Algorithm 952

DOI10.1145/2699467zbMath1347.65045OpenAlexW1971971263WikidataQ113310263 ScholiaQ113310263MaRDI QIDQ2828158

Bohan Dong, Rida T. Farouki

Publication date: 24 October 2016

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1145/2699467

zbMATH Keywords

computer-aided geometric designspline interpolationNewton-Raphson methodHermite interpolationPythagorean-hodograph curvesarc lengthoffset curvesbending energy

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Computer-aided design (modeling of curves and surfaces) (65D17) Packaged methods for numerical algorithms (65Y15)

Related Items (6)

Construction of \(G^1\) planar Hermite interpolants with prescribed arc lengths ⋮ Interactive design of cubic IPH spline curves ⋮ Unnamed Item ⋮ Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form ⋮ PHquintic ⋮ A new method to design cubic Pythagorean-hodograph spline curves with control polygon

Uses Software

• BPOLY

Cites Work

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• A unified Pythagorean hodograph approach to the medial axis transform and offset approximation
• On the generation of trajectories for multiple uavs in environments with obstacles
• Real-time CNC interpolators for Pythagorean-hodograph curves
• Rational curves and surfaces with rational offsets
• A generalisation of the Pythagorean hodograph quintic spiral
• A control polygon scheme for design of planar \(C^2\) PH quintic spline curves
• \(G^2\) Pythagorean hodograph quintic transition between two circles with shape control
• Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures
• Topological criterion for selection of quintic pythagorean-hodograph Hermite interpolants
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• On the numerical condition of polynomials in Bernstein form
• Real rational curves are not `unit speed'
• The conformal map \(z\to z^ 2\) of the hodograph plane
• The elastic bending energy of Pythagorean-hodograph curves
• Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves.
• Variable-feedrate CNC interpolators for constant material removal rates along Pythagorean-hodograph curves.
• Clifford algebra, spin representation, and rational parameterization of curves and surfaces
• Minkowski Pythagorean hodographs
• Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves
• Construction of \(C^ 2\) Pythagorean-hodograph interpolating splines by the homotopy method
• Pythagorean-hodograph space curves
• Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves
• Rotation-minimizing Euler-Rodrigues rigid-body motion interpolants
• Employing Pythagorean Hodograph Curves for Artistic Patterns
• Design of C 2 Spatial Pythagorean-Hodograph Quintic Spline Curves by Control Polygons
• Shape-preserving interpolation by G1 and G2 PH quintic splines
• Hermite Interpolation by Pythagorean Hodograph Quintics
• Design of rational rotation–minimizing rigid body motions by Hermite interpolation
• Algorithm 812: BPOLY
• Construction and shape analysis of PH quintic Hermite interpolants
• Efficient solution of the complex quadratic tridiagonal system for \(C^2\) PH quintic splines
• Planar \(G^2\) transition with a fair Pythagorean hodograph quintic curve

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