arXiv subjects

Amir Vaxman

Publications and source records attributed to Amir Vaxman.

At least 19 recordsLinked to original sources

arXiv2026

Convex Quadratic Distance Field Computation

Methods for computing distances from sources on discrete meshes commonly either compute geodesics directly on polyhedral surfaces or approximate the distance in a finite-element framework. Exact window-based polyhedral methods are highly accurate on clean manifold surfaces, but their unfolding construction does not extend to tetrahedral volumes and relies on manifold connectivity. Because their results are tied to the input polyhedron, geometric noise directly affects the computed distance field. Finite-element methods extend naturally to triangle surfaces and tetrahedral volumes, but state-of-the-art methods represent the distance field as a piecewise-linear (PL) function, limiting accuracy on coarse or poorly shaped meshes. We argue that the PL representation itself, rather than the algorithm built on top of it, limits the result. Geodesic distance exhibits cone-like behaviour at its source and is not piecewise linear even on flat domains. In contrast, the squared distance is exactly quadratic in such domains. Therefore, our Quadratic Distance Field method represents the squared distance using piecewise-quadratic (PQ) elements, reproducing flat squared distances exactly. We show that simply increasing the element order does not improve existing algorithms, and develop a convex formulation for the squared distance over PQ elements. The same formulation applies to both triangle surfaces and tetrahedral volumes, supports anisotropic metrics and nonmanifold connectivity, and remains robust under noise. Finally, we present an efficient solver based on the alternating direction method of multipliers and demonstrate its robustness and accuracy on a benchmark of thousands of real-world models.

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↗

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

BiMotion: B-spline Motion for Text-guided Dynamic 3D Character Generation

Text-guided dynamic 3D character generation has advanced rapidly, yet producing high-quality motion that faithfully reflects rich textual descriptions remains challenging. Existing methods tend to generate limited sub-actions or incoherent motion due to fixed-length temporal inputs and discrete frame-wise representations that fail to capture rich motion semantics. We address these limitations by representing motion with continuous differentiable B-spline curves, enabling more effective motion generation without modifying the capabilities of the underlying generative model. Specifically, our closed-form, Laplacian-regularized B-spline solver efficiently compresses variable-length motion sequences into compact representations with a fixed number of control points. Further, we introduce a normal-fusion strategy for input shape adherence along with correspondence-aware and local-rigidity losses for motion-restoration quality. To train our model, we collate BIMO, a new dataset containing diverse variable-length 3D motion sequences with rich, high-quality text annotations. Extensive evaluations show that our feed-forward framework BiMotion generates more expressive, higher-quality, and better prompt-aligned motions than existing state-of-the-art methods, while also achieving faster generation. Our project page is at: https://wangmiaowei.github.io/BiMotion.github.io/.

cs.CV↗

arXiv2026

Learned Adaptive Mesh Generation

Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer graphics since they encode global smoothness with local control leading to stable, well-behaved solutions. The Poisson equation is a linear elliptic PDE that serves as a prototypical candidate to assess newly-proposed solvers. Solving the Poisson equation on an arbitrary 3D domain, say a 3D scan of a turbine's blade, is computationally expensive and scales quadratically with discretization. Traditional workflows in research and industry exploit variants of the finite element method (FEM), but some key benefits of using Monte Carlo (MC) methods have been identified. Our key idea is to exploit a sparse and approximate solution (via FEM or MC) to the Poisson equation towards inferring an adaptive discretization in one shot. We achieve this by training a lightweight neural network that generalizes across shapes and boundary conditions. Our algorithm, Learned Adaptive Mesh Generation (LAMG), maps from a coarse solution to a sizing field that defines a local (adaptive) spatial resolution. This output space, rather than directly predicting a high-resolution solution, is a unique aspect of our approach. We use standard methods to generate tetrahedral meshes that respect the sizing field, and obtain the solution via one FEM computation on the adaptive mesh. That is, our neural network serves as a surrogate model of a computationally expensive method that requires multiple (iterative) FEM solves. We demonstrate the versatility, controllability, robustness and efficiency of LAMG via systematic experimentation.

cs.GR↗

arXiv2026

MotionPhysics: Learnable Motion Distillation for Text-Guided Simulation

Accurately simulating existing 3D objects and a wide variety of materials often demands expert knowledge and time-consuming physical parameter tuning to achieve the desired dynamic behavior. We introduce MotionPhysics, an end-to-end differentiable framework that infers plausible physical parameters from a user-provided natural language prompt for a chosen 3D scene of interest, removing the need for guidance from ground-truth trajectories or annotated videos. Our approach first utilizes a multimodal large language model to estimate material parameter values, which are constrained to lie within plausible ranges. We further propose a learnable motion distillation loss that extracts robust motion priors from pretrained video diffusion models while minimizing appearance and geometry inductive biases to guide the simulation. We evaluate MotionPhysics across more than thirty scenarios, including real-world, human-designed, and AI-generated 3D objects, spanning a wide range of materials such as elastic solids, metals, foams, sand, and both Newtonian and non-Newtonian fluids. We demonstrate that MotionPhysics produces visually realistic dynamic simulations guided by natural language, surpassing the state of the art while automatically determining physically plausible parameters. The code and project page are available at: https://wangmiaowei.github.io/MotionPhysics.github.io/.

cs.CV↗

arXiv2025

CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences

We introduce Canonical Consolidation Fields (CanFields). This novel method interpolates arbitrary-length sequences of independently sampled 3D point clouds into a unified, continuous, and coherent deforming shape. Unlike prior methods that oversmooth geometry or produce topological and geometric artifacts, CanFields optimizes fine-detailed geometry and deformation jointly in an unsupervised fitting with two novel bespoke modules. First, we introduce a dynamic consolidator module that adjusts the input and assigns confidence scores, balancing the optimization of the canonical shape and its motion. Second, we represent the motion as a diffeomorphic flow parameterized by a smooth velocity field. We have validated our robustness and accuracy on more than 50 diverse sequences, demonstrating its superior performance even with missing regions, noisy raw scans, and sparse data. Our project page is at: https://wangmiaowei.github.io/CanFields.github.io/.

cs.CV↗

arXiv2025

Power-Linear Polar Directional Fields

We introduce a novel method for directional-field design on meshes, enabling users to specify singularities at any location on a mesh. Our method uses a piecewise power-linear representation for phase and scale, offering precise control over field topology. The resulting fields are smooth and accommodate any singularity index and field symmetry. With this representation, we mitigate the artifacts caused by coarse or uneven meshes. We showcase our approach on meshes with diverse topologies and triangle qualities.

cs.GR↗

arXiv2025

CrossSDF: 3D Reconstruction of Thin Structures From Cross-Sections

Reconstructing complex structures from planar cross-sections is a challenging problem, with wide-reaching applications in medical imaging, manufacturing, and topography. Out-of-the-box point cloud reconstruction methods can often fail due to the data sparsity between slicing planes, while current bespoke methods struggle to reconstruct thin geometric structures and preserve topological continuity. This is important for medical applications where thin vessel structures are present in CT and MRI scans. This paper introduces CrossSDF, a novel approach for extracting a 3D signed distance field from 2D signed distances generated from planar contours. Our approach makes the training of neural SDFs contour-aware by using losses designed for the case where geometry is known within 2D slices. Our results demonstrate a significant improvement over existing methods, effectively reconstructing thin structures and producing accurate 3D models without the interpolation artifacts or over-smoothing of prior approaches.

cs.CV↗

arXiv2025

Non-planar 3D Printing of Double Shells

We present a method to fabricate double shell structures printed in trans-versal directions using multi-axis fused-deposition-modeling (FDM) robot-ic 3D printing. Shell structures, characterized by lightweight, thin walls, fast buildup, and minimal material usage, find diverse applications in pro-totyping and architecture for uses such as façade panels, molds for concrete casting, or full-scale pavilions. We leverage an underlying representation of transversal strip networks generated using existing methods and propose a methodology for converting them into printable partitions. Each partition is printed separately and assembled into a double-shell structure. We out-line the specifications and workflow that make the printing of each piece and the subsequent assembly process feasible. The versatility and robust-ness of our method are demonstrated with both digital and fabricated re-sults on surfaces of different scales and geometric complexity.

cs.RO↗

arXiv2024

Spatially-Adaptive Hash Encodings For Neural Surface Reconstruction

Positional encodings are a common component of neural scene reconstruction methods, and provide a way to bias the learning of neural fields towards coarser or finer representations. Current neural surface reconstruction methods use a "one-size-fits-all" approach to encoding, choosing a fixed set of encoding functions, and therefore bias, across all scenes. Current state-of-the-art surface reconstruction approaches leverage grid-based multi-resolution hash encoding in order to recover high-detail geometry. We propose a learned approach which allows the network to choose its encoding basis as a function of space, by masking the contribution of features stored at separate grid resolutions. The resulting spatially adaptive approach allows the network to fit a wider range of frequencies without introducing noise. We test our approach on standard benchmark surface reconstruction datasets and achieve state-of-the-art performance on two benchmark datasets.

cs.CV↗

arXiv2023

Explicit Neural Surfaces: Learning Continuous Geometry With Deformation Fields

We introduce Explicit Neural Surfaces (ENS), an efficient smooth surface representation that directly encodes topology with a deformation field from a known base domain. We apply this representation to reconstruct explicit surfaces from multiple views, where we use a series of neural deformation fields to progressively transform the base domain into a target shape. By using meshes as discrete surface proxies, we train the deformation fields through efficient differentiable rasterization. Using a fixed base domain allows us to have Laplace-Beltrami eigenfunctions as an intrinsic positional encoding alongside standard extrinsic Fourier features, with which our approach can capture fine surface details. Compared to implicit surfaces, ENS trains faster and has several orders of magnitude faster inference times. The explicit nature of our approach also allows higher-quality mesh extraction whilst maintaining competitive surface reconstruction performance and real-time capabilities.

cs.CV↗

arXiv2023

Constrained Delaunay Tetrahedrization: A Robust and Practical Approach

We present a numerically robust algorithm for computing the constrained Delaunay tetrahedrization (CDT) of a piecewise-linear complex, which has a 100% success rate on the 4408 valid models in the Thingi10k dataset. We build on the underlying theory of the well-known TetGen software, but use a floating-point implementation based on indirect geometric predicates to implicitly represent Steiner points: this new approach dramatically simplifies the implementation, removing the need for ad-hoc tolerances in geometric operations. Our approach leads to a robust and parameter-free implementation, with an empirically manageable number of added Steiner points. Furthermore, our algorithm addresses a major gap in TetGen's theory which may lead to algorithmic failure on valid models, even when assuming perfect precision in the calculations. Our output tetrahedrization conforms with the input geometry without approximations. We can further round our output to floating-point coordinates for downstream applications, which almost always results in valid floating-point meshes unless the input triangulation is very close to being degenerate.

cs.CG↗

arXiv2023

Fabrication-Aware Strip-Decomposable Quadrilateral Meshes

Strip-decomposable quadrilateral (SDQ) meshes, i.e., quad meshes that can be decomposed into two transversal strip networks, are vital in numerous fabrication processes; examples include woven structures, surfaces from sheets, custom rebar, or cable-net structures. However, their design is often challenging and includes tedious manual work, and there is a lack of methodologies for editing such meshes while preserving their strip decomposability. We present an interactive methodology to generate and edit SDQ meshes aligned to user-defined directions, while also incorporating desirable properties to the strips for fabrication. Our technique is based on the computation of two coupled transversal tangent direction fields, integrated into two overlapping networks of strips on the surface. As a case study, we consider the fabrication scenario of robotic non-planar 3D printing of freefrom shell surfaces and apply the presented methodology to design and fabricate non-planar print paths.

cs.GR↗

arXiv2023

BPM: Blended Piecewise Moebius Maps

We propose a novel Moebius interpolator that takes as an input a discrete map between the vertices of two planar triangle meshes, and outputs a smooth map on the input domain. The output map interpolates the discrete map, is continuous between triangles, and has low quasi-conformal distortion when the input map is discrete conformal. Our map leads to considerably smoother texture transfer compared to the alternatives, even on very coarse triangulations. Furthermore, our approach has a closed-form expression, is local, applicable to any discrete map, and leads to smooth results even for extreme deformations. Finally, by working with local intrinsic coordinates, our approach is easily generalizable to discrete maps between a surface triangle mesh and a planar mesh, i.e., a planar parameterization. We compare our method with existing approaches, and demonstrate better texture transfer results, and lower quasi-conformal errors.

cs.GR↗

arXiv2023

OReX: Object Reconstruction from Planar Cross-sections Using Neural Fields

Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.

cs.CV↗

arXiv2023

Approximating the Earth Mover's Distance between sets of geometric objects

Given two distributions $P$ and $S$ of equal total mass, the Earth Mover's Distance measures the cost of transforming one distribution into the other, where the cost of moving a unit of mass is equal to the distance over which it is moved. We give approximation algorithms for the Earth Mover's Distance between various sets of geometric objects. We give a $(1 + \varepsilon)$-approximation when $P$ is a set of weighted points and $S$ is a set of line segments, triangles or $d$-dimensional simplices. When $P$ and $S$ are both sets of line segments, sets of triangles or sets of simplices, we give a $(1 + \varepsilon)$-approximation with a small additive term. All algorithms run in time polynomial in the size of $P$ and $S$, and actually calculate the transport plan (that is, a specification of how to move the mass), rather than just the cost. To our knowledge, these are the first combinatorial algorithms with a provable approximation ratio for the Earth Mover's Distance when the objects are continuous rather than discrete points.

cs.CG↗

arXiv2021

Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable Surfaces

We introduce an algorithm to remesh triangle meshes representing developable surfaces to planar quad dominant meshes. The output of our algorithm consists of planar quadrilateral (PQ) strips that are aligned to principal curvature directions and closely approximate the curved parts of the input developable, and planar polygons representing the flat parts of the input. Developable PQ-strip meshes are useful in many areas of shape modeling, thanks to the simplicity of fabrication from flat sheet material. Unfortunately, they are difficult to model due to their restrictive combinatorics and locking issues. Other representations of developable surfaces, such as arbitrary triangle or quad meshes, are more suitable for interactive freeform modeling, but generally have non-planar faces or are not aligned to principal curvatures. Our method leverages the modeling flexibility of non-ruling based representations of developable surfaces, while still obtaining developable, curvature aligned PQ-strip meshes. Our algorithm optimizes for a scalar function on the input mesh, such that its level sets are extrinsically straight and align well to the locally estimated ruling directions. The condition that guarantees straight level sets is nonlinear of high order and numerically difficult to enforce in a straightforward manner. We devise an alternating optimization method that makes our problem tractable and practical to compute. Our method works automatically on any developable input, including multiple patches and curved folds, without explicit domain decomposition. We demonstrate the effectiveness of our approach on a variety of developable surfaces and show how our remeshing can be used alongside handle based interactive freeform modeling of developable shapes.

cs.GR↗