\(C^1\) Hermite interpolation with PH curves using the Enneper surface
type: Item
instance of: scholarly article
title: \(C^1\) Hermite interpolation with PH curves using the Enneper surface
zbMATH Open document ID: 1470.65013
DOI: 10.1155/2018/5680723
author: Hyun Chol Lee
author: Jae Hoon Kong
author: Gwang-Il Kim
published in: Abstract and Applied Analysis
publication date: 2018-08-30T00:00:00Z
review text: Summary: We show that the geometric and PH-preserving properties of the Enneper surface allow us to find PH interpolants for all regular \(C^1\) Hermite data-sets. Each such data-set is satisfied by two scaled Enneper surfaces, and we can obtain four interpolants on each surface. Examples of these interpolants were found to be better, in terms of bending energy and arc-length, than those obtained using a previous PH-preserving mapping.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 6929589
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/5680723
OpenAlex ID: W2800128467
cites work: Q4026160
cites work: Pythagorean-hodograph curves. Algebra and geometry inseparable
cites work: Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves.
cites work: Pythagorean hodograph curves: a survey of recent advances
cites work: Rational curves and surfaces with rational offsets
cites work: Construction of \(C^ 2\) Pythagorean-hodograph interpolating splines by the homotopy method
cites work: Clifford algebra, spin representation, and rational parameterization of curves and surfaces
cites work: The conformal map \(z\to z^ 2\) of the hodograph plane
cites work: Hermite Interpolation by Pythagorean Hodograph Quintics
cites work: Minkowski Pythagorean hodographs
cites work: Mathematical theory of medial axis transform
cites work: Minkowski Pythagorean-hodograph preserving mappings
cites work: \(C^{1}\) Hermite interpolation by Pythagorean hodograph quintics in Minkowski space
cites work: Topological criterion for selection of quintic pythagorean-hodograph Hermite interpolants
cites work: Hermite interpolation using Möbius transformations of planar Pythagorean-hodograph cubics
cites work: Special issue: Advances in geometrical algorithms and representations
cites work: Pythagorean-hodograph space curves
cites work: First order Hermite interpolation with spherical Pythagorean-hodograph curves
cites work: Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics
cites work: On the approximation order of a space data-dependent PH quintic Hermite interpolation scheme
cites work: \(G^2\) Pythagorean hodograph quintic transition between two circles with shape control
cites work: Geometric Hermite interpolation with Tschirnhausen cubics
cites work: Pythagorean-hodograph preserving mappings
cites work: \(C^1\)-Hermite interpolation with simple planar PH curves by speed reparametrization
cites work: \(C^1\) Hermite interpolation with PH curves by boundary data modification
cites work: Planar \(C^1\) Hermite interpolation with PH cuts of degree \((1,3)\) of Laurent series
cites work: Q4494308
cites work: \(C^{2}\) Hermite interpolation by Minkowski Pythagorean hodograph curves and medial axis transform approximation
description: scientific article; zbMATH DE number 6929589