Related papers: Surface and hypersurface meshing techniques for sp…
We present a novel approach for 3D indoor scene reconstruction that combines 3D Gaussian Splatting (3DGS) with mesh representations. We use meshes for the room layout of the indoor scene, such as walls, ceilings, and floors, while employing…
Mesh plays an indispensable role in dense real-time reconstruction essential in robotics. Efforts have been made to maintain flexible data structures for 3D data fusion, yet an efficient incremental framework specifically designed for…
We perform a generalization of the geometrical approach to describing extended objects for studying the doubly supersymmetric twistor--like formulation of super--p--branes. Some basic features of embedding world supersurface into target…
The 3D mesh is an important representation of geometric data. In the generation of mesh data, geometric deficiencies (e.g., duplicate elements, degenerate faces, isolated vertices, self-intersection, and inner faces) are unavoidable and may…
Geophysical model domains typically contain irregular, complex fractal-like boundaries and physical processes that act over a wide range of scales. Constructing geographically constrained boundary-conforming spatial discretizations of these…
4D mesh generation has recently emerged as a powerful paradigm for recovering dynamic 3D structure from videos, but existing methods remain slow, computationally expensive, and difficult to scale to longer sequences. We introduce a…
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…
The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end…
In this paper, we analyze and provide numerical illustrations for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. We follow a method of lines approach and utilize an underlying…
We present an approach for robust high-order mesh generation specially tailored to streamlined bodies. The method is based on a semi-sructured approach which combines the high quality of structured meshes in the near-field with the…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
Recent advancements in 2D/3D generative techniques have facilitated the generation of dynamic 3D objects from monocular videos. Previous methods mainly rely on the implicit neural radiance fields (NeRF) or explicit Gaussian Splatting as the…
Open-vocabulary panoptic reconstruction is essential for advanced robotics perception and simulation. However, existing methods based on 3D Gaussian Splatting (3DGS) often struggle to simultaneously achieve geometric accuracy, coherent…
A general technique for synthesizing both planar and conformal beamforming metasurfaces is presented that utilizes full-wave modeling techniques and rapid optimization methods. The synthesized metasurfaces consist of a patterned metallic…
We present a new approach for computing planar hexagonal meshes that approximate a given surface, represented as a triangle mesh. Our method is based on two novel technical contributions. First, we introduce Coordinate Power Fields, which…
We develop a finite element method for elliptic partial differential equations on so called composite surfaces that are built up out of a finite number of surfaces with boundaries that fit together nicely in the sense that the intersection…
Trace finite element methods have become a popular option for solving surface partial differential equations, especially in problems where surface and bulk effects are coupled. In such methods a surface mesh is formed by approximately…
A spatio-temporal metasurface is proposed to decompose in real time the temporal frequencies of electromagnetic waves into spatial frequencies onto a two-dimensional plane. The metasurface is analyzed and demonstrated using Fourier…
Polyhedral meshes (PM) - meshes having planar faces - have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate.…
We introduce a fast and invertible approximation for data simulated as 2D planar meshes with connectivities along the poloidal dimension in deforming 3D toroidal (donut-like) spaces generated by fusion simulations. In fusion simulations,…