Related papers: Intrinsic Mesh Simplification
Reconstructing 3D point clouds into triangle meshes is a key problem in computational geometry and surface reconstruction. Point cloud triangulation solves this problem by providing edge information to the input points. Since no vertex…
3D Gaussian splatting (3DGS) has demonstrated exceptional performance in image-based 3D reconstruction and real-time rendering. However, regions with complex textures require numerous Gaussians to capture significant color variations…
The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper…
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…
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements…
Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of…
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…
We present a topology-informed inverse rendering approach for reconstructing high-genus surface meshes from multi-view images. Compared to 3D representations like voxels and point clouds, mesh-based representations are preferred as they…
Generalized winding numbers provide a robust measure of point insidedness for 3D surfaces - whether open, self-intersecting, or non-manifold - and are central to numerous geometry processing tasks. However, existing methods trade off…
We propose a computation of curvature of arbitrary two-dimensional surfaces of three-dimensional objects, which is a contribution to discrete gravity with potential applications in network geometry. We begin by linking each point of the…
We give necessary and sufficient criteria for elementary operations in a two-dimensional terrain to preserve the persistent homology induced by the height function. These operations are edge flips and removals of interior vertices,…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
This paper introduces a volume-conserving interface tracking algorithm on unstructured triangle meshes. We propose to discretize the interface via triangle edge cuts which represent the intersections between the interface and the triangle…
We develop a short-step interior point method to optimize a linear function over a convex body assuming that one only knows a membership oracle for this body. The approach is based on Abernethy and Hazan's sketch of a universal interior…
A fundamental task in data exploration is to extract simplified low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches to this task…
This paper introduces a novel method for reconstructing meshes from sparse point clouds by predicting edge connection. Existing implicit methods usually produce superior smooth and watertight meshes due to the isosurface extraction…
In this paper, we propose the differentiable voxelization of 3D meshes via the winding number and solid angles. The proposed approach achieves fast, flexible, and accurate voxelization of 3D meshes, admitting the computation of gradients…
3D Gaussian Splatting reconstructs scenes by starting from a sparse Structure-from-Motion initialization and refining under-reconstructed regions. This process is slow, as it requires multiple densification steps where Gaussians are…
Triangles are everywhere in the virtual world. The surface of nearly every graphical object is saved as a triangular mesh on a computer. Light effects and movements of virtual objects are computed on the basis of triangulations. Besides…
A recently proposed clustering method, called the Nearest Descent (ND), can organize the whole dataset into a sparsely connected graph, called the In-tree. This ND-based Intree structure proves able to reveal the clustering structure…