Pythagorean-hodograph space curves
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Publication:1895900
DOI10.1007/BF02519035zbMath0829.65011WikidataQ114233809 ScholiaQ114233809MaRDI QIDQ1895900
Rida T. Farouki, Takis Sakkalis
Publication date: 21 January 1996
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Related Items (68)
Hermite interpolation by piecewise polynomial surfaces with polynomial area element ⋮ Algebraic-trigonometric Pythagorean-hodograph space curves ⋮ Helical polynomial curves and double Pythagorean hodographs. I: Quaternion and Hopf map representations ⋮ Curve design with rational Pythagorean-hodograph curves ⋮ Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves ⋮ Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces ⋮ Almost rotation-minimizing rational parametrization of canal surfaces ⋮ Algorithms for computing the approximation of offsets of toric Bézier curves ⋮ \(C^2\) Hermite interpolation by Pythagorean-hodograph quintic triarcs ⋮ \(G^1\) Hermite interpolation method for spatial PH curves with PH planar projections ⋮ \(C^1\) Hermite interpolation with PH curves using the Enneper surface ⋮ A new selection scheme for spatial Pythagorean hodograph quintic Hermite interpolants ⋮ Identification and ``reverse engineering of Pythagorean-hodograph curves ⋮ Rational parametrization of quadrics and their offsets ⋮ A Laguerre geometric approach to rational offsets ⋮ Curves with rational Frenet-Serret motion ⋮ Controlling extremal Pythagorean hodograph curves by Gauss-Legendre polygons ⋮ Spatial Pythagorean-hodograph B-spline curves and 3D point data interpolation ⋮ Construction of Minkowski Pythagorean hodograph B-spline curves ⋮ Partition of the space of planar quintic Pythagorean-hodograph curves ⋮ Optimal interpolation with spatial rational Pythagorean hodograph curves ⋮ Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints ⋮ Partial fraction decomposition for rational Pythagorean hodograph curves ⋮ \(G^{1}\) Hermite interpolation by PH cubics revisited ⋮ Interactive design of cubic IPH spline curves ⋮ On control polygons of Pythagorean hodograph septic curves ⋮ Gauss-Legendre polynomial basis for the shape control of polynomial curves ⋮ Solvability of \(G^{1}\) Hermite interpolation by spatial Pythagorean-hodograph cubics and its selection scheme ⋮ On rational Minkowski Pythagorean hodograph curves ⋮ Rational Pythagorean-hodograph space curves ⋮ Characterization and construction of helical polynomial space curves. ⋮ Rotation-minimizing osculating frames ⋮ Note on planar Pythagorean hodograph curves of Tschirnhaus type ⋮ Pipe surfaces with rational spine curve are rational ⋮ A unified Pythagorean hodograph approach to the medial axis transform and offset approximation ⋮ Pythagorean-hodograph preserving mappings ⋮ Deformation of spatial septic Pythagorean hodograph curves using Gauss-Legendre polygon ⋮ Gauss-Lobatto polygon of Pythagorean hodograph curves ⋮ Performance analysis of CNC interpolators for time-dependent feedrates along PH curves ⋮ Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics ⋮ Construction of Rational Curves with Rational Rotation-Minimizing Frames via Möbius Transformations ⋮ Reparameterization of Curves and Surfaces with Respect to Their Convolution ⋮ Low Degree Euclidean and Minkowski Pythagorean Hodograph Curves ⋮ Real-time CNC interpolators for Bézier conics ⋮ Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form ⋮ A control polygon scheme for design of planar \(C^2\) PH quintic spline curves ⋮ A geometric product formulation for spatial pythagorean hodograph curves with applications to Hermite interpolation ⋮ Rational space curves are not ``unit speed ⋮ Rational hypersurfaces with rational convolutions ⋮ \(C^d\) Hermite interpolations with spatial Pythagorean hodograph B-splines ⋮ \(C^1\)-Hermite interpolation with simple planar PH curves by speed reparametrization ⋮ Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures ⋮ Weierstrass-type approximation theorems with Pythagorean hodograph curves ⋮ On quadratic two-parameter families of spheres and their envelopes ⋮ PN surfaces and their convolutions with rational surfaces ⋮ Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves ⋮ Contour machining of free-form surfaces with real-time PH curve CNC interpolators ⋮ Algorithm 952 ⋮ Planar projections of spatial Pythagorean-hodograph curves ⋮ Higher dimensional PH curves ⋮ Linear computational approach to interpolations with polynomial Minkowski Pythagorean hodograph curves ⋮ A new method to design cubic Pythagorean-hodograph spline curves with control polygon ⋮ Euclidean and Minkowski Pythagorean hodograph curves over planar cubics ⋮ Euler-Rodrigues frames on spatial Pythagorean-hodograph curves. ⋮ Polynomial curves with projections to PH curves ⋮ Rational framing motions and spatial rational Pythagorean hodograph curves ⋮ $C^2$ Hermite interpolation by Pythagorean Hodograph space curves ⋮ B-spline Pythagorean hodograph curves in Clifford algebras
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