Finding the topology of implicitly defined two algebraic plane curves

DOI10.1007/s11424-012-1145-7zbMath1314.68352OpenAlexW2045209339MaRDI QIDQ488901

Ben Gao, Yu-Fu Chen

Publication date: 27 January 2015

Published in: Journal of Systems Science and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11424-012-1145-7

zbMATH Keywords

topologyalgebraic curvescylindrical algebraic decompositiongeneric positionsubresultants sequence

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computer science aspects of computer-aided design (68U07) Computer-aided design (modeling of curves and surfaces) (65D17)

Related Items (7)

Asymptotic behavior of an implicit algebraic plane curve ⋮ On the complexity of computing the topology of real algebraic space curves ⋮ On the topology and isotopic meshing of plane algebraic curves ⋮ Isotopic meshing of a real algebraic space curve ⋮ Asymptotes of space curves ⋮ Characterizing the finiteness of the Hausdorff distance between two algebraic curves ⋮ Determining the asymptotic family of an implicit curve

Uses Software

• MAPC
• Lgp

Cites Work

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• Efficient and exact manipulation of algebraic points and curves
• Tracing surface intersections
• Efficient topology determination of implicitly defined algebraic plane curves.
• Rational quadratic approximation to real algebraic curves
• An exact and efficient approach for computing a cell in an arrangement of quadrics
• Root isolation for bivariate polynomial systems with local generic position method
• Cylindrical Algebraic Decomposition I: The Basic Algorithm
• Algorithms in real algebraic geometry

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