Efficient topology determination of implicitly defined algebraic plane curves

Authors:
Laureano Gonzalez-Vega;Ioana Necula
Affiliations:
Departamento de Matematicas, Estadistica y Computacion Facultad de Ciencias, Universidad de Cantabria, Santander 39005, Spain;Departamento de Matematicas, Estadistica y Computacion Facultad de Ciencias, Universidad de Cantabria, Santander 39005, Spain
Venue:
Computer Aided Geometric Design
Year:
2002

Citing 9
Cited 56

Algebraic decomposition of regular curves

Journal of Symbolic Computation
A polynomial-time algorithm for the topological type of a real algebraic curve

Journal of Symbolic Computation
Tracing surface intersections

Computer Aided Geometric Design
An improved upper complexity bound for the topology computation of a real algebraic plane curve

Journal of Complexity - Special issue for the Foundations of Computational Mathematics conference, Rio de Janeiro, Brazil, Jan. 1997
An efficient method for analyzing the topology of plane real algebraic curves

Selected papers presented at the international IMACS symposium on Symbolic computation, new trends and developments
Efficient and accurate B-rep generation of low degree sculptured solids using exact arithmetic: I—representations

Computer Aided Geometric Design
Efficient and accurate B-rep generation of low degree sculptured solids using arithmetic: II—computation

Computer Aided Geometric Design
New structure theorem for subresultants

Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Algorithms for the Shape of Semialgebraic Sets. A New Approach

AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Linear perturbation methods for topologically consistent representations of free-form surface intersections

Computer Aided Geometric Design
Rational quadratic approximation to real algebraic curves

Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
On the exact computation of the topology of real algebraic curves

SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Complete subdivision algorithms, I: intersection of Bezier curves

Proceedings of the twenty-second annual symposium on Computational geometry
Exact, efficient, and complete arrangement computation for cubic curves

Computational Geometry: Theory and Applications
Polygonization of multi-component non-manifold implicit surfaces through a symbolic-numerical continuation algorithm

Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
Computing roots of polynomials by quadratic clipping

Computer Aided Geometric Design
A delineability-based method for computing critical sets of algebraic surfaces

Journal of Symbolic Computation
Computing the topology of a real algebraic plane curve whose equation is not directly available

Proceedings of the 2007 international workshop on Symbolic-numeric computation
On the complexity of real solving bivariate systems

Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Fast and exact geometric analysis of real algebraic plane curves

Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Evaluating the boundary and covering degree of planar Minkowski sums and other geometrical convolutions

Journal of Computational and Applied Mathematics
ISSAC 2007 poster abstracts

ACM Communications in Computer Algebra
Dual evolution of planar parametric spline curves and T-spline level sets

Computer-Aided Design
Topology of real algebraic space curves

Journal of Symbolic Computation
Good global behavior of offsets to plane algebraic curves

Journal of Symbolic Computation
Exact geometric-topological analysis of algebraic surfaces

Proceedings of the twenty-fourth annual symposium on Computational geometry
On the computation of the topology of a non-reduced implicit space curve

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Improving the topology computation of an arrangement of cubics

Computational Geometry: Theory and Applications
Topology and arrangement computation of semi-algebraic planar curves

Computer Aided Geometric Design
Real algebraic numbers and polynomial systems of small degree

Theoretical Computer Science
Good local behavior of offsets to rational regular algebraic surfaces

Journal of Symbolic Computation
A BSP-based algorithm for dimensionally nonhomogeneous planar implicit curves with topological guarantees

ACM Transactions on Graphics (TOG)
On the asymptotic and practical complexity of solving bivariate systems over the reals

Journal of Symbolic Computation
On the topology of planar algebraic curves

Proceedings of the twenty-fifth annual symposium on Computational geometry
Isotopic triangulation of a real algebraic surface

Journal of Symbolic Computation
Root isolation for bivariate polynomial systems with local generic position method

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
An efficient algorithm for the stratification and triangulation of an algebraic surface

Computational Geometry: Theory and Applications
Solving the implicitization, inversion and reparametrization problems for rational curves through subresultants

Computer Aided Geometric Design
Exact, efficient, and complete arrangement computation for cubic curves

Computational Geometry: Theory and Applications
Rational quadratic approximation to real algebraic curves

Computer Aided Geometric Design
Some applications of scalar and vector fields to geometric processing of surfaces

Computers and Graphics
On the different shapes arising in a family of plane rational curves depending on a parameter

Computer Aided Geometric Design
Computation of the topology of real algebraic space curves

Journal of Symbolic Computation
Local parametrization of cubic surfaces

Journal of Symbolic Computation
Regularity criteria for the topology of algebraic curves and surfaces

Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Computing the topology of an arrangement of quartics

Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Topology of 2D and 3D rational curves

Computer Aided Geometric Design
On solving systems of bivariate polynomials

ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Collision and intersection detection of two ruled surfaces using bracket method

Computer Aided Geometric Design
A worst-case bound for topology computation of algebraic curves

Journal of Symbolic Computation
The SARAG library: some algorithms in real algebraic geometry

ICMS'06 Proceedings of the Second international conference on Mathematical Software
Fat arcs for implicitly defined curves

MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Determining the topology of real algebraic surfaces

IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Resultant-based methods for plane curves intersection problems

CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
Real solving of bivariate polynomial systems

CASC'05 Proceedings of the 8th international conference on Computer Algebra in Scientific Computing
On the isotopic meshing of an algebraic implicit surface

Journal of Symbolic Computation
Approximating algebraic space curves by circular arcs

Proceedings of the 7th international conference on Curves and Surfaces
Computing the shapes arising in a family of space rational curves depending on one parameter

Computer Aided Geometric Design
Arrangement computation for planar algebraic curves

Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation
Homeomorphic approximation of the intersection curve of two rational surfaces

Computer Aided Geometric Design
On the shape of curves that are rational in polar coordinates

Computer Aided Geometric Design
Using implicit equations of parametric curves and surfaces without computing them: Polynomial algebra by values

Computer Aided Geometric Design
A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points

Journal of Computational and Applied Mathematics
Certified rational parametric approximation of real algebraic space curves with local generic position method

Journal of Symbolic Computation
Special Section on CAD/Graphics 2013: A continuation algorithm for planar implicit curves with singularities

Computers and Graphics

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper is devoted to present a new algorithm computing in a very efficient way the topology of a real algebraic plane curve defined implicitly. This algorithm proceeds in a seminumerical way by performing a symbolic preprocessing which allows later to accomplish the numerical computations in a very accurate way.