Related papers: Approximation of conformal mappings by circle patt…
Circular arc graphs are graphs whose vertices can be represented as arcs on a circle such that any two vertices are adjacent if and only if their corresponding arcs intersect. Proper circular arc graphs are graphs which have a circular arc…
The aim of this paper is to prove that every continuous map from a compact subset of a real algebraic variety into a sphere can be approximated by piecewise-regular maps of class C^k, where k is an arbitrary integer.
The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial adjustment to the $\sinh$ map, and allows the treatment of a finite number of…
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using…
In this paper, we apply the classical Perron method to give a proof of the existence and uniqueness/rigidity result of a circle pattern on a closed surface equipped with conical spherical metric when prescribed measures of the angles of…
These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…
Discrete conformal mappings based on circle packing, vertex scaling, and related structures has had significant activity since Thurston proposed circle packing as a way to approximate conformal maps in the 1980s. The first convergence…
We consider the complexity of the recognition problem for two families of combinatorial structures. A graph $G=(V,E)$ is said to be an intersection graph of lines in space if every $v\in V$ can be mapped to a straight line $\ell (v)$ in…
A family of plane oriented continuous paths depending on a fixed real positive number $R$ is considered. For any point $x$ on the path, the previous points lie out of any circle of radius $R$ having at $x$ interior normal in a suitable…
We consider arrangements of axis-aligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of…
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
The problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the curvature error. Parametric polynomial curves of low degree are used and a geometric continuity is…
In this article, circular arcs are considered both individually and as elements of a piecewise circular curve. The endpoint parameterization proves to be quite advantageous here. The perspective of symplectic geometry provides new vectorial…
Spectral embedding provides a framework for solving perceptual organization problems, including image segmentation and figure/ground organization. From an affinity matrix describing pairwise relationships between pixels, it clusters pixels…
Multicriteria Decision Making problems are important both for individuals and groups. Pairwise comparisons have become popular in the theory and practice of preference modelling and quantification. We focus on decision problems where the…
Integer geometry on a plane deals with objects whose vertices are points in $\mathbb Z^2$. The congruence relation is provided by all affine transformations preserving the lattice $\mathbb Z^2$. In this paper we study circumscribed circles…
We consider a 3-dimensional Riemannian manifold V with a metric g and an affinor structure q. The local coordinates of these tensors are circulant matrices. In V we define an almost conformal transformation. Using that definition we…
The central problem of strip theory is the calculation of potential flowaround 2D sections. One particular method of solutions to this problem is conformal mapping of the body section to the unit circle over which a solution of potential…