Related papers: A Simple Method for Computing Singular or Nearly S…
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
This paper extends and analyzes the high-order kernel regularization framework of Beale & Tlupova (arXiv:2510.13639) to all four on-surface boundary integral operators of the Helmholtz Calderon calculus in three dimensions: the…
This paper presents a quadrature method for evaluating layer potentials in two dimensions close to periodic boundaries, discretized using the trapezoidal rule. It is an extension of the method of singularity swap quadrature, which recently…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…
This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular and nearly singular integral kernels present in 3D Helmholtz surface layer potentials and associated…
We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral…
This paper proposes a fast and accurate surface normal estimation method which can be directly used on depth maps (organized point clouds). The surface normal estimation process is formulated as a closed-form expression. In order to reduce…
To solve boundary integral equations for potential problems using collocation Boundary Element Method (BEM) on smooth curved 3D geometries, an analytical singularity extraction technique is employed. By adopting the isoparametric approach,…
This paper presents a method for mathematical modelling of surfaces conditioned on empirical data. It is based on solving a discrete biharmonic equation over a domain with given inner point and inner curve data. The inner curve data is used…
This paper presents a regularization technique for the high order efficient numerical evaluation of nearly singular, principal-value, and finite-part Cauchy-type integral operators. By relying on the Cauchy formula, the Cauchy-Goursat…
In this paper, we study the computational question of whether the Steklov spectrum of smooth simply connected planar domains can be approximated accurately by a boundary-only formulation based on harmonic conjugation. For the unit disk, the…
We present a generic scheme to construct corrected trapezoidal rules with spectral accuracy for integral operators with weakly singular kernels in arbitrary dimensions. We assume that the kernel factorization of the form,…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the curvature is integrable. Such points are called \emph{simple…
Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal…
We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in $\mathbb R^3$. The method is local, only modifying the original surface in a…
We prove a correspondence theorem for singular tropical surfaces in real three space, which recovers singular algebraic surfaces in an appropriate toric three-fold that tropicalize to a given singular tropical surface. Furthermore, we…