Related papers: Approximation of conformal mappings by circle patt…
We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the…
A matching in a graph $G$ is a set of independent edges in $G$. A perfect matching in a graph $G$ is a matching which saturates all the vertices of $G$. A fractional perfect matching in a graph $G$ is a function $h:E(G)\rightarrow [0,1]$…
Graph matching is the process of computing the similarity between two graphs. Depending on the requirement, it can be exact or inexact. Exact graph matching requires a strict correspondence between nodes of two graphs, whereas inexact…
We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship…
Map vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least a unit distance apart. The plane-width of a graph is the minimum diameter of the image of the vertex set over all…
A closed-form solution for the boundary of the flat state of an orthogonal cross section of contiguous surface geometry formed by the intersection of two cylinders of equal radii oriented in dual directions of rotation about their…
Geometric consistency, i.e. the preservation of neighbourhoods, is a natural and strong prior in 3D shape matching. Geometrically consistent matchings are crucial for many downstream applications, such as texture transfer or statistical…
A plane near-triangulation G can be decomposed into a collection of induced subgraphs, described here as the W-components of G, such that G is perfect (respectively, chordal) if and only if each of its W-components is perfect (respectively,…
This paper presents a complete Pascal interpolation scheme for use in the plane geometry mapping applied in association with numerical methods. The geometry of a domain element is approximated by a complete Pascal polynomial. The…
The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be…
Cycle consistency has long been exploited as a powerful prior for jointly optimizing maps within a collection of shapes. In this paper, we investigate its utility in the approaches of Deep Functional Maps, which are considered…
Quasiconformal maps in the complex plane are homeomorphisms that satisfy certain geometric distortion inequalities; infinitesimally, they map circles to ellipses with bounded eccentricity. The local distortion properties of these maps give…
A rectangulation is a tiling of a rectangle by a finite number of rectangles. The rectangulation is called generic if no four of its rectangles share a single corner. We initiate the enumeration of generic rectangulations up to…
Two triangle meshes are conformally equivalent if for any pair of incident triangles the absolute values of the corresponding cross-ratios of the four vertices agree. Such a pair can be considered as preimage and image of a discrete…
We consider ``hyperideal'' circle patterns, i.e. patterns of disks appearing in the definition of the Delaunay decomposition associated to a set of disjoint disks, possibly with cone singularities at the center of those disks. Hyperideal…
We consider circle packings and, more generally, Delaunay circle patterns - arrangements of circles arising from a Delaunay decomposition of a finite set of points - on surfaces equipped with a complex projective structure. Motivated by a…
This communication describes a representation of images as a set of edges characterized by their position and orientation. This representation allows the comparison of two images and the computation of their similarity. The first step in…
We address the problem of determining correspondences between two images in agreement with a geometric model such as an affine or thin-plate spline transformation, and estimating its parameters. The contributions of this work are…
Ortho-Radial drawings are a generalization of orthogonal drawings to grids that are formed by concentric circles and straight-line spokes emanating from the circles' center. Such drawings have applications in schematic graph layouts, e.g.,…
Planes are familiar mathematical objects which lie at the subtle boundary between continuous geometry and discrete combinatorics. A plane is geometrical, certainly, but the ways that two planes can interact break cleanly into discrete sets:…