\(\mu\)-bases for rational canal surfaces

DOI10.1016/j.cagd.2018.12.001zbMath1505.65108OpenAlexW2903819500MaRDI QIDQ669019

Shanshan Yao, Xiaohong Jia

Publication date: 20 March 2019

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2018.12.001

zbMATH Keywords

parametrizationinversion formula\(\mu\)-basissyzygycanal surface

Mathematics Subject Classification ID

Computational aspects of algebraic surfaces (14Q10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items

Bounds for degrees of syzygies of polynomials defining a grade two ideal

Cites Work

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• Role of moving planes and moving spheres following Dupin cyclides
• Using Smith normal forms and \(\mu\)-bases to compute all the singularities of rational planar curves
• Implicitizing rational surfaces of revolution using \(\mu \)-bases
• Using \(\mu \)-bases to implicitize rational surfaces with a pair of orthogonal directrices
• On the parameterization of rational ringed surfaces and rational canal surfaces
• \(\mu \)-bases for polynomial systems in one variable
• Computing self-intersection curves of rational ruled surfaces
• Implicitization and parametrization of quadratic and cubic surfaces by \(\mu\)-bases
• Minimal rational parametrizations of canal surfaces
• The moving line ideal basis of planar rational curves
• Computing rational parametrizations of canal surfaces
• Revisiting the \(\mu\)-basis of a rational ruled surface.
• Survey on the theory and applications of \(\mu\)-bases for rational curves and surfaces
• Algorithms for computing strong \(\mu\)-bases for rational tensor product surfaces
• The implicit equation of a canal surface
• The \(\mu \)-basis and implicitization of a rational parametric surface
• SOME CHARACTERIZATIONS OF CANAL SURFACES
• The μ-basis of a planar rational curve—properties and computation
• Polynomial matrix primitive factorization over arbitrary coefficient field and related results
• Computing μ-bases of rational curves and surfaces using polynomial matrix factorization
• Strong $\mu$-Bases for Rational Tensor Product Surfaces and Extraneous Factors Associated to Bad Base Points and Anomalies at Infinity
• Implicitization and parametrization of quadratic surfaces with one simple base point