Local shape of offsets to algebraic curves

DOI10.1016/j.jsc.2006.12.001zbMath1123.14031OpenAlexW2088782186MaRDI QIDQ2457426

Juan Gerardo Alcázar, Juan Rafael Sendra

Publication date: 23 October 2007

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

Full work available at URL: https://doi.org/10.1016/j.jsc.2006.12.001

zbMATH Keywords

curvatureoffset curveoffset shapeoffset topology

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Plane and space curves (14H50) Computational aspects of algebraic curves (14Q05) Singularities of curves, local rings (14H20)

Related Items (12)

Parameterizing surfaces with certain special support functions, including offsets of quadrics and rationally supported surfaces ⋮ Computing the topology of a plane or space hyperelliptic curve ⋮ The square-freeness of the offset equation to a rational planar curve, computed via resultants ⋮ Topology of 2D and 3D rational curves ⋮ Envelope computation in the plane by approximate implicitization ⋮ Good global behavior of offsets to plane algebraic curves ⋮ Local shape of offsets to algebraic curves ⋮ A new method to compute the singularities of offsets to rational plane curves ⋮ On convolutions of algebraic curves ⋮ Good local behavior of offsets to rational regular algebraic surfaces ⋮ Local shape of generalized offsets to algebraic curves ⋮ Envelopes and offsets of two algebraic plane curves: exploration of their similarities and differences

Uses Software

• CASA

Cites Work

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• Offset-rational parametric plane curves
• Rational curves and surfaces with rational offsets
• Algebraic properties of plane offset curves
• A Laguerre geometric approach to rational offsets
• Genus formula for generalized offset curves
• Parametric generalized offsets to hypersurfaces
• Algebraic analysis of offsets to hypersurfaces
• Degree formulae for offset curves
• Normal parametrizations of algebraic plane curves
• Computation of the topology of real algebraic space curves
• Local shape of offsets to algebraic curves
• Analytic properties of plane offset curves
• Rationality analysis and direct parametrization of generalized offsets to quadrics.

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