Pipe surfaces with rational spine curve are rational

DOI10.1016/0167-8396(95)00051-8zbMath0900.68410OpenAlexW2089493441MaRDI QIDQ671591

Helmut Pottmann, Wei Lu

Publication date: 27 February 1997

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

Full work available at URL: https://doi.org/10.1016/0167-8396(95)00051-8

zbMATH Keywords

Pythagorean-hodograph curveBlend surfaceNormal ringed surfaceOffset surfacePipe surfaceRational parameterizationRational surface

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Approximation by rational functions (41A20)

Related Items (11)

Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces ⋮ An algorithm for finding intersection between ball B-spline curves ⋮ A Laguerre geometric approach to rational offsets ⋮ \(G^{1}\) Hermite interpolation by PH cubics revisited ⋮ On the parameterization of rational ringed surfaces and rational canal surfaces ⋮ Rational fixed radius rolling ball blends between natural quadrics ⋮ Rational Offset Surfaces and their Modeling Applications ⋮ On quadratic two-parameter families of spheres and their envelopes ⋮ PN surfaces and their convolutions with rational surfaces ⋮ Rational two-parameter families of spheres and rational offset surfaces ⋮ Analysis and applications of pipe surfaces

Cites Work

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• Offset-rational parametric plane curves
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• The conformal map \(z\to z^ 2\) of the hodograph plane
• Rationality of the offsets to algebraic curves and surfaces
• Computing rational parametrizations of canal surfaces
• Construction of \(C^ 2\) Pythagorean-hodograph interpolating splines by the homotopy method
• Curvature continuous connections of cones and cylinders
• Pythagorean-hodograph space curves
• Curve design with rational Pythagorean-hodograph curves
• Hermite Interpolation by Pythagorean Hodograph Quintics

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