Automatic parametrization of rational curves and surfaces II: cubics and cubicoids
Computer-Aided Design
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Parametrization of cubic algebraic surfaces
Proceedings on Mathematics of surfaces II
Automatic parameterization of rational curves and surfaces IV: algebraic space curves
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
Symbolic parametrization of curves
Journal of Symbolic Computation
On the choice of pencils in the parametrization of curves
Journal of Symbolic Computation
Parameterization in finite precision
Proceedings of the conference on Graphics interface '92
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
Parametrization of algebraic curves over optimal field extensions
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Rational parametrizations of algebraic curves using a canonical divisor
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Computing rational parametrizations of canal surfaces
Journal of Symbolic Computation - Special issue: parametric algebraic curves and applications
Rational parametrization of surfaces
Journal of Symbolic Computation
Numerical parameterization of curves and surfaces
Computer Aided Geometric Design
Proper parametrization of real tubular surfaces
Journal of Symbolic Computation
Efficient topology determination of implicitly defined algebraic plane curves
Computer Aided Geometric Design
Near-optimal parameterization of the intersection of quadrics
Proceedings of the nineteenth annual symposium on Computational geometry
Approximate parameterization by planar rational curves
Proceedings of the 20th spring conference on Computer graphics
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
A predictor–corrector-type technique for the approximate parameterization of intersection curves
Applicable Algebra in Engineering, Communication and Computing
A Subdivision Arrangement Algorithm for Semi-Algebraic Curves: An Overview
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
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
On the topology of planar algebraic curves
Proceedings of the twenty-fifth annual symposium on Computational geometry
Circular spline fitting using an evolution process
Journal of Computational and Applied Mathematics
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
Local parametrization of cubic surfaces
Journal of Symbolic Computation
Journal of Symbolic Computation
Rational Hausdorff divisors: A new approach to the approximate parametrization of curves
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
A simple algorithm for computing an approximate parameterization of real space algebraic curves using their graphs of critical points is designed and studied in this paper. The first step is determining a suitable space graph which contains all critical points of a real algebraic space curve C implicitly defined as the complete intersection of two surfaces. The construction of this graph is based on one projection of C in a general position onto an xy-plane and on an intentional choice of vertices. The second part of the designed method is a computation of a spline curve which replaces the edges of the constructed graph by segments of a chosen free-form curve. This step is formulated as an optimization problem when the objective function approximates the integral of the squared Euclidean distance of the constructed approximate curve to the intersection curve. The presented method, based on combining symbolic and numerical steps to the approximation problem, provides approximate parameterizations of space algebraic curves from a small number of approximating arcs. It may serve as a first step to several problems originating in technical practice where approximation curve parameterizations are needed.