Implicitization and parametrization of quadratic and cubic surfaces by \(\mu\)-bases

DOI10.1007/s00607-006-0192-0zbMath1116.65023OpenAlexW2014666561WikidataQ57533659 ScholiaQ57533659MaRDI QIDQ884712

Jiansong Deng, Falai Chen, Li-Yong Shen

Publication date: 7 June 2007

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00607-006-0192-0

zbMATH Keywords

algorithmsparametrizationgeometric objectsimplicitizationcubic surfacesquadricsbase point

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18)

Related Items (13)

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 ⋮ Complex \(\mu\)-bases for real quadric surfaces ⋮ Two additional advantages of complex \(\mu\)-bases for non-ruled real quadric surfaces ⋮ 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 ⋮ Implicitization, parameterization and singularity computation of Steiner surfaces using moving surfaces ⋮ \(\mu\)-bases for rational canal surfaces ⋮ Behavior of the fiber and the base points of parametrizations under projections ⋮ Implicitizing rational surfaces without base points by moving planes and moving quadrics

Cites Work

• Unnamed Item
• Degree, multiplicity, and inversion formulas for rational surfaces using \(u\)-resultants
• Implicit representation of rational parametric surfaces
• 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
• Computing μ-bases of rational curves and surfaces using polynomial matrix factorization
• The \(\mu\)-basis of a rational ruled surface
• Implicitization and parametrization of nonsingular cubic surfaces

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