Related papers: An algorithm for two-dimensional mesh generation b…

Recent probabilistic methods for 3D triangular meshes capture diverse shapes by differentiable mesh connectivity, but face high computational costs with increased shape details. We introduce a new differentiable mesh processing method that…

Recently, we introduced a new class of shapes, called soft cells which fill space as soft tilings without gaps and overlaps while minimizing the number of sharp corners. We introduced the edge bending algorithm that deforms a polyhedral…

Image tiling -- the seamless connection of disparate images to create a coherent visual field -- is crucial for applications such as texture creation, video game asset development, and digital art. Traditionally, tiles have been constructed…

The main purpose of this paper is to present a kneading theory for two-dimensional triangular maps. This is done by defining a tensor product between the polynomials and matrices corresponding to the one-dimensional basis map and fiber map.…

We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature…

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed…

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…

The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods…

We describe a simple geometric transformation of triangles which leads to an efficient and effective algorithm to smooth triangle and tetrahedral meshes. Our focus lies on the convergence properties of this algorithm: we prove the…

Scaling artist-designed meshes to high triangle numbers remains challenging for autoregressive generative models. Existing transformer-based methods suffer from long-sequence bottlenecks and limited quantization resolution, primarily due to…

In this paper, we describe a robust algorithm for 2-Manifold generation of various kinds of ShapeNet Models. The input of our pipeline is a triangle mesh, with a set of vertices and triangular faces. The output of our pipeline is a…

The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not…

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

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…

In this paper we report a new promising idea on the design and manufacturing of ply composite structures, tailored to exhibit maximum stiffness under given weight constraints and loading conditions. It is based on the idea behind an…

We devise a generalization of tree approximation that generates conforming meshes, i.e., meshes with a particular structure like edge-to-edge triangulations. A key feature of this generalization is that the choices of the cells to be…

Triangle meshes play a crucial role in 3D applications for efficient manipulation and rendering. While auto-regressive methods generate structured meshes by predicting discrete vertex tokens, they are often constrained by limited face…

We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…

Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…

When folding a 3D object from a 2D material like paper, typically only an approximation of the original surface geometry is needed. Such an approximation can effectively be created by a (progressive) mesh simplification approach, e.g. using…