Related papers: Computing conformal maps onto circular domains
We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when…
Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Amano's method offers a straightforward numerical procedure for…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…
We study conformal maps from multiply connected domains in the extended complex plane onto lemniscatic domains. Walsh proved the existence of such maps in 1956 and thus obtained a direct generalization of the Riemann mapping theorem to…
Given a conformal mapping $f$ of the unit disk $\mathbb D$ onto a simply connected domain $D$ in the complex plane bounded by a closed Jordan curve, we consider the problem of constructing a matching conformal mapping, i.e., the mapping of…
Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be…
We study conformal mappings from the unit disk (or a rectangle) to one-tooth gear-shaped planar domains from the point of view of the Schwarzian derivative, with emphasis on numerical considerations. Applications are given to evaluation of…
We assume to be given structural equations over discrete variables inducing a directed acyclic graph, namely, a structural causal model, together with data about its internal nodes. The question we want to answer is how we can compute…
We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…
Conformal prediction provides a distribution-free framework for uncertainty quantification via prediction sets with exact finite-sample coverage. In low dimensions these sets are easy to interpret, but in high-dimensional or structured…
In the classical context of robotic mapping and localization, map matching is typically defined as the task of finding a rigid transformation (i.e., 3DOF rotation/translation on the 2D moving plane) that aligns the query and reference maps…
Conformal prediction is an assumption-lean approach to generating distribution-free prediction intervals or sets, for nearly arbitrary predictive models, with guaranteed finite-sample coverage. Conformal methods are an active research topic…
The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected…
This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: a)…
The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…
We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function $f$ on that domain; suitable functions have exactly one critical point, a maximum,…
We propose a method for efficiently computing orientation-preserving and approximately continuous correspondences between non-rigid shapes, using the functional maps framework. We first show how orientation preservation can be formulated…
We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate…
Two planar embedded circle patterns with the same combinatorics and the same intersection angles can be considered to define a discrete conformal map. We show that two locally finite circle patterns covering the unit disc are related by a…
Binary embeddings provide efficient and powerful ways to perform operations on large scale data. However binary embedding typically requires long codes in order to preserve the discriminative power of the input space. Thus binary coding…