Revisiting the \(\mu\)-basis of a rational ruled surface.

DOI10.1016/S0747-7171(03)00064-6zbMath1037.14014MaRDI QIDQ1426142

Wenping Wang, Falai Chen

Publication date: 14 March 2004

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

zbMATH Keywords

\(\mu\)-basisImplicitizationrational ruled surfaceMoving plane

Mathematics Subject Classification ID

Rational and ruled surfaces (14J26)

Related Items (30)

Algorithms for computing strong \(\mu\)-bases for rational tensor product surfaces ⋮ A survey of the representations of rational ruled 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 ⋮ Computing \(\mu\)-bases from algebraic ruled surfaces ⋮ Efficient Groebner walk conversion for implicitization of geometric objects ⋮ 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 ⋮ Computing \(\mu\)-bases of univariate polynomial matrices using polynomial matrix factorization ⋮ Survey on the theory and applications of \(\mu\)-bases for rational curves and surfaces ⋮ A constructive approach to implicitizing rational surfaces with LCI base points by moving planes and moving quadrics ⋮ Implicitization and parametrization of quadratic and cubic surfaces by \(\mu\)-bases ⋮ Bounds for degrees of syzygies of polynomials defining a grade two ideal ⋮ Role of moving planes and moving spheres following Dupin cyclides ⋮ Quaternion rational surfaces ⋮ Computing self-intersection curves of rational ruled surfaces ⋮ Axial moving planes and singularities of rational space curves ⋮ Implicitizing ruled translational surfaces ⋮ Using \(\mu \)-bases to implicitize rational surfaces with a pair of orthogonal directrices ⋮ A new class of term orders for elimination ⋮ The \(\mu \)-basis and implicitization of a rational parametric surface ⋮ \(\mu\)-bases for rational canal surfaces ⋮ Bounding the degrees of a minimal \(\mu\)-basis for a rational surface parametrization ⋮ Affine equivalences, isometries and symmetries of ruled rational surfaces ⋮ Division algorithms for Bernstein polynomials ⋮ A computational study of ruled surfaces ⋮ Implicitization of rational ruled surfaces with \(\mu \)-bases ⋮ Implicitizing rational surfaces without base points by moving planes and moving quadrics

Cites Work

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• The moving line ideal basis of planar rational curves
• Curve implicitization using moving lines
• The \(\mu\)-basis of a rational ruled surface

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