Related papers: Constrained Delaunay Tetrahedrization: A Robust an…
We propose the first GPU algorithm for the 3D triangulation refinement problem. For an input of a piecewise linear complex $\mathcal{G}$ and a constant $B$, it produces, by adding Steiner points, a constrained Delaunay triangulation…
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…
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 present the winning implementation of the Seventh Computational Geometry Challenge (CG:SHOP 2025). The task in this challenge was to find non-obtuse triangulations for given planar regions, respecting a given set of constraints…
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…
<incorrect proofs; does not consider an important case because of which the proofs are wrong. The paper was withdrawn from submission> One of the objectives of a Delaunay mesh refinement algorithm is to produce meshes with tetrahedral…
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…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
We describe an algorithm to construct an intrinsic Delaunay triangulation of a smooth closed submanifold of Euclidean space. Using results established in a companion paper on the stability of Delaunay triangulations on $\delta$-generic…
As incremental Structure from Motion algorithms become effective, a good sparse point cloud representing the map of the scene becomes available frame-by-frame. From the 3D Delaunay triangulation of these points, state-of-the-art algorithms…
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,…
Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated…
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…
Deep convolutional neural networks (DCNN) are currently ubiquitous in medical imaging. While their versatility and high quality results for common image analysis tasks including segmentation, localisation and prediction is astonishing, the…
We describe an algorithm that takes as input n points in the plane and a parameter {\epsilon}, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 +…
The concept of comprehensive triangular decomposition (CTD) was first introduced by Chen et al. in their CASC'2007 paper and could be viewed as an analogue of comprehensive Grobner systems for parametric polynomial systems. The first…
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…
We propose a differentiable nonparametric algorithm, the Delaunay triangulation learner (DTL), to solve the functional approximation problem on the basis of a $p$-dimensional feature space. By conducting the Delaunay triangulation algorithm…
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…
This paper proposes a novel CTA (Combine-Then-Adapt)-based decentralized algorithm for solving convex composite optimization problems over undirected and connected networks. The local loss function in these problems contains both smooth and…