\(\mu \)-bases and singularities of rational planar curves

DOI10.1016/j.cagd.2009.08.001zbMath1205.14033OpenAlexW1964098848MaRDI QIDQ625249

Xiaohong Jia, Ronald N. Goldman

Publication date: 15 February 2011

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

Full work available at URL: https://doi.org/10.1016/j.cagd.2009.08.001

zbMATH Keywords

singularitiesblow upintersection multiplicityinfinitely near pointsrational planar curve\(\mu \)-basis\(\delta \)-invariant

Mathematics Subject Classification ID

Plane and space curves (14H50) Singularities of curves, local rings (14H20)

Related Items (16)

Algorithms for computing strong \(\mu\)-bases for rational tensor product surfaces ⋮ Complex \(\mu\)-bases for real quadric surfaces ⋮ Explicit \(\mu\)-bases for conic sections and planar rational cubic curves ⋮ Algebraic distance estimations for enriched isogeometric analysis ⋮ 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 ⋮ Role of moving planes and moving spheres following Dupin cyclides ⋮ Implicitization of rational hypersurfaces via linear syzygies: a practical overview ⋮ A study of nonlinear multiview varieties ⋮ Using Smith normal forms and \(\mu\)-bases to compute all the singularities of rational planar curves ⋮ Algorithm for computing \(\mu\)-bases of univariate polynomials ⋮ \(\mu\)-bases for complex rational curves ⋮ Rational curves over generalized complex numbers ⋮ Analysis and construction of rational curve parametrizations with non-ordinary singularities ⋮ Bounding the degrees of a minimal \(\mu\)-basis for a rational surface parametrization ⋮ Representing rational curve segments and surface patches using semi-algebraic sets

Cites Work

• Using Smith normal forms and \(\mu\)-bases to compute all the singularities of rational planar curves
• Computing self-intersection curves of rational ruled surfaces
• On the equations of the moving curve ideal of a rational algebraic plane curve
• The moving line ideal basis of planar rational curves
• A new implicit representation of a planar rational curve with high order singularity
• Computation of the singularities of parametric plane curves
• Computing singular points of plane rational curves
• The μ-basis of a planar rational curve—properties and computation
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