arXiv subjects

Oded Stein

Publications and source records attributed to Oded Stein.

At least 19 recordsLinked to original sources

arXiv2026

RADmesh: Remesh-Aware Mesh Deformation

We propose a remeshing-enhanced method for generatively deforming shapes with visual losses. It is intuitive that sufficiently drastic deformations of a mesh without changing its triangulation can easily compromise element quality, even if such large geometry changes may be semantically desired. Shape deformation methods could thus benefit from changing the triangulation; however, this is not done by most generative, text-based, visually-supervised mesh deformation methods. Remeshing is a discrete operation, proven to be especially challenging to couple with the notoriously noisy supervision signal provided by visual losses. We propose a vertex-based deformation optimization quantity capable of large deformations and robustness to such noise; we periodically remesh using an isotropic remesher that interpolates and carries forward the deformation optimization state. This enables continuous, geometry-informed progress in coarse-to-fine addition of resolution. The resulting shapes' triangulations fit their optimized geometry and have neat isotropic elements. Further, our method is localizable, able to grow new features on a base shape with expressive detail, leaving the rest unchanged. We showcase the effectiveness of our method on a variety of shapes and prompts, both local and global deformations, and demonstrate its superior visual quality and triangle efficiency. Our project page is at https://threedle.github.io/radmesh.

cs.GR↗

arXiv2026

PINNsur: Physics-Informed Neural Networks for PDEs on Curved Surfaces

Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete geometric elements (usually triangles). Recently, physics-informed neural networks (PINNs) have emerged as a continuous, mesh-free alternative that does not suffer from FEM's sensitivity to mesh quality or geometric discretization errors. We present PINNSur, a simple framework for using PINNs on curved surfaces: we train a neural field to approximate the surface's normals, and then we express surface differential operators using their projection from $\mathbb{R}^3$ onto the surface. Since every orientable manifold has well-defined normals, our method is suitable for all such surfaces, regardless of curvature or topology, enabling many geometry processing applications. Moreover, despite their empirical success in solving PDEs in flat Euclidean domains, PINNs lack convergence guarantees to the true solution of the underlying PDE, and there is limited systematic experimental evidence demonstrating such convergence. This gap restricts their adoption as reliable solvers compared to established methods like FEM, where convergence to the true solution is well understood and theoretically grounded. These surface PDEs are particularly challenging to solve convergently, as one must not only deal with the convergence of the function approximation, but also with the convergence of the geometric approximation of the surface itself. In this work, we empirically investigate the convergence behavior of PINNs for solving surface PDEs by introducing a simple empirical convergence test.

cs.GR↗

arXiv2026

Look Both Ways Before You Cross: Lifting Cross Fields From 2D Visual Priors

We present CrossLift, a technique for computing cross fields on meshes guided by visual features in images. We leverage powerful text-to-image priors that are capable of synthesizing images of feature-aligned quad meshes in 2D. We extract this signal as explicit per-pixel directions in the 2D images, which we then back-project to the mesh surface. We aggregate these candidate surface directions by performing two smooth interpolations on the mesh surface (first within each view and second across multiple views). We propose custom confidence-based weights for the candidate directions in each interpolation that allow us to resolve conflicts between candidates on the same face and smoothly interpolate our field to occluded faces. Our method is modular and can be used with many different 2D visual priors. We show additional applications to texture-aligned quad meshing as well as interactive cross-field design using coarse, user-drawn lines as signal. We demonstrate the effectiveness of CrossLift on a diverse set of both organic and mechanical shapes and produce quad meshes that exhibit superior semantic alignment as compared to existing methods. Project page at: https://crosslift.github.io/

cs.GR↗

arXiv2026

Greed for the Spheres: A Signed Distance Interpolation Method

We propose a method to interpolate Signed Distance Function (SDF) data from a discrete set of samples. Unlike prior work, our approach ensures that the new SDF data values are fully consistent with the input and each other, such that the augmented data still corresponds to a geometrically realizable surface. We express the theoretical properties of SDFs as hard geometric constraints, and construct an efficient greedy algorithm for consistent SDF interpolation that is made even faster with powerful parallelized GPU preprocessing. We exemplify the usefulness of our method by evaluating it on three practical applications: global SDF refinement, in which the SDF data is upsampled without knowledge of the ground truth; mesh reconstruction, where our method can reconstruct highly detailed surfaces using global information from coarse input SDFs; and repair of pseudo-SDFs, which result from many pipelines such as CSG Boolean operations and must be turned into valid SDFs for downstream processing tasks. Our refined SDFs are guaranteed to be consistent with the input, where previous methods have no such guarantee.

cs.GR↗

arXiv2026

SpUDD: Superpower Contouring of Unsigned Distance Data

Unsigned distance functions offer a powerful and flexible implicit surface representation that, unlike their signed counterparts, allow for surfaces that are open, non-orientable, or non-manifold. We consider the problem of reconstructing arbitrary surfaces from a finite set of samples of unsigned distance data. Existing methods for mesh reconstruction from distance data rely on sign information, accurate gradients, a corresponding continuous distance function, or extensive data-dependent training. However, they fail when applied to input that is both discrete and unsigned. Inspired by this challenge, we study the power diagram generated by the distance samples and propose a novel theoretical concept, the superpower contour, which we prove converges to the true surface in the limit of sampling density. We use this superpower contour as an initial surface proxy and design an algorithm that leverages it to produce a polygonal mesh approximating the unknown true geometry. Our method vastly outperforms other conceivable strategies for the discrete unsigned distance reconstruction task, and sets the stage for future work on this mathematically rich problem.

cs.GR↗

arXiv2026

Dual Contouring of Signed Distance Data

We propose an algorithm to reconstruct explicit polygonal meshes from discretely sampled Signed Distance Function (SDF) data, which is especially effective at recovering sharp features. Building on the traditional Dual Contouring of Hermite Data method, we design and solve a quadratic optimization problem to decide the optimal placement of the mesh's vertices within each cell of a regular grid. Critically, this optimization relies solely on discretely sampled SDF data, without requiring arbitrary access to the function, gradient information, or training on large-scale datasets. Our method sets a new state of the art in surface reconstruction from SDFs at medium and high resolutions, and opens the door for applications in 3D modeling and design.

cs.GR↗

arXiv2026

Phong-Rodrigues Extrinsic Vector-Field Processing

We introduce a new extrinsic discretization of tangent vector fields on triangle meshes that is continuous, with bounded derivatives that are continuous almost everywhere, supporting pointwise evaluation and integration of differential operators. We achieve this by building a continuous normal field over the mesh via Phong interpolation and using minimal Rodrigues rotations to transport vertex-based tangent vectors into triangle interiors. Unlike most existing discretizations, which typically sacrifice either continuity or the ability to evaluate derivatives pointwise, our approach supports both. Because it is pointwise evaluatable, and using the fact that the covariant derivative can be decomposed into its symmetric, antisymmetric, and scalar components, our discretization supports the construction of standard vector-field processing operators including the connection and Hodge Laplacians, Killing energy, divergence, curl, and the Lie bracket. This framework provides a simple and practical finite-element formulation for vector-field processing on meshes, supporting both integration-based operators and pointwise queries. To our knowledge, ours is the first discretization that jointly enables extrinsic continuous vector fields, bounded derivatives, and pointwise evaluation of this collection of operators.

cs.GR↗

arXiv2025

Geometry in Style: 3D Stylization via Surface Normal Deformation

We present Geometry in Style, a new method for identity-preserving mesh stylization. Existing techniques either adhere to the original shape through overly restrictive deformations such as bump maps or significantly modify the input shape using expressive deformations that may introduce artifacts or alter the identity of the source shape. In contrast, we represent a deformation of a triangle mesh as a target normal vector for each vertex neighborhood. The deformations we recover from target normals are expressive enough to enable detailed stylizations yet restrictive enough to preserve the shape's identity. We achieve such deformations using our novel differentiable As-Rigid-As-Possible (dARAP) layer, a neural-network-ready adaptation of the classical ARAP algorithm which we use to solve for per-vertex rotations and deformed vertices. As a differentiable layer, dARAP is paired with a visual loss from a text-to-image model to drive deformations toward style prompts, altogether giving us Geometry in Style. Our project page is at https://threedle.github.io/geometry-in-style.

cs.GR↗

arXiv2024

Robust Biharmonic Skinning Using Geometric Fields

Bounded bihramonic weights are a popular tool used to rig and deform characters for animation, to compute reduced-order simulations, and to define feature descriptors for geometry processing. They necessitate tetrahedralizing the volume bounded by the surface, introducing the possibility of meshing artifacts or tetrahedralization failure. We introduce a mesh-free and robust automatic skinning technique that generates weights comparable to the current state of the art, but works reliably even on open surfaces, triangle soups, and point clouds where current methods fail. We achieve this through the use of a specialized Lagrangian representation enabled by the advent of hardware ray-tracing, which circumvents the need for finite elements while optimizing the biharmonic energy and enforcing boundary conditions. The flexibility of our formulation allows us to integrate artistic control through weight painting during the optimization. We offer a thorough qualitative and quantitative evaluation of our method.

cs.GR↗

arXiv2023

A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains

We introduce a framework for solving a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker-Planck equation. PDE in this class often have nonlinear or stiff terms that cannot be resolved with standard methods on curved triangle meshes. To address this challenge, we leverage a splitting integrator combined with a convex optimization step to solve these PDE. Our machinery can be used to compute entropic approximation of optimal transport distances on geometric domains, overcoming the numerical limitations of the state-of-the-art method. In addition, we demonstrate the versatility of our method on a number of linear and nonlinear PDE that appear in diffusion and front propagation tasks in geometry processing.

math.NA↗

arXiv2023

An Adaptive Fast-Multipole-Accelerated Hybrid Boundary Integral Equation Method for Accurate Diffusion Curves

In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary conditions. Previous applications of the boundary element method to diffusion curves have relied on polygonal approximations, which either forfeit the high-order smoothness of Bézier curves, or, when the polygonal approximation is extremely detailed, result in large and costly systems of equations that must be solved. In this paper, we utilize the boundary integral equation method to accurately and efficiently solve the underlying partial differential equation. Given a desired resolution and viewport, we then interpolate this solution and use the boundary element method to render it. We couple this hybrid approach with the fast multipole method on a non-uniform quadtree for efficient computation. Furthermore, we introduce an adaptive strategy to enable truly scalable infinite-resolution diffusion curves.

math.NA↗

arXiv2023

Variational Barycentric Coordinates

We propose a variational technique to optimize for generalized barycentric coordinates that offers additional control compared to existing models. Prior work represents barycentric coordinates using meshes or closed-form formulae, in practice limiting the choice of objective function. In contrast, we directly parameterize the continuous function that maps any coordinate in a polytope's interior to its barycentric coordinates using a neural field. This formulation is enabled by our theoretical characterization of barycentric coordinates, which allows us to construct neural fields that parameterize the entire function class of valid coordinates. We demonstrate the flexibility of our model using a variety of objective functions, including multiple smoothness and deformation-aware energies; as a side contribution, we also present mathematically-justified means of measuring and minimizing objectives like total variation on discontinuous neural fields. We offer a practical acceleration strategy, present a thorough validation of our algorithm, and demonstrate several applications.

cs.GR↗

arXiv2023

The Effect of Smoothing on the Interpretation of Time Series Data: A COVID-19 Case Study

We conduct a controlled crowd-sourced experiment of COVID-19 case data visualization to study if and how different plotting methods, time windows, and the nature of the data influence people's interpretation of real-world COVID-19 data and people's prediction of how the data will evolve in the future. We find that a 7-day backward average smoothed line successfully reduces the distraction of periodic data patterns compared to just unsmoothed bar data. Additionally, we find that the presence of a smoothed line helps readers form a consensus on how the data will evolve in the future. We also find that the fixed 7-day smoothing window size leads to different amounts of perceived recurring patterns in the data depending on the time period plotted -- this suggests that varying the smoothing window size together with the plot window size might be a promising strategy to influence the perception of spurious patterns in the plot.

cs.HC↗

arXiv2023

Reach For the Spheres: Tangency-Aware Surface Reconstruction of SDFs

Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an SDF, traditional isosurfacing methods, such as Marching Cubes and and its variants, are typically used. However, these methods overlook fundamental properties of SDFs, resulting in reconstructions that exhibit severe oversmoothing and feature loss. To address this shortcoming, we propose a novel method based on a key insight: each SDF sample corresponds to a spherical region that must lie fully inside or outside the surface, depending on its sign, and that must be tangent to the surface at some point. Leveraging this understanding, we formulate an energy that gauges the degree of violation of tangency constraints by a proposed surface. We then employ a gradient flow that minimizes our energy, starting from an initial triangle mesh that encapsulates the surface. This algorithm yields superior reconstructions to previous methods, even with sparsely sampled SDFs. Our approach provides a more nuanced understanding of SDFs and offers significant improvements in surface reconstruction.

cs.GR↗

arXiv2022

Symmetric Volume Maps: Order-Invariant Volumetric Mesh Correspondence with Free Boundary

Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces. The neglected task of volumetric correspondence--a natural extension relevant to shapes extracted from simulation, medical imaging, and volume rendering--presents unique challenges that do not appear in the two-dimensional case. In this work, we propose a method for mapping between volumes represented as tetrahedral meshes. Our formulation minimizes a distortion energy designed to extract maps symmetrically, i.e., without dependence on the ordering of the source and target domains. We accompany our method with theoretical discussion describing the consequences of this symmetry assumption, leading us to select a symmetrized ARAP energy that favors isometric correspondences. Our final formulation optimizes for near-isometry while matching the boundary. We demonstrate our method on a diverse geometric dataset, producing low-distortion matchings that align closely to the boundary.

cs.GR↗

arXiv2022

A Splitting Scheme for Flip-Free Distortion Energies

We introduce a robust optimization method for flip-free distortion energies used, for example, in parametrization, deformation, and volume correspondence. This method can minimize a variety of distortion energies, such as the symmetric Dirichlet energy and our new symmetric gradient energy. We identify and exploit the special structure of distortion energies to employ an operator splitting technique, leading us to propose a novel Alternating Direction Method of Multipliers (ADMM) algorithm to deal with the non-convex, non-smooth nature of distortion energies. The scheme results in an efficient method where the global step involves a single matrix multiplication and the local steps are closed-form per-triangle/per-tetrahedron expressions that are highly parallelizable. The resulting general-purpose optimization algorithm exhibits robustness to flipped triangles and tetrahedra in initial data as well as during the optimization. We establish the convergence of our proposed algorithm under certain conditions and demonstrate applications to parametrization, deformation, and volume correspondence.

cs.GR↗

arXiv2022

A Dataset and Benchmark for Mesh Parameterization

UV parameterization is a core task in computer graphics, with applications in mesh texturing, remeshing, mesh repair, mesh editing, and more. It is thus an active area of research, which has led to a wide variety of parameterization methods that excel according to different measures of quality. There is no single metric capturing parameterization quality in practice, since the quality of a parameterization heavily depends on its application; hence, parameterization methods can best be judged by the actual users of the computed result. In this paper, we present a dataset of meshes together with UV maps collected from various sources and intended for real-life use. Our dataset can be used to test parameterization methods in realistic environments. We also introduce a benchmark to compare parameterization methods with artist-provided UV parameterizations using a variety of metrics. This strategy enables us to evaluate the performance of a parameterization method by computing the quality indicators that are valued by the designers of a mesh.

cs.GR↗

arXiv2022

A mixed finite element method with piecewise linear elements for the biharmonic equation on surfaces

The biharmonic equation with Dirichlet and Neumann boundary conditions discretized using the mixed finite element method and piecewise linear (with the possible exception of boundary triangles) finite elements on triangular elements has been well-studied for domains in R2. Here we study the analogous problem on polyhedral surfaces. In particular, we provide a convergence proof of discrete solutions to the corresponding smooth solution of the biharmonic equation. We obtain convergence rates that are identical to the ones known for the planar setting. Our proof focuses on three different problems: solving the biharmonic equation on the surface, solving the biharmonic equation in a discrete space in the metric of the surface, and solving the biharmonic equation in a discrete space in the metric of the polyhedral approximation of the surface. We employ inverse discrete Laplacians to bound the error between the solutions of the two discrete problems, and generalize a flat strategy to bound the remaining error between the discrete solutions and the exact solution on the curved surface.

math.NA↗