Related papers: Fast and Accurate Intersections on a Sphere
There are many applications in which a bounding sphere containing the given triangle E3 is needed, e.g. fast collision detection, ray-triangle intersecting in raytracing etc. This is a typical geometrical problem in E3 and it has also…
We consider the solution of initial value problems within the context of hybrid systems and emphasise the use of high precision approximations (in software for exact real arithmetic). We propose a novel algorithm for the computation of…
Coordinated multi-robot motion planning at intersections is key for safe mobility in roads, factories and warehouses. The rapidly exploring random tree (RRT) algorithms are popular in multi-robot motion planning. However, generating the…
This article introduces a novel approach to constructing a topometric map that allows for efficient navigation and decision-making in mobile robotics applications. The method generates the topometric map from a 2D grid-based map. The…
We study shortest-path routing in large weighted, undirected graphs, where expanding search frontiers raise time and memory costs for exact solvers. We propose \emph{SPHERE}, a query-aware partitioning heuristic that adaptively splits the…
The convolution potential arises in a wide variety of application areas, and its efficient and accurate evaluation encounters three challenges: singularity, nonlocality and anisotropy. We introduce a fast algorithm based on a far-field…
We present a general algorithm for finding the overlap area between two ellipses. The algorithm is based on finding a segment area (the area between an ellipse and a secant line) given two points on the ellipse. The Gauss-Green formula is…
We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…
We propose a fast approximate algorithm for large graph matching. A new projected fixed-point method is defined and a new doubly stochastic projection is adopted to derive the algorithm. Previous graph matching algorithms suffer from high…
We present an accurate quadrature formula on the sphere with less localized quadrature points for efficient numerical computation of the radiative transport equation (RTE) in the three dimensions. High accuracy of the present method…
We derive a factorization formula for inclusive jet production in heavy-ion collisions using the tools of Effective Field Theory (EFT). We show how physics at widely separated scales in this process can be systematically separated by…
We use conformal maps to study a free boundary problem for a two-fluid electromechanical system, where the interface between the fluids is determined by the combined effects of electrostatic forces, gravity and surface tension. The free…
We discuss an effective field theory (EFT) approach to the computation of fluctuation-induced interactions between particles bound to a thermally fluctuating fluid surface controlled by surface tension. By describing particles as points,…
In the realm of computer-aided design (CAD) software, the intersection of B-spline surfaces stands as a fundamental operation. Despite the extensive history of surface intersection algorithms, the challenge of handling complex intersection…
This paper attacks the following problem. We are given a large number $N$ of rectangles in the plane, each with horizontal and vertical sides, and also a number $r<N$. The given list of $N$ rectangles may contain duplicates. The problem is…
In the complex of curves of a closed orientable surface of genus $g,$ $\mathcal{C}(S_g),$ a preferred finite set of geodesics between any two vertices, called \emph{efficient geodesics} introduced by Birman, Margalit, and Menasco in…
For problems of time-harmonic scattering by rational polygonal obstacles, embedding formulae express the far-field pattern induced by any incident plane wave in terms of the far-field patterns for a relatively small (frequency-independent)…
The use of infrastructure sensor technology for traffic detection has already been proven several times. However, extrinsic sensor calibration is still a challenge for the operator. While previous approaches are unable to calibrate the…
Spatial join processing techniques that identify intersections between complex geometries (e.g., polygons) commonly follow a two-step filter-and-refine pipeline. The filter step evaluates the query predicate on the minimum bounding…
In this paper we develop finite difference schemes for elliptic problems with piecewise continuous coefficients that have (possibly huge) jumps across fixed internal interfaces. In contrast with such problems involving one smooth…