Explicit \(\mu\)-bases for conic sections and planar rational cubic curves

DOI10.1016/j.cagd.2015.11.003zbMath1417.65096OpenAlexW2196283150MaRDI QIDQ1632396

Thomas W. Sederberg, Xuhui Wang, Ronald N. Goldman

Publication date: 14 December 2018

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2015.11.003

zbMATH Keywords

\(\mu\)-basisconic sectiondouble pointimplicit equationrational cubic curve

Mathematics Subject Classification ID

Singularities of curves, local rings (14H20) Computer-aided design (modeling of curves and surfaces) (65D17)

Cites Work

• A basis for the implicit representation of planar rational cubic Bézier curves
• Using Smith normal forms and \(\mu\)-bases to compute all the singularities of rational planar curves
• \(\mu \)-bases for polynomial systems in one variable
• \(\mu \)-bases and singularities of rational planar curves
• Axial moving lines and singularities of rational planar curves
• The moving line ideal basis of planar rational curves
• On the closed image of a rational map and the implicitization problem.
• Computing singular points of plane rational curves
• Computing the singularities of rational space curves
• Implicitization, inversion, and intersection of planar rational cubic curves
• The μ-basis of a planar rational curve—properties and computation
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