entity.We provide an open-source and platform-independent implementation of the proposed data structure written in C++ using dynamic typing paradigms. The library is equipped with a set of STL compliant iterators, a generic property system to dynamically attach properties to all entities at run-time, and a serializer/deserializer supporting a simple file format. Due to its similarity to the OpenMesh data structure, it is easy to use, in particular for those familiar with OpenMesh. Since the presented data structure is compact, intuitive, and efficient, it is suitable for a variety of applications, such as meshing, visualization, and numerical analysis. OpenVolumeMesh is open-source software licensed under the terms of the LGPL.

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“…Van Gelder et al [1999] implemented vertex removal via half-edge contractions and suggested a local density metric to guide the selection of vertices to remove. Trotts et al [1998;1999], Cignoni et al [2000], and Chopra and Meyer [2002] have all developed contraction-based simplification algorithms. Trotts et al propose an error metric that provides a conservative bound on the maximum deviation of the data field.…”

Section: Related Workmentioning

confidence: 99%

Quadric-based simplification in any dimension

Garland

Zhou

2005

ACM Trans. Graph.

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We present a new method for simplifying simplicial complexes of any type embedded in Euclidean spaces of any dimension. At the heart of this system is a novel generalization of the quadric error metric used in surface simplification. We demonstrate that our generalized simplification system can produce high quality approximations of plane and space curves, triangulated surfaces, tetrahedralized volume data, and simplicial complexes of mixed type. Our method is both efficient and easy to implement. It is capable of processing complexes of arbitrary topology, including nonmanifolds, and can preserve intricate boundaries.

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Simplification of tetrahedral meshes

Cited by 36 publications

References 16 publications

Volume decimation of irregular tetrahedral grids

Volume decimation of irregular tetrahedral grids

OpenVolumeMesh – A Versatile Index-Based Data Structure for 3D Polytopal Complexes

Quadric-based simplification in any dimension

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