A control polygon scheme for design of planar \(C^2\) PH quintic spline curves

DOI10.1016/j.cagd.2006.09.005zbMath1171.65347OpenAlexW1988593714MaRDI QIDQ733392

Carla Manni, Rida T. Farouki, Maria Lucia Sampoli, Francesca Pelosi

Publication date: 16 October 2009

Published in: Computer Aided Geometric Design (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cagd.2006.09.005

zbMATH Keywords

spline interpolationNewton-Raphson methodPythagorean-hodograph curvescontrol polygonscubic B-spline curvesknot sequencemultiple knots

Mathematics Subject Classification ID

Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (20)

Construction of \(G^2\) planar Hermite interpolants with prescribed arc lengths ⋮ A note on Pythagorean hodograph quartic spiral ⋮ \(C^2\) Hermite interpolation by Pythagorean-hodograph quintic triarcs ⋮ Interpolation of \(G^1\) Hermite data by \(C^1\) cubic-like sparse Pythagorean hodograph splines ⋮ Algebraic and geometric characterizations of a class of planar quartic curves with rational offsets ⋮ Controlling extremal Pythagorean hodograph curves by Gauss-Legendre polygons ⋮ Planar Pythagorean-hodograph B-spline curves ⋮ Construction of planar quintic Pythagorean-hodograph curves by control-polygon constraints ⋮ On control polygons of quartic Pythagorean-hodograph curves ⋮ Interactive design of cubic IPH spline curves ⋮ On control polygons of Pythagorean hodograph septic curves ⋮ \(C^1\) Hermite interpolation with spatial Pythagorean-hodograph cubic biarcs ⋮ On interpolation by Planar cubic $G^2$ pythagorean-hodograph spline curves ⋮ Design of \(C^2\) algebraic-trigonometric Pythagorean hodograph splines with shape parameters ⋮ Local modification of Pythagorean-hodograph quintic spline curves using the B-spline form ⋮ 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 ⋮ Algorithm 952 ⋮ A new method to design cubic Pythagorean-hodograph spline curves with control polygon

Cites Work

• Real-time CNC interpolators for Pythagorean-hodograph curves
• The conformal map \(z\to z^ 2\) of the hodograph plane
• The elastic bending energy of Pythagorean-hodograph curves
• Characterization and construction of helical polynomial space curves.
• Clifford algebra, spin representation, and rational parameterization of curves and surfaces
• 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
• On calculating with B-splines
• Hermite interpolation by Pythagorean hodograph curves of degree seven
• Hermite Interpolation by Pythagorean Hodograph Quintics
• The Newton-Kantorovich Theorem
• The Kantorovich Theorem for Newton's Method
• The Numerical Evaluation of B-Splines
• Construction and shape analysis of PH quintic Hermite interpolants
• Performance analysis of CNC interpolators for time-dependent feedrates along PH curves
• Efficient solution of the complex quadratic tridiagonal system for \(C^2\) PH quintic splines
• A practical guide to splines.
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