Related papers: Optimizing Mesh to Improve the Triangular Expansio…
Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation.…
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…
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…
This paper introduces a Delaunay triangulation algorithm based on the external incremental method. Unlike traditional random incremental methods, this approach uses convex hull and points as basic operational units instead of triangles.…
Triangular meshes are a widely used representation in the field of 3D modeling. In this paper, we present a novel approach for edge length-based linear subdivision on triangular meshes, along with two auxiliary techniques. We conduct a…
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 data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, and small memory occupation. The location structure is organized into…
We present a differentiable representation, DMesh, for general 3D triangular meshes. DMesh considers both the geometry and connectivity information of a mesh. In our design, we first get a set of convex tetrahedra that compactly tessellates…
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…
Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have…
Data envelopment analysis (DEA) is a linear program (LP)-based method used to determine the efficiency of a decision making unit (DMU), which transforms inputs to outputs, by peer comparison. This paper presents a new computation algorithm…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with…
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…
Recent developments for mathematical modeling and numerical simulation of biomolecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in implicit-solvent modeling. In our former work, we have…
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…
To efficiently process visual data at scale, researchers have proposed two techniques for lowering the computational overhead associated with the underlying deep learning models. The first approach consists of leveraging a specialized,…
We describe a randomized algorithm that, given a set $P$ of points in the plane, computes the best location to insert a new point $p$, such that the Delaunay triangulation of $P\cup\{p\}$ has the largest possible minimum angle. The expected…
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…
Embedded deep learning platforms have witnessed two simultaneous improvements. First, the accuracy of convolutional neural networks (CNNs) has been significantly improved through the use of automated neural-architecture search (NAS)…