A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
AQFC method estimates mesh curvatures using quadratic surfaces.
Two algorithms create high-quality triangular meshes for surfaces with guaranteed angles.
Approximates smooth surfaces using Laguerre geometry meshes.
Paper proves discrete uniformizations converge to continuous for surfaces of genus ≥1.
Approximates surfaces using Laguerre geometry with spherical faces.
Paper studies superconvergence on surface meshes using gradient recovery.
PolyGen models 3D meshes directly, predicting vertices and faces sequentially.
Paper generalizes discrete uniformization for genus-zero surfaces.
Unified framework designs LK structures using integer twists on non-manifold meshes.
Generative model creates high-quality meshes from point clouds.
In this paper we are interested in defining affine structures on discrete quadrangular surfaces of the affine three-space. We introduce, in a constructive way, two classes of such surfaces, called respectively indefinite and definite surfaces. The underlying meshes for indefinite surfaces are asymptotic nets satisfying…
Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networ…
In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami…
We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean curvature integrand locally. We show that this class is Möbius invariant. Isoth…
New method for surface analysis using restricted deformation bases.
STM maps improve terrain perception for autonomous robots.
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equatio…
New method avoids surface self-collision in geometric optimization.
Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh st…
Optimally estimate distances on surfaces using reconstructed meshes.
Unsupervised mesh disentanglement separates identity and pose.
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
A pair of pants is a genus zero orientable surface with three boundary components. A pants decomposition of a surface is a finite collection of unordered pairwise disjoint simple closed curves embedded in the surface that decompose the surface into pants. In this paper we present two Morse theory based algorithms for p…
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 corresponding functions measuring the quality of meshes are easily seen to be convex…
Differentiable voxelization for 3D meshes with GPU acceleration.
In this paper we study geometric, algebraic, and computational aspects of flexibility and infinitesimal flexibility of Kokotsakis meshes. A Kokotsakis mesh is a mesh that consists of a face in the middle and a certain band of faces attached to the middle face by its perimeter. In particular any 3x3-mesh made of quadran…
We create a smooth manifold of triangular meshes with a geodesically complete metric.
Generalized meshes for non-regular geometries, including fractures.
New method improves human mesh recovery for obese people.
Extends geometric decompositions to arbitrary meshes and forms.
The paper explores the topology of polygonal meshes and their properties.
Paper presents a consistent discretization for Hodge decomposition on volumetric meshes.
Proposes a new CNN for meshes that can handle orientation.
Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data, dense 3D surface meshes are common nowadays. While meshes with higher resolution …
New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.
We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are di…
The spectral geometry of mesh matrices of graphs is explored, leading to new formulas and eigenvalue estimates.
We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discre…
Highly expressive models such as deep neural networks (DNNs) have been widely applied to various applications. However, recent studies show that DNNs are vulnerable to adversarial examples, which are carefully crafted inputs aiming to mislead the predictions. Currently, the majority of these studies have focused on per…
Batch-splitting (data-parallelism) is the dominant distributed Deep Neural Network (DNN) training strategy, due to its universal applicability and its amenability to Single-Program-Multiple-Data (SPMD) programming. However, batch-splitting suffers from problems including the inability to train very large models (due to…
A new numerical framework simplifies elastic surface matching and comparison.
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a systematic approach to global optimization-based versions of such methods for mixed volu…
Differential quantities, including normals, curvatures, principal directions, and associated matrices, play a fundamental role in geometric processing and physics-based modeling. Computing these differential quantities consistently on surface meshes is important and challenging, and some existing methods often produce …
Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as 3D coordinates each vertex is mapped to, which often requires lots of storage memory. This causes inconvenien…
Discrete approximation solves Björling's minimal surface problem.
Eliciting semantic similarity between concepts in the biomedical domain remains a challenging task. Recent approaches founded on embedding vectors have gained in popularity as they risen to efficiently capture semantic relationships The underlying idea is that two words that have close meaning gather similar contexts. …
A relatively recent advance in cognitive neuroscience has been multi-voxel pattern analysis (MVPA), which enables researchers to decode brain states and/or the type of information represented in the brain during a cognitive operation. MVPA methods utilize machine learning algorithms to distinguish among types of inform…
A new model for simulating cloth manipulation in robots, accurate to within 1cm.