Related papers: Newton-Puiseux algorithm and triple points for pla…
Let $Y=\{f(x,y)=0\}$ be the germ of an irreducible plane curve. We present an algorithm to obtain polynomials, whose valuations coincide with the semigroup generators of $Y$. These polynomials are obtained sequentially, adding terms to the…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
Pretropisms are candidates for the leading exponents of Puiseux series that represent solutions of polynomial systems. To find pretropisms, we propose an exact gift wrapping algorithm to prune the tree of edges of a tuple of Newton…
We present an algorithm for detecting basepoints of linear series of curves in the plane. Moreover, we give an algorithm for constructing a linear series of curves in the plane for given basepoints. The underlying method of these algorithms…
We present a procedure to approximate a plane contour by piecewise polynomial functions, depending on various parameters, such as degree, number of local patches, selection of knots. This procedure aims to be adopted to study how…
In this article we give an implementation of the standard algorithm to segment a real algebraic plane curve defined implicitly. Our implementation is efficient and simpler than previous. We use global information to count the number of…
We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is…
In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
We study the relation between the type of a double point of a plane curve and the curvilinear 0-dimensional subschemes of the curve at the point. An Algorithm related to a classical procedure for the study of double points via osculating…
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
In this paper, we present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. That is, we deal with mathematical objects that are assumed to be given approximately. More precisely, given a tolerance…
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…
We provide a very effective and explicit algorithm of finding a Puiseux expansion of a cuspidal singularity of a plane curve, when this singularity is given in a parametric form.
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main…
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main…
We give an algorithm to compute term by term multivariate Puiseux series expansions of series arising as local parametrizations of zeroes of systems of algebraic equations at singular points. The algorithm is an extension of Newton's method…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two…
We show how the Eulcidean algorithm for polynomials can be used to find the intersection points, with multiplicities, of two plane algebraic curves.
We study deformations of plane curve singularities from an analytic point of view and obtain some new concrete results. We show some rather unexpected properties of Puiseux coefficients treated as functions on a suitably defined parameter…