Using Smith normal forms and \(\mu\)-bases to compute all the singularities of rational planar curves

DOI10.1016/j.cagd.2012.02.001zbMath1298.65028OpenAlexW1819431723MaRDI QIDQ448987

Xiaohong Jia, 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.2012.02.001

zbMATH Keywords

singularitiesblow-upintersection multiplicity\(\mu\)-basisinfinitely near pointsrational planar curve

Mathematics Subject Classification ID

Computational aspects of algebraic curves (14Q05) Singularities of curves, local rings (14H20) Computer-aided design (modeling of curves and surfaces) (65D17)

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Complex \(\mu\)-bases for real quadric surfaces, Explicit \(\mu\)-bases for conic sections and planar rational cubic curves, 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, \(\mu \)-bases and singularities of rational planar curves, \(\mu\)-bases for complex rational curves, Analysis and construction of rational curve parametrizations with non-ordinary singularities, An in depth analysis, via resultants, of the singularities of a parametric curve, \(\mu\)-bases for rational canal surfaces, Singular factors of rational plane curves, Hybrid second order method for orthogonal projection onto parametric curve in \(n\)-dimensional Euclidean space

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