Related papers: Geodesics using Waves: Computing Distances using W…
This paper introduces a novel method to estimate distance fields from noisy point clouds using Gaussian Process (GP) regression. Distance fields, or distance functions, gained popularity for applications like point cloud registration,…
Given a polygon $P$, for two points $s$ and $t$ contained in the polygon, their \emph{geodesic distance} is the length of the shortest $st$-path within $P$. A \emph{geodesic disk} of radius $r$ centered at a point $v \in P$ is the set of…
Computing intrinsic distances on discrete surfaces is at the heart of many minimization problems in geometry processing and beyond. Solving these problems is extremely challenging as it demands the computation of on-surface distances along…
In this work, we study the cellular decomposition of $S$ induced by a filling pair of curves $v$ and $w$, $Dec_{v,w}(S) = S - (v \cup w)$, and its connection to the distance function $d(v,w)$ in the curve graph of a closed orientable…
Given two distributions $P$ and $S$ of equal total mass, the Earth Mover's Distance measures the cost of transforming one distribution into the other, where the cost of moving a unit of mass is equal to the distance over which it is moved.…
We present a novel method to compute the approximate global penetration depth (PD) between two non-convex geometric models. Our approach consists of two phases: offline precomputation and run-time queries. In the first phase, our…
When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…
Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the…
The geodesic as well as the geodesic deviation equation for impulsive gravitational waves involve highly singular products of distributions $(\theta\de$, $\theta^2\de$, $\de^2$). A solution concept for these equations based on embedding the…
Wasserstein distance, which measures the discrepancy between distributions, shows efficacy in various types of natural language processing (NLP) and computer vision (CV) applications. One of the challenges in estimating Wasserstein distance…
We propose an efficient finite-element analysis of the vector wave equation in a class of relatively general curved polygons. The proposed method is suitable for an accurate and efficient calculation of the propagation constants of…
Superpositions of plane waves are known to approximate well the solutions of the Helmholtz equation. Their use in discretizations is typical of Trefftz methods for Helmholtz problems, aiming to achieve high accuracy with a small number of…
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…
In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to…
We introduce the concept of a metasurface system able to route space wave via surface waves. This concept may be used to laterally shift or modulate the beam width of scattered waves. We propose two corresponding synthesis techniques, one…
We study geodesic motion in expanding spherical impulsive gravitational waves propagating in a Minkowski background. Employing the continuous form of the metric we find and examine a large family of geometrically preferred geodesics. For…
Solving the so-called geodesic endpoint problem, i.e., finding a geodesic that connects two given points on a manifold, is at the basis of virtually all data processing operations, including averaging, clustering, interpolation and…
This article reports on the efficiency of a co-located diffuse approximation method coupled with a projection algorithm for the solution of two and three-dimensional incompressible flow equations. Three typical examples show the accuracy of…