Uniform convergence of discrete curvatures from nets of curvature lines

Ulrich Bauer; Konrad Polthier; Max Wardetzky

doi:10.1007/s00454-009-9237-4

Uniform convergence of discrete curvatures from nets of curvature lines

Ulrich Bauer, Konrad Polthier, Max Wardetzky

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We study discrete curvatures computed from nets of curvature lines on a given smooth surface and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.

Original language	English
Pages (from-to)	798-823
Number of pages	26
Journal	Discrete and Computational Geometry
Volume	43
Issue number	4
DOIs	https://doi.org/10.1007/s00454-009-9237-4
State	Published - Jun 2010
Externally published	Yes

Keywords

Cotangent formula
Curvature lines
Discrete curvatures
Polyhedral surfaces

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10.1007/s00454-009-9237-4

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title = "Uniform convergence of discrete curvatures from nets of curvature lines",

abstract = "We study discrete curvatures computed from nets of curvature lines on a given smooth surface and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.",

keywords = "Cotangent formula, Curvature lines, Discrete curvatures, Polyhedral surfaces",

author = "Ulrich Bauer and Konrad Polthier and Max Wardetzky",

year = "2010",

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doi = "10.1007/s00454-009-9237-4",

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T1 - Uniform convergence of discrete curvatures from nets of curvature lines

AU - Bauer, Ulrich

AU - Polthier, Konrad

AU - Wardetzky, Max

PY - 2010/6

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N2 - We study discrete curvatures computed from nets of curvature lines on a given smooth surface and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.

AB - We study discrete curvatures computed from nets of curvature lines on a given smooth surface and prove their uniform convergence to smooth principal curvatures. We provide explicit error bounds, with constants depending only on properties of the smooth limit surface and the shape regularity of the discrete net.

KW - Cotangent formula

KW - Curvature lines

KW - Discrete curvatures

KW - Polyhedral surfaces

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U2 - 10.1007/s00454-009-9237-4

DO - 10.1007/s00454-009-9237-4

M3 - Article

AN - SCOPUS:77952010711

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JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 4

ER -

Uniform convergence of discrete curvatures from nets of curvature lines

Abstract

Keywords

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