Efficient topology determination of implicitly defined algebraic plane curves.

DOI10.1016/S0167-8396(02)00167-XzbMath1043.68105OpenAlexW1966047467MaRDI QIDQ1852882

Laureano Gonzalez-Vega, Ioana Necula

Publication date: 21 January 2003

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

Full work available at URL: https://doi.org/10.1016/s0167-8396(02)00167-x

zbMATH Keywords

Algebraic curves Seminumerical algorithms Topology computation

Mathematics Subject Classification ID

Computer science aspects of computer-aided design (68U07) Computational aspects of algebraic curves (14Q05) Computer-aided design (modeling of curves and surfaces) (65D17) Topology of real algebraic varieties (14P25)

Related Items

An algebraic framework for computing the topology of offsets to rational curves ⋮ Real algebraic numbers and polynomial systems of small degree ⋮ Linear perturbation methods for topologically consistent representations of free-form surface intersections ⋮ Rational quadratic approximation to real algebraic curves ⋮ Asymptotic behavior of an implicit algebraic plane curve ⋮ Identifying and approximating monotonous segments of algebraic curves using support function representation ⋮ On the complexity of computing the topology of real algebraic space curves ⋮ Computing the topology of a plane or space hyperelliptic curve ⋮ On the topology and isotopic meshing of plane algebraic curves ⋮ Exact symbolic-numeric computation of planar algebraic curves ⋮ Computing the topology of the image of a parametric planar curve under a birational transformation ⋮ Globally certified \(G^1\) approximation of planar algebraic curves ⋮ Solving the implicitization, inversion and reparametrization problems for rational curves through subresultants ⋮ On the isotopic meshing of an algebraic implicit surface ⋮ On the topology of real algebraic plane curves ⋮ Avoiding the general position condition when computing the topology of a real algebraic plane curve defined implicitly ⋮ On the different shapes arising in a family of plane rational curves depending on a parameter ⋮ Topology of 2D and 3D rational curves ⋮ Collision and intersection detection of two ruled surfaces using bracket method ⋮ On the Topology of the Intersection Curve of Two Real Parameterized Algebraic Surfaces ⋮ Certified rational parametric approximation of real algebraic space curves with local generic position method ⋮ Computing the shapes arising in a family of space rational curves depending on one parameter ⋮ Computing the topology of a real algebraic plane curve whose defining equations are available only ``by values ⋮ Sixty-Four Curves of Degree Six ⋮ Isotopic meshing of a real algebraic space curve ⋮ An evolution-based approach for approximate parameterization of implicitly defined curves by polynomial parametric spline curves ⋮ Parallel computation of real solving bivariate polynomial systems by zero-matching method ⋮ Asymptotes of space curves ⋮ Good global behavior of offsets to plane algebraic curves ⋮ Separating linear forms and rational univariate representations of bivariate systems ⋮ A delineability-based method for computing critical sets of algebraic surfaces ⋮ Computation of the topology of real algebraic space curves ⋮ Local parametrization of cubic surfaces ⋮ Determination of the tangents for a real plane algebraic curve ⋮ Computing the intersection of two ruled surfaces by using a new algebraic approach ⋮ Characterizing the finiteness of the Hausdorff distance between two algebraic curves ⋮ Finding the topology of implicitly defined two algebraic plane curves ⋮ Continuous detection of the variations of the intersection curve of two moving quadrics in 3-dimensional projective space ⋮ Computing the asymptotes for a real plane algebraic curve ⋮ Improving the topology computation of an arrangement of cubics ⋮ Evaluating the boundary and covering degree of planar Minkowski sums and other geometrical convolutions ⋮ On the shape of curves that are rational in polar coordinates ⋮ Topology of real algebraic space curves ⋮ Computation of the topological type of a real Riemann surface ⋮ TOPOLOGY OF FAMILIES OF ALGEBRAIC CURVES CONTINUOUSLY DEPENDING ON A PARAMETER, AND APPLICATIONS ⋮ Homeomorphic approximation of the intersection curve of two rational surfaces ⋮ Tools for analyzing the intersection curve between two quadrics through projection and lifting ⋮ Fat Arcs for Implicitly Defined Curves ⋮ Exact, efficient, and complete arrangement computation for cubic curves ⋮ Guaranteed consistency of surface intersections and trimmed surfaces using a coupled topology resolution and domain decomposition scheme ⋮ Good local behavior of offsets to rational regular algebraic surfaces ⋮ Computing roots of polynomials by quadratic clipping ⋮ Topology and arrangement computation of semi-algebraic planar curves ⋮ On the asymptotic and practical complexity of solving bivariate systems over the reals ⋮ Isotopic triangulation of a real algebraic surface ⋮ A worst-case bound for topology computation of algebraic curves ⋮ An efficient algorithm for the stratification and triangulation of an algebraic surface ⋮ Determining the asymptotic family of an implicit curve ⋮ Computing the topology of an arrangement of implicitly defined real algebraic plane curves ⋮ Boundary evaluation algorithms for Minkowski combinations of complex sets using topological analysis of implicit curves ⋮ Bounds for polynomials on algebraic numbers and application to curve topology

Cites Work