\(C^{1}\) Hermite interpolation by Pythagorean hodograph quintics in Minkowski space

DOI10.1007/s10444-007-9059-yzbMath1173.65008OpenAlexW2048663671WikidataQ114227767 ScholiaQ114227767MaRDI QIDQ1016129

Bert Jüttler, Jiří Kosinka

Publication date: 4 May 2009

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-007-9059-y

zbMATH Keywords

quintic splineClifford algebraHermite interpolationLorentz transformationsmedial axis transformMinkowski Pythagorean hodograph curves

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical interpolation (65D05) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (14)

Medial axis transforms yielding rational envelopes ⋮ \(C^1\) Hermite interpolation with PH curves using the Enneper surface ⋮ A new selection scheme for spatial Pythagorean hodograph quintic Hermite interpolants ⋮ Unnamed Item ⋮ Construction of Minkowski Pythagorean hodograph B-spline curves ⋮ Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints ⋮ \(C^{2}\) Hermite interpolation by Minkowski Pythagorean hodograph curves and medial axis transform approximation ⋮ On rational Minkowski Pythagorean hodograph curves ⋮ Mappings that preserve helices in the n-dimensional Minkowski spaces ⋮ A unified Pythagorean hodograph approach to the medial axis transform and offset approximation ⋮ Interpolation of Hermite data by clamped Minkowski Pythagorean hodograph B-spline curves ⋮ Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves ⋮ Minkowski Pythagorean-hodograph preserving mappings ⋮ Linear computational approach to interpolations with polynomial Minkowski Pythagorean hodograph curves

Cites Work

• Topological criterion for selection of quintic pythagorean-hodograph Hermite interpolants
• Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves.
• Cubic Pythagorean hodograph spline curves and applications to sweep surface modeling.
• Clifford algebra, spin representation, and rational parameterization of curves and surfaces
• Applications of Laguerre geometry in CAGD
• Minkowski Pythagorean hodographs
• Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves
• Mathematical theory of medial axis transform
• \(C^1\) Hermite interpolation using MPH quartic
• Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces
• Exploiting curvatures to compute the medial axis for domains with smooth boundary
• \(G^{1}\) Hermite interpolation by Minkowski Pythagorean hodograph cubics
• $C^2$ Hermite interpolation by Pythagorean Hodograph space curves
• Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves
• Mathematics of Surfaces XI

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