A polynomial-time algorithm for the topological type of a real algebraic curve
Journal of Symbolic Computation
Computer Aided Geometric Design
On local implicit approximation and its applications
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Automatic parameterization of rational curves and surfaces IV: algebraic space curves
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Mathematics for computer algebra
Mathematics for computer algebra
Symbolic parametrization of curves
Journal of Symbolic Computation
On the choice of pencils in the parametrization of curves
Journal of Symbolic Computation
Surface-to-Surface Intersections
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
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
Rational parametrizations of algebraic curves using a canonical divisor
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Fundamental problems of algorithmic algebra
Fundamental problems of algorithmic algebra
Numerical parameterization of curves and surfaces
Computer Aided Geometric Design
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
An Improved Projection Operation for Cylindrical Algebraic Decomposition
EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Enhancing Levin's method for computing quadric-surface intersections
Computer Aided Geometric Design
On the exact computation of the topology of real algebraic curves
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)
A predictor–corrector-type technique for the approximate parameterization of intersection curves
Applicable Algebra in Engineering, Communication and Computing
Near-optimal parameterization of the intersection of quadrics: II. A classification of pencils
Journal of Symbolic Computation
Near-optimal parameterization of the intersection of quadrics: I. The generic algorithm
Journal of Symbolic Computation
Journal of Symbolic Computation
Exact and efficient 2D-arrangements of arbitrary algebraic curves
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Topology of real algebraic space curves
Journal of Symbolic Computation
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
Complete subdivision algorithms, II: isotopic meshing of singular algebraic curves
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
Topology and arrangement computation of semi-algebraic planar curves
Computer Aided Geometric Design
Using signature sequences to classify intersection curves of two quadrics
Computer Aided Geometric Design
On the asymptotic and practical complexity of solving bivariate systems over the reals
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
Rational quadratic approximation to real algebraic curves
Computer Aided Geometric Design
Approximate parametrization of plane algebraic curves by linear systems of curves
Computer Aided Geometric Design
Computation of the topology of real algebraic space curves
Journal of Symbolic Computation
A worst-case bound for topology computation of algebraic curves
Journal of Symbolic Computation
Root isolation of zero-dimensional polynomial systems with linear univariate representation
Journal of Symbolic Computation
On the isotopic meshing of an algebraic implicit surface
Journal of Symbolic Computation
Certified approximation of parametric space curves with cubic B-spline curves
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
When Newton meets Descartes: a simple and fast algorithm to isolate the real roots of a polynomial
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
Rational Hausdorff divisors: A new approach to the approximate parametrization of curves
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
In this paper, an algorithm is given for determining the topology of an algebraic space curve and to compute a certified G^1 rational parametric approximation of the algebraic space curve. The algorithm works by extending to dimension one the local generic position method for solving zero-dimensional polynomial equation systems. Here, certified means that the approximation curve and the original curve have the same topology and their Hausdorff distance is smaller than a given precision. The main advantage of the algorithm, inherited from the local generic position method, is that the topology computation and approximation for a space curve are directly reduced to the same tasks for two plane curves. In particular, an error bound of the approximation space curve is deduced explicitly from the error bounds of the approximation plane curves. The complexity of the algorithm is also analyzed. Its effectivity is shown on some non-trivial examples.