Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces

Helmut Pottmann; Karsten Opitz

doi:10.1016/0167-8396(94)90057-4

Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces

Helmut Pottmann^*, Karsten Opitz

^*Corresponding author for this work

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

31 Scopus citations

Abstract

Visualization of a scalar-valued function f{hook} defined on Euclidean n-space Eⁿ is often based on its graph-hypersurface Γ(f{hook}) ⊂ Rⁿ⁺¹. Particularly for curvature interrogation, it is natural to equip R^n-1 with a so-called isotropic metric and use isotropic measures of the graph instead of Euclidean invariants. The ideas are extended to functions defined on surfaces in E³. We present the central formulae for a curvature analysis of functions defined on surfaces. It is shown how to use them for visualization purposes and as a mathematical basis for the construction of interpolating or approximating functions on surfaces.

Original language	English (US)
Pages (from-to)	655-674
Number of pages	20
Journal	Computer Aided Geometric Design
Volume	11
Issue number	6
DOIs	https://doi.org/10.1016/0167-8396(94)90057-4
State	Published - Dec 1994
Externally published	Yes

Keywords

Curvature analysis
Differential geometry
Functions on surfaces
Isotropic geometry
Scattered data interpolation and approximation
Scientific visualization

ASJC Scopus subject areas

Modeling and Simulation
Automotive Engineering
Aerospace Engineering
Computer Graphics and Computer-Aided Design

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10.1016/0167-8396(94)90057-4

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title = "Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces",

abstract = "Visualization of a scalar-valued function f{hook} defined on Euclidean n-space En is often based on its graph-hypersurface Γ(f{hook}) ⊂ Rn+1. Particularly for curvature interrogation, it is natural to equip Rn-1 with a so-called isotropic metric and use isotropic measures of the graph instead of Euclidean invariants. The ideas are extended to functions defined on surfaces in E3. We present the central formulae for a curvature analysis of functions defined on surfaces. It is shown how to use them for visualization purposes and as a mathematical basis for the construction of interpolating or approximating functions on surfaces.",

keywords = "Curvature analysis, Differential geometry, Functions on surfaces, Isotropic geometry, Scattered data interpolation and approximation, Scientific visualization",

author = "Helmut Pottmann and Karsten Opitz",

year = "1994",

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doi = "10.1016/0167-8396(94)90057-4",

language = "English (US)",

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T1 - Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces

AU - Pottmann, Helmut

AU - Opitz, Karsten

PY - 1994/12

Y1 - 1994/12

N2 - Visualization of a scalar-valued function f{hook} defined on Euclidean n-space En is often based on its graph-hypersurface Γ(f{hook}) ⊂ Rn+1. Particularly for curvature interrogation, it is natural to equip Rn-1 with a so-called isotropic metric and use isotropic measures of the graph instead of Euclidean invariants. The ideas are extended to functions defined on surfaces in E3. We present the central formulae for a curvature analysis of functions defined on surfaces. It is shown how to use them for visualization purposes and as a mathematical basis for the construction of interpolating or approximating functions on surfaces.

AB - Visualization of a scalar-valued function f{hook} defined on Euclidean n-space En is often based on its graph-hypersurface Γ(f{hook}) ⊂ Rn+1. Particularly for curvature interrogation, it is natural to equip Rn-1 with a so-called isotropic metric and use isotropic measures of the graph instead of Euclidean invariants. The ideas are extended to functions defined on surfaces in E3. We present the central formulae for a curvature analysis of functions defined on surfaces. It is shown how to use them for visualization purposes and as a mathematical basis for the construction of interpolating or approximating functions on surfaces.

KW - Curvature analysis

KW - Differential geometry

KW - Functions on surfaces

KW - Isotropic geometry

KW - Scattered data interpolation and approximation

KW - Scientific visualization

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DO - 10.1016/0167-8396(94)90057-4

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AN - SCOPUS:0028752468

SN - 0167-8396

VL - 11

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EP - 674

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

IS - 6

ER -

Curvature analysis and visualization for functions defined on Euclidean spaces or surfaces

Abstract

Keywords

ASJC Scopus subject areas

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