Implicitizing rational surfaces of revolution using \(\mu \)-bases

DOI10.1016/j.cagd.2012.02.003zbMath1256.65016OpenAlexW1987971723MaRDI QIDQ448991

Xiaoran Shi, Ronald N. Goldman

Publication date: 11 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.2012.02.003

zbMATH Keywords

numerical examplesimplicitization\(\mu\)-basisrational surface of revolutionresulting matrix

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 (15)

Algorithms for computing strong \(\mu\)-bases for rational tensor product surfaces ⋮ Implicitizing rational surfaces using moving quadrics constructed from moving planes ⋮ An improved algorithm for constructing moving quadrics from moving planes ⋮ 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 ⋮ Ruled Surfaces of Revolution with Moving Axes and Angles ⋮ Using \(\mu \)-bases to reduce the degree in the computation of projective equivalences between rational curves in \(n\)-space ⋮ Survey on the theory and applications of \(\mu\)-bases for rational curves and surfaces ⋮ Role of moving planes and moving spheres following Dupin cyclides ⋮ Using \(\mu \)-bases to implicitize rational surfaces with a pair of orthogonal directrices ⋮ On tubular vs. swung surfaces ⋮ Determining surfaces of revolution from their implicit equations ⋮ \(\mu\)-bases for rational canal surfaces ⋮ Reparametrizing swung surfaces over the reals ⋮ Implicitizing rational surfaces without base points by moving planes and moving quadrics

Cites Work

• Shifting planes always implicitize a surface of revolution
• The moving line ideal basis of planar rational curves
• The \(\mu \)-basis and implicitization of a rational parametric surface
• The μ-basis of a planar rational curve—properties and computation
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