Related papers: Numerical Reparametrization of Rational Parametric…
Computing the topology of an algebraic plane curve $\mathcal{C}$ means to compute a combinatorial graph that is isotopic to $\mathcal{C}$ and thus represents its topology in $\mathbb{R}^2$. We prove that, for a polynomial of degree $n$ with…
We consider the problem of answering connectivity queries on a real algebraic curve. The curve is given as the real trace of an algebraic curve, assumed to be in generic position, and being defined by some rational parametrizations. The…
Tropical geometry is sensitive to embeddings of algebraic varieties inside toric varieties. The purpose of this paper is to advertise tropical modifications as a tool to locally repair bad embeddings of plane curves, allowing the…
We present an algorithm to fair a given planar curve by a log-aesthetic curve (LAC). We show how a general LAC segment can be uniquely characterized by seven parameters and present a method of parametric approximation based on this fact.…
Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, the existing methods mostly suffer from the…
Offset curves for planar trajectories are interesting in the generation of tool paths for numerically controlled industrial machines and in trajectory planning methods for autonomous driving systems. Theoretical offset curves may exhibit…
In this paper, we study unirational differential curves and the corresponding differential rational parametrizations. We first investigate basic properties of proper differential rational parametrizations for unirational differential…
A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition. As a by-product it finds all such similarities, and…
The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…
In [Computer Aided Geometric Design 27 (2010), 212-231] the authors present an algorithm to parametrize approximately $\epsilon$-rational curves, and they show in 2 examples that the Hausdorff distance, w.r.t. to the Euclidean distance,…
In this paper, we describe an algorithm for fitting an analytic and bandlimited closed or open curve to interpolate an arbitrary collection of points in $\mathbb{R}^{2}$. The main idea is to smooth the parametrization of the curve by…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
The common approach to radial distortion is by the means of polynomial approximation, which introduces distortion-specific parameters into the camera model and requires estimation of these distortion parameters. The task of estimating…
We present the technique of parametrization of plane algebraic curves from a number theorist's point of view and present Kapferer's simple and beautiful (but little known) proof that nonsingular curves of degree > 2 cannot be parametrized…
We present an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces.
In this paper, we first summarize the existing algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. From these previous results, we derive a method that allows to easily…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
We consider the problem of computing the topology and describing the geometry of a parametric curve in $\mathbb{R}^n$. We present an algorithm, PTOPO, that constructs an abstract graph that is isotopic to the curve in the embedding space.…
Identification of model parameters in computer simulations is an important topic in computer experiments. We propose a new method, called the projected kernel calibration method, to estimate these model parameters. The proposed method is…
In this paper we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves belonging to the linear system are…