Using \(\mu \)-bases to implicitize rational surfaces with a pair of orthogonal directrices

DOI10.1016/j.cagd.2012.03.026zbMath1256.65017OpenAlexW2040266128WikidataQ57756669 ScholiaQ57756669MaRDI QIDQ450250

Xuhui Wang, Xiaoran Shi, Ronald N. Goldman

Publication date: 13 September 2012

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2012.03.026

zbMATH Keywords

numerical examplesimplicitizationmoving planerational surface\(\mu\)-basissparse resultantdirectrixmoving lineorthogonal directrices

Mathematics Subject Classification ID

Computer science aspects of computer-aided design (68U07) Computer-aided design (modeling of curves and surfaces) (65D17) Descriptive geometry (51N05)

Related Items (8)

Algorithms for computing strong \(\mu\)-bases for rational tensor product surfaces ⋮ Strong $\mu$-Bases for Rational Tensor Product Surfaces and Extraneous Factors Associated to Bad Base Points and Anomalies at Infinity ⋮ Using moving planes to implicitize rational surfaces generated from a planar curve and a space curve ⋮ Syzygies for translational surfaces ⋮ Survey on the theory and applications of \(\mu\)-bases for rational curves and surfaces ⋮ Role of moving planes and moving spheres following Dupin cyclides ⋮ Algorithm for computing \(\mu\)-bases of univariate polynomials ⋮ \(\mu\)-bases for rational canal surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Implicitizing rational surfaces of revolution using \(\mu \)-bases
• The moving line ideal basis of planar rational curves
• Revisiting the \(\mu\)-basis of a rational ruled surface.
• The \(\mu \)-basis and implicitization of a rational parametric surface
• The μ-basis of a planar rational curve—properties and computation
• Implicitization and parametrization of quadratic surfaces with one simple base point
• The \(\mu\)-basis of a rational ruled surface

This page was built for publication: Using \(\mu \)-bases to implicitize rational surfaces with a pair of orthogonal directrices