Curvature computations for the intersection curves of hypersurfaces in Euclidean n-space

Özçetin, Bedia Merih; Düldül, Mustafa

doi:10.1016/j.cagd.2020.101954

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2021

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Cited by 2 publications

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“…Aléssio [5] derived the second and the third curvatures of intersection curves of (n − 1)-implicit hypersurfaces in E n by generalizing the method of Goldman. Recently, the intersection curve of (n − 1) transversally intersecting hypersurfaces has been studied in E n by [17].…”

Section: Introductionmentioning

confidence: 99%

Intersection curve of two parametric surfaces in Euclidean n-space

Düldül

Özçetin

2021

ACUTM

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The aim of this paper is to study the differential geometric properties of the intersection curve of two parametric surfaces in Euclidean n-space. For this aim, we first present the mth order derivative formula of a curve lying on a parametric surface. Then, we obtain curvatures and Frenet vectors of the transversal intersection curve of two parametric surfaces in Euclidean n-space. We also provide computer code produced in MATLAB to simplify determining the coefficients relative to Frenet frame of higher order derivatives of a curve.

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Section: Introductionmentioning

confidence: 99%

Intersection curve of two parametric surfaces in Euclidean n-space

Düldül

Özçetin

2021

ACUTM

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New Methods and Novel Framework for HypersurfaceCurvature Determination and Analysis

Hauenstein

Newman

2021

JWSCG

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New methods for hypersurface (that is, 3-dimensional manifold) curvature determination in volumetric data areintroduced. One method is convolution-based. Another method is spline-based. Method accuracy is also analyzed,with that analysis involving comparison of the methods with each other as well as against two existing convolution-based methods. The accuracy analysis utilizes a novel framework that enables curvature determination methodaccuracy analysis via dynamically generated synthetic test datasets formed from continuous trivariate functions.Such functions enable accuracy analysis versus ground truth. The framework is also described here.

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Curvature computations for the intersection curves of hypersurfaces in Euclidean n-space

Cited by 2 publications

References 14 publications

Intersection curve of two parametric surfaces in Euclidean n-space

Intersection curve of two parametric surfaces in Euclidean n-space

New Methods and Novel Framework for HypersurfaceCurvature Determination and Analysis

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