Discrete Differential-Geometry Operators for Triangulated 2-Manifolds

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

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by Mark Meyer , Mathieu Desbrun , Peter Schröder , Alan H. Barr

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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