Related papers: Ambient Isotopic Meshing of Implicit Algebraic Sur…
To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…
We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…
During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the…
Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging…
The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…
A multiple group rack (MGR) is an algebraic system which is used to construct invariants of spatial surfaces, which are compact surfaces embedded in the $3$-sphere $S^{3}$. Seifert surfaces for links are spatial surfaces. In this paper, we…
We propose an algorithm to construct a certified approximation of a surface by generalizing the Krawczyk test. The Krawczyk test is based on interval arithmetic, and confirms the existence and uniqueness of a solution to a square system of…
Light scattering from self-affine homogeneous isotropic random rough surfaces is studied using the ray-optics approximation. Numerical methods are developed to accelerate the first-order scattering simulations from surfaces represented as…
We present a novel isogeometric method, namely the Immersed Boundary-Conformal Method (IBCM), that features a layer of discretization conformal to the boundary while employing a simple background mesh for the remaining domain. In this…
An accurate implicit description of geometries is enabled by the level-set method. Level-set data is given at the nodes of a higher-order background mesh and the interpolated zero-level sets imply boundaries of the domain or interfaces…
This paper describes a method for fast simplification of surface meshes. Whereas past methods focus on visual appearance, our goal is to solve equations on the surface. Hence, rather than approximate the extrinsic geometry, we construct a…
The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods…
The goal of this paper is to compute the motivic local density of an isolated algebraic surface singularity, in order to explain its link with algebraic multiplicity. In this context, we can use an additional data: the inner rate related to…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
We give an algorithm to decide whether an algebraic plane foliation F has a rational first integral and to compute it in the affirmative case. The algorithm runs whenever we assume the polyhedrality of the cone of curves of the surface…
This paper solves the problem of computing conformal structures of general 2-manifolds represented as triangle meshes. We compute conformal structures in the following way: first compute homology bases from simplicial complex structures,…
Regular algebraic surfaces isogenous to a higher product of curves can be obtained from finite groups with ramification structures. We find unmixed ramification structures for finite groups constructed as p-quotients of particular infinite…
The first result of the present paper is to provide classes of explicit solutions for integrable boundary matrices for the multi-species ASEP with an arbitrary number of species. All the solutions we have obtained can be seen as…
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…