Meshes
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Related Articles from SNS
Mesh Field Theory: Port-Hamiltonian Formulation of Mesh-Based Physics
Announce Type: replace Abstract: We present Mesh Field Theory (MeshFT) and its neural realization, MeshFT-Net: a structure-preserving framework for mesh-based continuum physics that cleanly separates the physics' topological structure from its metric structure. Imposing minimal physical principles (locality, permutation equivariance, orientation covariance, and energy balance/dissipation inequality), we prove a reduction theorem for mesh-based physics. Under these conditions, the physical...
QuadLink: Autoregressive Quad-Dominant Mesh Generation via Point-Relation Learning
arXiv:2605.16813v2 Announce Type: replace Abstract: The generation of production-ready quad-dominant meshes is a cornerstone of modern 3D content creation. Generating anisotropic quad-dominant meshes from point clouds is challenging, as existing methods are typically limited to producing either pure triangular meshes or pure quadrilateral meshes with isotropic densities. In this paper, we present QuadLink, a unified framework consisting of three stages for quad-dominant mesh generation by...
MeshFlow: Efficient Artistic Mesh Generation via MeshVAE and Flow-based Diffusion Transformer
arXiv:2606.04621v1 Announce Type: new Abstract: We present MeshFlow, a new method for generating artist-like 3D meshes. Current mesh generators often adopt Auto-Regressive (AR) next-token prediction, a natural choice given the discrete nature of mesh topology. However, AR methods scale poorly because the inference cost is quadratic in mesh size.
Basis construction for polynomial spline spaces over arbitrary T-meshes
arXiv:2508.12950v3 Announce Type: replace Abstract : This paper presents the first method for constructing bases for polynomial spline spaces over an arbitrary T-meshes (PT-splines for short). We construct spline basis functions for an arbitrary T-mesh by first converting the T-mesh into a diagonalizable one via edge extension, ensuring a stable dimension of the spline space.
MeshWeaver: Sparse-Voxel-Guided Surface Weaving for Autoregressive Mesh Generation
arXiv:2606.04688v1 Announce Type: new Abstract: Autoregressive mesh generation has gained attention by tokenizing meshes into sequences and training models in a language-modeling fashion. However, existing approaches suffer from two fundamental limitations: (i) low tokenization efficiency, which yields long token sequences and prevents scaling to high-poly meshes, and (ii) absence of geometry-aware guidance, as generation is conditioned only on global shape embeddings rather than local...
A Parallel and Adaptive Mesh-Free Method for Discontinuous Coefficient Fields in Heterogeneous Porous Media
arXiv:2605.16564v2 Announce Type: replace Abstract: Discontinuous coefficient fields arise in many computational physics problems and are often represented as cellwise constant data tied to a given spatial discretization. Such representations are inherently mesh-dependent, requiring interpolation or projection whenever they are transferred to a different discretization. In this work, we develop \emph{Parallel and Adaptive Mesh-Free Approximation (PAM)}, a mesh-independent framework that...
ExMesh: EXplicit Mesh Reconstruction with Topology Adaptation
arXiv:2606.07288v1 Announce Type: new Abstract: Reconstructing surface meshes from multi-view images has remained a core challenge in recent years. Most existing methods, whether implicit or explicit, depend on intermediate representations and post-processing steps like Marching Cubes or TSDF fusion, often resulting in artifacts and fragmented geometry. Directly optimizing explicit meshes is a promising approach.
CADFit: Precise Mesh-to-CAD Program Generation with Hybrid Optimization
Announce Type: replace Abstract: Despite recent progress, recovering parametric CAD construction sequences from geometric input, such as meshes or point clouds, is a key challenge for design and manufacturing, as existing CAD reconstruction and generation methods are largely restricted to difficult-to-edit formats like meshes or Breps or editable simple sketch-and-extrude pipelines and low-complexity datasets. We introduce CADFit, a hybrid optimization-based CAD reconstruction framework that...
Locality-Aware Automatic Differentiation on the GPU for Mesh-Based Computations
arXiv:2509.00406v3 Announce Type: replace Abstract: We present a GPU-based system for automatic differentiation (AD) of functions defined on triangle meshes, designed to exploit the locality and sparsity in mesh-based computation. Our system evaluates derivatives using per-element forward-mode AD, confining all computation to registers and shared memory and assembling global gradients, sparse Jacobians, and sparse Hessians directly on the GPU. By avoiding global computation graphs,...
Exploring Neural Network Surrogates for High-Order Mesh-Free Interpolants
arXiv:2503.23230v3 Announce Type: replace Abstract: Mesh-free numerical methods offer flexibility in the discretisation of complex geometries, showing significant potential for problems where mesh-based methods struggle. Although high-order approximations can be obtained through consistency-correction linear systems, such approaches remain prohibitively expensive for Lagrangian formulations, which commonly exhibit low-order convergence. Here we investigate the use of machine learning (ML) to...