Related papers: Variable resolution Poisson-disk sampling for mesh…

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…

In this paper we present a scalable approach for robustly computing a 3D surface mesh from multi-scale multi-view stereo point clouds that can handle extreme jumps of point density (in our experiments three orders of magnitude). The…

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on…

We present a fast method for generating random samples according to a variable density Poisson-disc distribution. A minimum threshold distance is used to create a background grid array for keeping track of those points that might affect any…

Learning efficient representations of local features is a key challenge in feature volume-based 3D neural mapping, especially in large-scale environments. In this paper, we introduce Decomposition-based Neural Mapping (DNMap), a…

We introduce a new approach for identifying and characterizing voids within two-dimensional (2D) point distributions through the integration of Delaunay triangulation and Voronoi diagrams, combined with a Minimal Distance Scoring algorithm.…

In this paper, we present a novel parallel dimension-independent node positioning algorithm that is capable of generating nodes with variable density, suitable for meshless numerical analysis. A very efficient sequential algorithm based on…

We introduce PolyDiff, the first diffusion-based approach capable of directly generating realistic and diverse 3D polygonal meshes. In contrast to methods that use alternate 3D shape representations (e.g. implicit representations), our…

This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the…

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.…

We introduce radiance meshes, a technique for representing radiance fields with constant density tetrahedral cells produced with a Delaunay tetrahedralization. Unlike a Voronoi diagram, a Delaunay tetrahedralization yields simple triangles…

Motivation: Microarray experiments result in large scale data sets that require extensive mining and refining to extract useful information. We have been developing an efficient novel algorithm for nonmetric multidimensional scaling (nMDS)…

We propose a novel approach which employs random sampling to generate an accurate non-uniform mesh for numerically solving Partial Differential Equation Boundary Value Problems (PDE-BVP's). From a uniform probability distribution U over a…

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…

Scanning devices often produce point clouds exhibiting highly uneven distributions of point samples across the surfaces being captured. Different point cloud subsampling techniques have been proposed to generate more evenly distributed…

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…

We present As-Plausible-as-Possible (APAP) mesh deformation technique that leverages 2D diffusion priors to preserve the plausibility of a mesh under user-controlled deformation. Our framework uses per-face Jacobians to represent mesh…

Computational technologies for the approximate solution of multidimensional boundary value problems often rely on irregular computational meshes and finite-volume approximations. In this framework, the discrete problem represents the…

For large-scale point cloud processing, resampling takes the important role of controlling the point number and density while keeping the geometric consistency. % in related tasks. However, current methods cannot balance such different…

Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational…