Related papers: Parallel Delaunay Refinement: Algorithms and Analy…

I present a generalization of Chew's first algorithm for Delaunay mesh refinement. In his algorithm, Chew splits the line segments of the input planar straight line graph (PSLG) into shorter subsegments whose lengths are nearly identical.…

This paper presents a new scalable parallelization scheme to generate the 3D Delaunay triangulation of a given set of points. Our first contribution is an efficient serial implementation of the incremental Delaunay insertion algorithm. A…

We propose a new refinement algorithm to generate size-optimal quality-guaranteed Delaunay triangulations in the plane. The algorithm takes $O(n \log n + m)$ time, where $n$ is the input size and $m$ is the output size. This is the first…

In this paper we show that many sequential randomized incremental algorithms are in fact parallel. We consider algorithms for several problems including Delaunay triangulation, linear programming, closest pair, smallest enclosing disk,…

A Frontal-Delaunay refinement algorithm for mesh generation in piecewise smooth domains is described. Built using a restricted Delaunay framework, this new algorithm combines a number of novel features, including: (i) an unweighted,…

This paper presents a GPU parallel algorithm to generate a new kind of polygonal meshes obtained from Delaunay triangulations. To generate the polygonal mesh, the algorithm first uses a classification system to label each edge of an input…

I present a 3D advancing-front mesh refinement algorithm that generates a constrained Delaunay mesh for any piecewise linear complex (PLC) and extend this algorithm to produce truly Delaunay meshes for any PLC. First, as in my recently…

Several classic problems in graph processing and computational geometry are solved via incremental algorithms, which split computation into a series of small tasks acting on shared state, which gets updated progressively. While the…

In this work we introduce a triangular Delaunay mesh generator that can be trained using reinforcement learning to maximize a given mesh quality metric. Our mesh generator consists of a graph neural network that distributes and modifies…

An extension of the restricted Delaunay-refinement algorithm for surface mesh generation is described, where a new point-placement scheme is introduced to improve element quality in the presence of mesh size constraints. Specifically, it is…

We propose a two-stage algorithm for generating Delaunay triangulations in 2D and Delaunay tetrahedra in 3D that employs near maximal Poisson-disk sampling. The method generates a variable resolution mesh in 2- and 3-dimensions in linear…

We present a method for reconstructing triangle meshes from point clouds. Existing learning-based methods for mesh reconstruction mostly generate triangles individually, making it hard to create manifold meshes. We leverage the properties…

This paper presents some of our findings on the scalability of parallel 3D mesh generation on distributed memory machines. The primary objective of this study was to evaluate a distributed memory approach for implementing a 3D parallel…

We present a set of rules to guide the design of GPU algorithms. These rules are grounded on the principle of reducing waste in GPU utility to achieve good speed up. In accordance to these rules, we propose GPU algorithms for 2D…

We present a new algorithm that produces a well-spaced superset of points conforming to a given input set in any dimension with guaranteed optimal output size. We also provide an approximate Delaunay graph on the output points. Our…

In diffusion models, samples are generated through an iterative refinement process, requiring hundreds of sequential model evaluations. Several recent methods have introduced approximations (fewer discretization steps or distillation) to…

This paper proposes improvements to the physically-based surface triangulation method, bubble meshing. The method simulates physical bubbles to automatically generate mesh vertices, resulting in high-quality Delaunay triangles. Despite its…

We present TriMe++, a multi-threaded software library designed for generating two-dimensional meshes for intricate geometric shapes using the Delaunay triangulation. Multi-threaded parallel computing is implemented throughout the meshing…

There are very few mathematical results governing the interpolation of functions or their gradients on Delaunay meshes in more than two dimensions. Unfortunately, the standard techniques for proving optimal interpolation properties are…

Intrinsic Delaunay triangulation (IDT) is a fundamental data structure in computational geometry and computer graphics. However, except for some theoretical results, such as existence and uniqueness, little progress has been made towards…