Volume decimation of irregular tetrahedral grids

Gelder, van Isabelle; Verma,; Wilhelms,

doi:10.1109/cgi.1999.777958

Cited by 9 publications

(7 citation statements)

References 10 publications

(11 reference statements)

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“…Van Gelder et al [18] have already demonstrated that the mass-metric is superior to the density-metric. The massmetric is based on the changes in mass (the integral of density over a volume) of the material during decimation.…”

Section: Gradient Magnitude Based Error Metricsmentioning

confidence: 99%

“…Chopra and Meyer [2] have introduced an algorithm to take all of the four vertices of a tetrahedron, and fuse them onto the barycenter of the tetrahedron, while still taking care of complex mesh-inconsistency problems. Van Gelder et al [18] have presented a method for rapidly decimating volumetric data defined on a tetrahedral grid. They compared the mass-based and density-based decimation error metrics, and the mass-based metric is found to be superior.…”

Section: Related Workmentioning

confidence: 99%

“…In Van Gelder et al's algorithm [18], a surface vertex can be merged only with another surface vertex. They use a weighted combination of the data-based error and a geometry error to evaluate the deviation.…”

Section: Sharp Boundary Featuresmentioning

confidence: 99%

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Feature preserved volume simplification

Hong

Kaufman

2003

Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications

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The goal of this work is to simplify volumetric datasets while preserving the sharp boundary features and the topology of the 3D scalar field. The simplification is performed on the volumetric datasets defined as a tetrahedral mesh. The sharp boundary features are detected and preserved in the simplification to conserve the salient details of the tetrahedral mesh. The topology of the 3D scalar field is preserved by maintaining critical points extracted from the original dataset. No critical vertices are removed or generated during the simplification process. A gradient magnitude based error metric is used to estimate the error associated with a simplification step. The simplified tetrahedral mesh is rendered using a hardware-accelerated unstructured volume rendering algorithm. This method produces results which are visually similar to the original dataset.

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Section: Gradient Magnitude Based Error Metricsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Feature preserved volume simplification

Hong

Kaufman

2003

Proceedings of the Eighth ACM Symposium on Solid Modeling and Applications

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“…Van Gelder et al [5] remove vertices based on mass and data error metrics. Uesu et al [6] provide a fast point-based method which works directly on the underlying scalar field.…”

Section: Related Workmentioning

confidence: 99%

Streaming Simplification of Tetrahedral Meshes

2007

IEEE Trans. Visual. Comput. Graphics

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Abstract-Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can accomplish real-time visualization necessary for scientific analysis. We propose a two-step approach for streaming simplification of large tetrahedral meshes. Our algorithm arranges the data on disk in a streaming, I/O-efficient format that allows coherent access to the tetrahedral cells. A quadric-based simplification is sequentially performed on small portions of the mesh in-core. Our output is a coherent streaming mesh which facilitates future processing. Our technique is fast, produces high quality approximations, and operates out-of-core to process meshes too large for main memory.

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“…Preventing inversion by explicit orientation checks is quite common. It has been used for planar graphs [Ciarlet and Lamour 1996], triangular meshes Hoppe 1996;Ronfard and Rossignac 1996], and tetrahedral volumes [Staadt and Gross 1998;Gelder et al 1999;Trotts et al 1999;Cignoni et al 2000;Chopra and Meyer 2002]. In our quadric-based system, it is in planar regions where mesh inversions are most likely to occur.…”

Section: Preventing Mesh Inversionmentioning

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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Volume decimation of irregular tetrahedral grids

Abstract: Rendering

Cited by 9 publications

References 10 publications

Feature preserved volume simplification

Feature preserved volume simplification

Streaming Simplification of Tetrahedral Meshes

Quadric-based simplification in any dimension

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