Related papers: A Simple Method for Computing Singular or Nearly S…
A discrete harmonic surface is a trivalent graph which satisfies the balancing condition in the 3-dimensional Euclidean space and achieves energy minimizing under local deformations. Given a topological trivalent graph, a holomorphic…
We consider an elliptic optimal control problem where the objective functional contains an integral along a surface of codimension 1, also known as a hypersurface. In particular, we use a fidelity term that encourages the state to take…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
For generic maps from compact surfaces with boundary into the plane we develop an explicit algorithm for minimizing both the number of cusps and the number of components of the singular locus. More precisely, we minimize among maps with…
This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…
By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
Motivated by geometry processing for surfaces with non-trivial topology, we study discrete harmonic maps between closed surfaces of genus at least two. Harmonic maps provide a natural framework for comparing surfaces by minimizing…
In the calculation of thermodynamic properties and three dimensional structures of macromolecules, such as proteins, it is important to have a good algorithm for computing solvent accessible surface area of macromolecules. Here we propose a…
In this paper, we introduce novel methods for computing middle surfaces between various 3D data sets such as point clouds and/or discrete surfaces. Traditionally the middle surface is obtained by detecting singularities in computed distance…
In this paper, we consider deformations of singular complex curves on complex surfaces. Despite the fundamental nature of the problem, little seems to be known for curves on general surfaces. Let $C\subset S$ be a complete integral curve on…
For an oriented surface $S$, the singular set of a fold map $f:S\rightarrow \mathbb{R}^2$ is a collection of smooth curves, also known as fold singularities. We construct a sharp lower bound on the number of self-intersections of such fold…
We present a family of high order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity. The singular part of the integrand is expanded in a Taylor series involving terms of…
We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a…
A discrete conformality for polyhedral metrics on surfaces is introduced in this paper which generalizes earlier work on the subject. It is shown that each polyhedral metric on a surface is discrete conformal to a constant curvature…
Recently published formulas for the surface and regular solid spherical harmonics and for the expansion of the product of two normalized associated Legendre functions with different centers in ellipsoidal coordinates (Telhat Ozdogan, Metin…
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…
A non-singular formulation of the boundary integral method (BIM) is presented for the Laplace equation whereby the well-known singularities that arise from the fundamental solution are eliminated analytically. A key advantage of this…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…