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Discrete Differential-Geometry Operators for Triangulated 2-Manifolds (2002)

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by Mark Meyer , Mathieu Desbrun , Peter Schröder , Alan H. Barr
Citations:448 - 14 self
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BibTeX

@MISC{Meyer02discretedifferential-geometry,
    author = {Mark Meyer and Mathieu Desbrun and Peter Schröder and Alan H. Barr},
    title = {Discrete Differential-Geometry Operators for Triangulated 2-Manifolds},
    year = {2002}
}

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Abstract

This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Voronoi cells and the mixed Finite-Element/FiniteVolume method, and compare them to existing formulations. Building upon previous work in discrete geometry, these new operators are closely related to the continuous case, guaranteeing an appropriate extension from the continuous to the discrete setting: they respect most intrinsic properties of the continuous differential operators.

Keyphrases

discrete differential-geometry operator    continuous case    intrinsic property    second order differential property    arbitrary triangle mesh    mixed finite-element finitevolume method    continuous differential operator    discrete setting    consistent set    normal vector    new operator    previous work    voronoi cell    important geometric attribute    flexible tool    consistent derivation    discrete geometry    appropriate extension   

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