Related papers: Computing Three-dimensional Constrained Delaunay R…
Binary convolutional networks have lower computational load and lower memory foot-print compared to their full-precision counterparts. So, they are a feasible alternative for the deployment of computer vision applications on limited…
Two-dimensional Delaunay triangulation is a fundamental aspect of computational geometry. This paper presents a novel algorithm that is specifically designed to ensure the correctness of 2D Delaunay triangulation, namely the Polygonal…
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…
We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel…
We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we…
These notes accompany the open-source code published in GitHub which implements a GPU-based line-segment, surface-triangle intersection algorithm in CUDA. It mentions some relevant works and discusses issues specific to this implementation.…
Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two…
The paper considers the problem of implementation on graphics processors of numerical integration routines for higher order finite element approximations. The design of suitable GPU kernels is investigated in the context of general purpose…
Consider a set $P$ of $n$ points picked uniformly and independently from $[0,1]^d$ for a constant dimension $d$ -- such a point set is extremely well behaved in many aspects. For example, for a fixed $r \in [0,1]$, we prove a new…
In this paper, we analyze the complexity of natural parallelizations of Delaunay refinement methods for mesh generation. The parallelizations employ a simple strategy: at each iteration, they choose a set of ``independent'' points to insert…
3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…
In this article, recent works on 2D Constrained Delaunay triangulation(CDT) algorithms have been reported. Since the review of CDT algorithms presented by de Floriani(Issues on Machine Vision, Springer Vienna, pg. 95--104, 1989), different…
As recurrent neural networks become larger and deeper, training times for single networks are rising into weeks or even months. As such there is a significant incentive to improve the performance and scalability of these networks. While…
Convolutional gridding is a processor-intensive step in interferometric imaging. While it is possible to use graphics processing units (GPUs) to accelerate this operation, existing methods use only a fraction of the available flops. We…
The Kernel Polynomial Method (KPM) is one of the fast diagonalization methods used for simulations of quantum systems in research fields of condensed matter physics and chemistry. The algorithm has a difficulty to be parallelized on a…
Given a set $P$ of $n$ points in the plane, we show how to compute in $O(n \log n)$ time a subgraph of their Delaunay triangulation that has maximum degree 7 and is a strong planar $t$-spanner of $P$ with $t =(1+ \sqrt{2})^2 *\delta$, where…
We study the accuracy of triangulation in multi-camera systems with respect to the number of cameras. We show that, under certain conditions, the optimal achievable reconstruction error decays quadratically as more cameras are added to the…
A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function of two variables, the algorithm produces a hierarchy of triangulations and piecewise polynomial approximations…
We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the…
The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric…