Construction of \(C^ 2\) Pythagorean-hodograph interpolating splines by the homotopy method
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Publication:1815867
DOI10.1007/BF02124754zbMath0866.65008OpenAlexW2022994234WikidataQ114233882 ScholiaQ114233882MaRDI QIDQ1815867
Gudrun Albrecht, Rida T. Farouki
Publication date: 18 December 1996
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02124754
Numerical computation using splines (65D07) Numerical interpolation (65D05) Spline approximation (41A15)
Related Items (40)
Planar \(C^1\) Hermite interpolation with PH cuts of degree \((1,3)\) of Laurent series ⋮ Construction of \(G^1\) planar Hermite interpolants with prescribed arc lengths ⋮ \(C^2\) Hermite interpolation by Pythagorean-hodograph quintic triarcs ⋮ \(C^1\) Hermite interpolation with PH curves using the Enneper surface ⋮ A new selection scheme for spatial Pythagorean hodograph quintic Hermite interpolants ⋮ Sparse Pythagorean hodograph curves ⋮ A Laguerre geometric approach to rational offsets ⋮ Interpolating \(G^1\)-splines with rational offsets ⋮ Unnamed Item ⋮ Planar Pythagorean-hodograph B-spline curves ⋮ Arc length preserving \(G^2\) Hermite interpolation of circular arcs ⋮ Interactive design of cubic IPH spline curves ⋮ On control polygons of Pythagorean hodograph septic curves ⋮ Hermite interpolation using Möbius transformations of planar Pythagorean-hodograph cubics ⋮ Rational Pythagorean-hodograph space curves ⋮ Characterization and construction of helical polynomial space curves. ⋮ Hermite interpolation by Pythagorean hodograph curves of degree seven ⋮ Design of rational rotation–minimizing rigid body motions by Hermite interpolation ⋮ Real-time CNC interpolators for Pythagorean-hodograph curves ⋮ Pipe surfaces with rational spine curve are rational ⋮ \(C^1\) Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs ⋮ An approach to geometric interpolation by Pythagorean-hodograph curves ⋮ Pythagorean-hodograph preserving mappings ⋮ On interpolation by Planar cubic $G^2$ pythagorean-hodograph spline curves ⋮ Construction and shape analysis of PH quintic Hermite interpolants ⋮ Performance analysis of CNC interpolators for time-dependent feedrates along PH curves ⋮ Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics ⋮ Design of \(C^2\) algebraic-trigonometric Pythagorean hodograph splines with shape parameters ⋮ 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 ⋮ \(C^1\)-Hermite interpolation with simple planar PH curves by speed reparametrization ⋮ Absolute hodograph winding number and planar PH quintic splines ⋮ Weierstrass-type approximation theorems with Pythagorean hodograph curves ⋮ Topological criterion for selection of quintic pythagorean-hodograph Hermite interpolants ⋮ Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curves ⋮ Contour machining of free-form surfaces with real-time PH curve CNC interpolators ⋮ Algorithm 952 ⋮ A new method to design cubic Pythagorean-hodograph spline curves with control polygon
Uses Software
Cites Work
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- A homotopy for solving general polynomial systems that respects m- homogeneous structures
- Computing all solutions to polynomial systems using homotopy continuation
- Constructing roadmaps of semi-algebraic sets. I: Completeness
- The conformal map \(z\to z^ 2\) of the hodograph plane
- The elastic bending energy of Pythagorean-hodograph curves
- Algorithm 652
- A Simple Homotopy Method for Determining all Isolated Solutions to Polynomial Systems
- Hermite Interpolation by Pythagorean Hodograph Quintics
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