Approximate 3D elastic curves with exact constraints
problem Designing and approximating 3D elastic curves
method Numerically stable method for recovering 11 parameters
result Fast and stable approximation of arbitrary curves
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arXiv research
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.
168,742 papers · 148 categories
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48 results for “3D surface approximation”
Computes elastic grids that approximate 3D surfaces without physical simulations.
problem Creating planar grids that fit complex 3D surfaces efficiently.
method Uses differential geometry to minimize bending energy and nestle to the surface.
result Elastic grids can approximate 3D surfaces without physical simulations.
In this paper, a new algorithm based on differential geometry viewpoint to solve the 3D rotating Navier-Stokes equations with complex Boundary is proposed, which is called Bi-parallel algorithm. For xample, it can be applied to passage flow between two blades in impeller and circulation flow through aircrafts with comp…
Unified interpretation of sub-Riemannian Gauss-Bonnet theorem for surfaces in 3D contact manifolds.
problem Proving a sub-Riemannian Gauss-Bonnet theorem for surfaces in 3D contact manifolds.
method Measure-theoretic perspective, focusing on singular measures and characteristic points.
result Unified interpretation of previous results and natural geometric conditions for the theorem.
Study on 3D surfaces and tangles formed by Poncelet triangles.
problem Geometric and topological properties of 3D surfaces and tangles.
method Exploration of Poncelet triangles and associated points.
result Properties of 3D surfaces and tangles formed by Poncelet triangles.
Dimofte, Gaiotto and Gukov introduced a powerful invariant, the 3D-index, associated to a suitable ideal triangulation of a 3-manifold with torus boundary components. The 3D-index is a collection of formal power series in with integer coefficients. Our goal is to explain how the 3D-index is a generating serie…
The paper explores squircles and their 3D applications.
problem None explicitly stated; focuses on squircle equations and 3D surfaces.
method Examined and discussed squircle equations, then developed 3D surfaces based on these shapes.
result Developed 3D surfaces based on squircle equations.
The study characterizes constant curvature manifolds using ruled surfaces.
problem Characterizing manifolds of constant curvature using ruled surfaces.
method Investigating ruled surfaces in 3d Riemannian manifolds, finding stiction curve, distribution parameter, and fundamental forms.
result Identifies necessary and sufficient conditions for extrinsically flat surfaces to be ruled and proves manifold properties.
The paper proves Calabi-Bernstein type results for minimal and maximal surfaces in 3D and 3D-L spacetime.
problem Characterizing minimal and maximal surfaces in 3D and 3D-L spacetime.
method Analyzing surfaces with specific properties and using geometric and functional methods.
result Calabi-Bernstein type results for critical points of a weighted area functional in and .
Enhanced 3D shape analysis using information geometry.
problem Challenges in comparing 3D point clouds due to their unstructured nature and complex geometry.
method Information geometric framework for 3D point cloud shape analysis using Gaussian Mixture Models (GMMs) on a statistical manifold. Proposed MSKL divergence with upper and lower bounds.
result MSKL provides stable and monotonically varying values that directly reflect geometric variation, outperforming traditional distances and existing KL approximations.
Synthetic images rendered by graphics engines are a promising source for training deep networks. However, it is challenging to ensure that they can help train a network to perform well on real images, because a graphics-based generation pipeline requires numerous design decisions such as the selection of 3D shapes and …
Paper proves stable minimal surfaces in 3D are flat.
problem Understanding stable minimal surfaces in 3D.
method Analyzes quadratic area growth and stability conditions.
result Stable minimal Plateau surfaces in 3D are flat.
Build Boy's Surfacemath.HO
Easy-to-assemble 3D model of Boy's surface.
problem Visualizing Boy's surface in 3D.
method Printable card stock model kit.
result Accessible 3D representation of Boy's surface.
Study nonlocal minimal surfaces for minimal surfaces in 3D manifolds.
problem Existence and regularity of minimal surfaces in 3D manifolds.
method Min-max methods, fractional perimeters, uniform estimates.
result Uniform estimates for min-max -minimal surfaces in 3-manifolds, convergence to smooth minimal surfaces.
New Flat surfaces in math.GT
New flat surfaces found in 3D sphere space.
problem Constructing flat surfaces in 3D sphere.
method Using Ribaucour transformations and flat torus theory.
result Families of complete flat surfaces in determined by parameters.
Proves Steiner and tube formulae for 3D contact sub-Riemannian surfaces.
problem Calculating surface properties in complex geometric structures.
method Develops a local Steiner formula for regular surfaces in 3D contact sub-Riemannian manifolds.
result Establishes a formula for surface expansion in arbitrary regions of contact sub-Riemannian manifolds.
We study supersymmetric probe M5-branes in the AdS_4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M_3. This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS_4 requires it to wrap a surfac…
The study classifies minimal translation surfaces in 3D and 3D_1.
problem Classifying minimal translation surfaces in specific geometric settings.
method Defined and classified minimal translation surfaces with semi-symmetric connections.
result New classification of minimal translation surfaces in and .
Study bends 2D surfaces in 3D space using special equations.
problem Investigate infinitesimal bendings of 2D surfaces in 3D space.
method Use Bers-Vekua type equations and systems of differential equations with periodic coefficients.
result Construct bending fields for specific classes of 2D surfaces.
Study on curvatures of surfaces in specific Lie groups.
problem Analyzing curvatures of surfaces in 3D contact sub-Riemannian Lie groups.
method Riemannian approximation scheme to derive formulas for curvatures.
result Classification of surfaces with constant horizontal curvatures.
Standardizes surfaces in 3D handlebodies using Morse theory.
problem Classifying and identifying incompressible surfaces in 3D handlebodies.
method Applied Morse theory to provide a standard form and a condition for incompressibility.
result Developed a practical algorithm to determine incompressibility of surfaces in standard form.
Alternative proof for ribbon surfaces in 3D space.
problem Proving ribbonness of surfaces in 3D space.
method Using a compact oriented proper surface in upper half 4-space.
result Link bounds a ribbon surface in upper half 4-space.
New method classifies HCMU surfaces in 3D space forms as Weingarten surfaces.
problem Classifying HCMU surfaces in 3D space forms as Weingarten surfaces.
method Totally different method from previous work.
result Criteria for Weingarten surfaces that are also HCMU surfaces.
Study Schrödinger evolution on surfaces in 3D contact sub-Riemannian manifolds.
problem Analyzing the Schrödinger evolution on surfaces embedded in 3D contact sub-Riemannian manifolds.
method Relating self-adjointness of the Schrödinger operator to geometric invariants of the foliation.
result Classification of self-adjoint extensions yielding disjoint dynamics.
A neural flow method minimizes Willmore energy for 2-surfaces in 3D space.
problem Minimizing Willmore energy for closed oriented 2-surfaces in 3D space.
method Introducing neural Willmore flow to model and minimize the Willmore energy using neural architectures.
result The neural flow reproduces expected round sphere and Clifford torus for genus 0 and 1 surfaces, respectively, and finds minimal Willmore surfaces for genus 2.
Establishes smooth Ricci flows from convex surfaces in 3D space.
problem Existence and uniqueness of Ricci flow starting from convex surfaces.
method Smooth Ricci flows starting from smooth convex surfaces.
result Uniform convergence of metrics to initial convex surface.
Study on surfaces of genus g≥1 in 3D contact sub-Riemannian manifolds, proving finiteness or infiniteness of induced distance.
problem Determining the finiteness of the induced distance on surfaces of genus g≥1 in 3D contact sub-Riemannian manifolds.
method Analyzing the structural stability of the finiteness/not-finiteness of the induced distance on closed surfaces of genus g≥1.
result Closed surfaces of genus g≥1 can be embedded in such a way that the induced distance is either always finite or always infinite.
EuLearn creates diverse 3D topological datasets for machine learning.
problem Training machine learning systems to discern topological features.
method Developed novel sampling and neural network architectures for graph and manifold data.
result Incorporating topological information improves deep learning performance on EuLearn datasets.
Study investigates induced geometry on surfaces in 3D contact manifolds.
problem Understanding the metric structure on surfaces embedded in 3D contact sub-Riemannian manifolds.
method Defined a coefficient to characterize characteristic points and identified global conditions for finite induced distance.
result Proved induced distance finite for certain surfaces with isolated characteristic points.
SU(2) flat connection on 2D Riemann surface is shown to relate to the generalized twisted geometry in 3D space with cosmological constant. Various flat connection quantities on Riemann surface are mapped to the geometrical quantities in discrete 3D space. We propose that the moduli space of SU(2) flat connections on Ri…
This note shows surfaces in stable 3D data are bounded by area and diameter.
problem Bounding stable surfaces in 3D initial data sets.
method Demonstrating area and diameter bounds for stable, marginally outer trapped surfaces.
result Stable surfaces in 3D data sets are bounded by both area and diameter.
LION generates high-quality 3D shapes using hierarchical latent diffusion models.
problem Creating high-quality 3D shapes for digital artists.
method Hierarchical Latent Point Diffusion Model (LION) with a global shape latent and point-structured latent space.
result LION achieves state-of-the-art generation performance on ShapeNet benchmarks.
GAGA accelerates 3D molecular generation by replacing long trajectories with Gaussian approximations.
problem High computational cost of long generative trajectories in 3D molecular generation.
method GAGA identifies a characteristic step where molecular data becomes sufficiently Gaussian, replacing the trajectory with a Gaussian approximation.
result Significant improvement in both generation quality and computational efficiency.
We address the problem of surface inpainting, which aims to fill in holes or missing regions on a Riemann surface based on its surface geometry. In practical situation, surfaces obtained from range scanners often have holes where the 3D models are incomplete. In order to analyze the 3D shapes effectively, restoring the…
Refines knot defect measurement in 3D and 4D.
problem Measuring how far knots are from being alternating.
method Extends spanning surface defect to 4-ball, making comparisons and proving formulas.
result Connected sum formula proven.
The study finds an infinite number of minimal surfaces in 3D spheres.
problem Finding minimal surfaces in 3D spheres.
method Two-parameter min-max scheme in lens spaces, Heegaard foliations flipping.
result Constructs an infinite number of minimal surfaces in .
In an earlier work we identified the types and numbers of static equilibrium points of solids arising from fine, equidistant -discretrizations of smooth, convex surfaces. We showed that such discretizations carry equilibrium points on two scales: the local scale corresponds to the discretization, the global scale to…
Proposes QMC-based QSW for 3D SW distance.
problem Intractable SW distance in 3D.
method Quasi-Monte Carlo (QMC) for QSW approximations.
result QMC-based QSW improves SW estimation.
The paper extends Pappus-Guldin theorems to 3D-Heisenberg group surfaces.
problem Extending classical theorems to a new geometric setting.
method Deriving formulas for p-areas and volumes in the Heisenberg group.
result Pappus-Guldin theorems hold for surfaces in the Heisenberg group.
The paper studies minimal surfaces in 3D spheres and balls, confirming conjectures and identifying new surfaces.
problem Understanding minimal surfaces in 3D spheres and balls with low area.
method Equivariant optimization of Laplace and Steklov eigenvalues to construct minimal surfaces of prescribed topology.
result Sharp area estimates and varifold limits for minimal surfaces in large topology regimes.
Modeling 3D continua with singular points using Yin sets.
problem Treat singular points as central subjects in 3D continuum topology.
method Model 3D continua as Yin sets, regular open semianalytic sets with bounded boundary.
result Characterize local and global topology of Yin sets.
3D Convolutional Neural Networks (3D-CNN) have been used for object recognition based on the voxelized shape of an object. However, interpreting the decision making process of these 3D-CNNs is still an infeasible task. In this paper, we present a unique 3D-CNN based Gradient-weighted Class Activation Mapping method (3D…
PolyGen models 3D meshes directly, predicting vertices and faces sequentially.
problem Efficiently modeling 3D geometry for computer graphics, robotics, and games.
method Transformer-based autoregressive model for predicting mesh vertices and faces.
result PolyGen produces high-quality, usable 3D meshes and competitive conditional performance.
Study on minimal surfaces in a 3D space with 2m-norm.
problem Characterizing minimal surfaces in a specific geometric space.
method Examining translation, homothetical, and separable minimal surfaces.
result New insights into minimal surfaces in a 3D space with 2m-norm.
Minimal surfaces span periodic curves in 3D space.
problem Existence of minimal surfaces spanning periodic curves.
method Proof of existence for minimal surfaces using periodic curves in .
result Existence of noncompact simply connected periodic minimal surfaces.
Prove an isoperimetric inequality for compact bodies in 3D contact non-unimodular Lie groups.
problem Isoperimetric inequality for compact bodies in contact non-unimodular 3D Lie groups.
method Prove an isoperimetric inequality.
result Prove an isoperimetric inequality.
New minimal surfaces found in a specific type of 3D space.
problem Finding minimal surfaces in a particular class of 3D spaces.
method Investigated minimal surfaces invariant under a specific group action in unimodular semidirect products.
result Described new examples of minimal surfaces in a specific 3D space.
Researchers classify and visualize 5-cube cubical surfaces.
problem Classifying and visualizing surfaces in a 5-dimensional cube.
method Exhaustive search, classification by genus and demigenus, 3D visualization, reinforcement learning for optimization.
result 2690 connected closed cubical surfaces in the 5-cube, visualized and optimized for 3D printing.