Related papers: The Modified Direct Method: an Approach for Smooth…
Conventional lithography methods involving pattern transfer through resist templating face challenges of material compatibility with various process solvents. Other approaches of direct material writing often compromise pattern complexity…
Current structured pruning methods often result in considerable accuracy drops due to abrupt network changes and loss of information from pruned structures. To address these issues, we introduce the Decay Pruning Method (DPM), a novel…
An arbitrary Lagrangian--Eulerian finite element method and numerical implementation for curved and deforming lipid membranes is presented here. The membrane surface is endowed with a mesh whose in-plane motion need not depend on the…
We examine the use of domain decomposition for potentially more efficient mean curvature flow of surface meshes, whose faces are arbitrary simple polygons. We first test traditional domain decomposition methods with and without overlap of…
Current direct modeling systems limit users to low-level interactions with vertices, edges, and faces, forcing designers to manage detailed geometric elements rather than focusing on high-level design intent. This paper introduces semantic…
Smoothing is an essential tool in many NLP tasks, therefore numerous techniques have been developed for this purpose in the past. One of the most widely used smoothing methods are the Kneser-Ney smoothing (KNS) and its variants, including…
This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…
Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…
3D Gaussian Splatting (3DGS) has enabled high-fidelity virtualization with fast rendering and optimization for novel view synthesis. On the other hand, triangle mesh models still remain a popular choice for surface reconstruction but suffer…
Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…
Neural implicit representations have become a popular choice for modeling surfaces due to their adaptability in resolution and support for complex topology. While previous works have achieved impressive reconstruction quality by training on…
In this work, we develop a discretisation method for the mixed formulation of the magnetostatic problem supporting arbitrary orders and polyhedral meshes. The method is based on a global discrete de Rham (DDR) sequence, obtained by patching…
In this paper, we propose an algorithmic framework, dubbed inertial alternating direction methods of multipliers (iADMM), for solving a class of nonconvex nonsmooth multiblock composite optimization problems with linear constraints. Our…
Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models for language modeling, yet the effective design of transformer architectures for MDMs remains underexplored. In this paper, we show that…
We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…
Accurately reconstructing a 3D scene including explicit geometry information is both attractive and challenging. Geometry reconstruction can benefit from incorporating differentiable appearance models, such as Neural Radiance Fields and 3D…
There is a great need in several areas of astrophysics and space-physics to carry out high order of accuracy, divergence-free MHD simulations on spherical meshes. This requires us to pay careful attention to the interplay between mesh…
We show that the driving force behind the regularizing effect of Laplacian smoothing on surface elements is the popular mean ratio quality measure. We use these insights to provide natural generalizations to polygons and polyhedra. The…
Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…