Related papers: An algorithm for two-dimensional mesh generation b…
For the numerical solution of shape optimization problems, particularly those constrained by partial differential equations (PDEs), the quality of the underlying mesh is of utmost importance. Particularly when investigating complex…
Minimax designs provide a uniform coverage of a design space $\mathcal{X} \subseteq \mathbb{R}^p$ by minimizing the maximum distance from any point in this space to its nearest design point. Although minimax designs have many useful…
Wang tiles enable efficient pattern compression while avoiding the periodicity in tile distribution via programmable matching rules. However, most research in Wang tilings has considered tiling the infinite plane. Motivated by emerging…
Mesh generation is essential for accurate and efficient computational fluid dynamics simulations. To resolve critical features in the flow, adaptive mesh refinement (AMR) is routinely employed in certain regions of the computational domain,…
Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution, and sometimes pooling, operations on triangle meshes. These methods,…
We propose MeshOn, a method that finds physically and semantically realistic compositions of two input meshes. Given an accessory, a base mesh with a user-defined target region, and optional text strings for both meshes, MeshOn uses a…
Despite the rapidly evolving field of computational electromagnetics, few open-source tools have managed to tackle the problem of automatic mesh generation for properly discretizing the problem of interest into a finite set of elements…
The efficient generation of meshes is an important step in the numerical solution of various problems in physics and engineering. We are interested in situations where global mesh quality and tight coupling to the physical solution is…
3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation…
Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…
Controllable, high-fidelity mesh editing remains a significant challenge in 3D content creation. Existing generative methods often struggle with complex geometries and fail to produce detailed results. We propose CraftMesh, a novel…
This work describes a concise algorithm for the generation of triangular meshes with the help of standard adaptive finite element methods. We demonstrate that a generic adaptive finite element solver can be repurposed into a triangular mesh…
Rapid aerodynamic screening of turbomachinery blades across wide operating envelopes remains a major computational bottleneck in preliminary design, particularly for energy-conversion and storage systems such as emerging Carnot batteries.…
We derive a homeomorphism invariant for those tiling spaces which are made by rather general substitution rules on polygonal tiles, including those tilings, like the pinwheel, which contain tiles in infinitely many orientations. The…
We study the number of tilings of skew Young diagrams by ribbon tiles shaped like Dyck paths, in which the tiles are "vertically decreasing". We use these quantities to compute pairing probabilities in the double-dimer model: Given a planar…
As humans, we regularly associate shape of an object with its built material. In the context of geometric modeling, however, this interrelation between form and material is rarely explored. In this work, we propose a novel data-driven…
We describe a method for discretizing planar C2-regular domains immersed in non-conforming triangulations. The method consists in constructing mappings from triangles in a background mesh to curvilinear ones that conform exactly to the…
We present Text2Room, a method for generating room-scale textured 3D meshes from a given text prompt as input. To this end, we leverage pre-trained 2D text-to-image models to synthesize a sequence of images from different poses. In order to…
A generalization of vector fields, referred to as N-direction fields or cross fields when N = 4, has been recently introduced and studied for geometry processing, with applications in quadrilateral (quad) meshing, texture mapping, and…
In this letter, a new approach to perform edge detection is presented using an all-dielectric CMOS-compatible metasurface. The design is based on guided-mode resonance which provides a high quality factor resonance to make the edge…