Related papers: Conformal polynomial parameterizations
Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…
The traditional view in numerical conformal mapping is that once the boundary correspondence function has been found, the map and its inverse can be evaluated by contour integrals. We propose that it is much simpler, and 10-1000 times…
P. Baird and the second author studied harmonic morphisms from a three-dimensional simply-connected space form to a surface and obtained a complete local and global classification of them. In this paper, we obtain a description of all…
Harmonic maps are important in generating parameterizations for various domains, particularly in two and three dimensions. General extensions of two-dimensional harmonic parameterizations for volumetric parameterizations are known to fail…
We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can…
The rich analytic structure of hadronic form factors makes a theoretically consistent yet easily applicable parametrisation cumbersome. Consequently, most parametrisations are limited to reproducing the simplest analytic features sufficient…
The algebraic translational surface is a typical modeling surface in computer aided design and architecture industry. In this paper, we give a necessary and sufficient condition for that algebraic surface having a standard parametric…
Given a unirational parameterization of a surface, we present a general algorithm to determine a birational parameterization without using parameterization algorithms. Additionally, if the surface is assumed to have a birational…
In this paper, we characterize the polynomiality of surfaces of revolution by means of the polynomiality of an associated plane curve. In addition, if the surface of revolution is polynomial, we provide formulas for computing a polynomial…
It is shown that a superconformal surface with arbitrary codimension in flat Euclidean space has a (necessarily unique) dual superconformal surface if and only if the surface is S-Willmore, the latter a well-known necessary condition to…
A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different…
We investigate the conformal and superconformal properties of a non-relativistic spinning particle propagating in a curved background coupled to a magnetic field and with a scalar potential. We derive the conditions on the couplings for a…
Via Gauge theory, we give a new proof of partial regularity for harmonic maps in dimension m>2 into arbitrary targets. This proof avoids the use of adapted frames and permits to consider targets of "minimal" C^2 regularity. The proof we…
Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
The conformational behavior of a coarse-grained finite polymer chain near an attractive spherical surface was investigated by means of multicanonical Monte Carlo computer simulations. In a detailed analysis of canonical equilibrium data…
We consider positive solutions to parametrized systems of generalized polynomial equations (with real exponents and positive parameters). By a fundamental result obtained in parallel work, polynomial systems are determined by geometric…
We prove that for any open Riemann surface $N,$ natural number $n\geq 3,$ non-constant harmonic map $h:N\to \mathbb{R}^{n-2}$ and holomorphic 2-form $H$ on $N,$ there exists a weakly complete harmonic map $X=(X_j)_{j=1,\ldots,n}:N \to…
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…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
The roots of a smooth curve of hyperbolic polynomials may not in general be parameterized smoothly, even not $C^{1,\alpha}$ for any $\alpha > 0$. A sufficient condition for the existence of a smooth parameterization is that no two of the…