arXiv subjects

Denis Zorin

Publications and source records attributed to Denis Zorin.

At least 19 recordsLinked to original sources

arXiv2026

BijectiveRemesh: Maintaining Bijective Mappings for Data Transfer Across Remeshed Manifolds

We introduce BijectiveRemesh, a robust algorithm for maintaining a continuous, bijective mapping across complex remeshing sequences on both 2D triangle surfaces and 3D tetrahedral meshes. Unlike traditional data transfer methods that rely on interpolation or projection, our approach constructs a mathematically rigorous composite map from the input mesh to the output mesh by chaining local bijective atlases defined for each primitive remeshing operation. Our framework represents the overall mapping as a composition of local bijective atlases, one per remeshing operation. Building upon successive self-parameterization, we introduce a Shared Scaffold structure for 2D triangle meshes that enforces global bijectivity through local orientation preservation. We extend this approach to handle edge splits, edge swaps, and vertex smoothing beyond the original edge collapses. For 3D tetrahedral meshes, we generalize the local atlas construction using Steinitz's Theorem and Maxwell-Cremona lifting to ensure valid embeddings. This enables exact tracking of geometric entities, including points, curves, and surfaces, across remeshing, with applications from texture transfer to volumetric simulations.

cs.GR↗

arXiv2025

eFlesh: Highly customizable Magnetic Touch Sensing using Cut-Cell Microstructures

If human experience is any guide, operating effectively in unstructured environments -- like homes and offices -- requires robots to sense the forces during physical interaction. Yet, the lack of a versatile, accessible, and easily customizable tactile sensor has led to fragmented, sensor-specific solutions in robotic manipulation -- and in many cases, to force-unaware, sensorless approaches. With eFlesh, we bridge this gap by introducing a magnetic tactile sensor that is low-cost, easy to fabricate, and highly customizable. Building an eFlesh sensor requires only four components: a hobbyist 3D printer, off-the-shelf magnets (<$5), a CAD model of the desired shape, and a magnetometer circuit board. The sensor is constructed from tiled, parameterized microstructures, which allow for tuning the sensor's geometry and its mechanical response. We provide an open-source design tool that converts convex OBJ/STL files into 3D-printable STLs for fabrication. This modular design framework enables users to create application-specific sensors, and to adjust sensitivity depending on the task. Our sensor characterization experiments demonstrate the capabilities of eFlesh: contact localization RMSE of 0.5 mm, and force prediction RMSE of 0.27 N for normal force and 0.12 N for shear force. We also present a learned slip detection model that generalizes to unseen objects with 95% accuracy, and visuotactile control policies that improve manipulation performance by 40% over vision-only baselines -- achieving 91% average success rate for four precise tasks that require sub-mm accuracy for successful completion. All design files, code and the CAD-to-eFlesh STL conversion tool are open-sourced and available on https://e-flesh.com.

cs.RO↗

arXiv2025

Codimensional MultiMeshing: Synchronizing the Evolution of Multiple Embedded Geometries

Complex geometric tasks such as geometric modeling, physical simulation, and texture parametrization often involve the embedding of many complex sub-domains with potentially different dimensions. These tasks often require evolving the geometry and topology of the discretizations of these sub-domains, and guaranteeing a \emph{consistent} overall embedding for the multiplicity of sub-domains is required to define boundary conditions. We propose a data structure and algorithmic framework for hierarchically encoding a collection of meshes, enabling topological and geometric changes to be automatically propagated with coherent correspondences between them. We demonstrate the effectiveness of our approach in surface mesh decimation while preserving UV seams, periodic 2D/3D meshing, and extending the TetWild algorithm to ensure topology preservation of the embedded structures.

cs.GR↗

arXiv2024

Seamless Parametrization in Penner Coordinates

We introduce a conceptually simple and efficient algorithm for seamless parametrization, a key element in constructing quad layouts and texture charts on surfaces. More specifically, we consider the construction of parametrizations with prescribed holonomy signatures i.e., a set of angles at singularities, and rotations along homology loops, preserving which is essential for constructing parametrizations following an input field, as well as for user control of the parametrization structure. Our algorithm performs exceptionally well on a large dataset based on Thingi10k [Zhou and Jacobson 2016], (16156 meshes) as well as on a challenging smaller dataset of [Myles et al. 2014], converging, on average, in 9 iterations. Although the algorithm lacks a formal mathematical guarantee, presented empirical evidence and the connections between convex optimization and closely related algorithms, suggest that a similar formulation can be found for this algorithm in the future.

cs.GR↗

arXiv2024

Topological Offsets

We introduce Topological Offsets, a novel approach to generate manifold and self-intersection-free offset surfaces that are topologically equivalent to an offset infinitesimally close to the surface. Our approach, by construction, creates a manifold, watertight, and self-intersection-free offset surface strictly enclosing the input, while doing a best effort to move it to a prescribed distance from the input. Differently from existing approaches, we embed the input in a background mesh and insert a topological offset around the input with purely combinatorial operations. The topological offset is then inflated/deflated to match the user-prescribed distance while enforcing that no intersections or non-manifold configurations are introduced. We evaluate the effectiveness and robustness of our approach on the Thingi10k dataset, and show that topological offsets are beneficial in multiple graphics applications, including (1) converting non-manifold surfaces to manifold ones, (2) creating layered offsets, and (3) reliably computing finite offsets.

cs.CG↗

arXiv2024

High-Order Continuous Geometrical Validity

We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a piecewise-linear trajectory. Our algorithm uses a combination of adaptive B\'ezier refinement and bisection search to determine if, when, and where the Jacobian determinant of an element's polynomial geometric map becomes negative in the transition from one configuration to another. Unlike previous approaches, our method preserves its properties also when implemented using floating point arithmetic: This feature comes at a small additional runtime cost compared to existing inexact methods, making it a drop-in replacement for current validity tests, while providing superior robustness and generality. To prove the practical effectiveness of our algorithm, we demonstrate its use in a high-order Incremental Potential Contact (IPC) elastodynamic simulator, and we experimentally show that it prevents invalid, simulation-breaking configurations that would otherwise occur using inexact methods, without the need for manual parameter tuning.

cs.CG↗

arXiv2024

Geometric Contact Potential

Barrier potentials gained popularity as a means for robust contact handling in physical modeling and for modeling self-avoiding shapes. The key to the success of these approaches is adherence to geometric constraints, i.e., avoiding intersections, which are the cause of most robustness problems in complex deformation simulation with contact. However, existing barrier-potential methods may lead to spurious forces and imperfect satisfaction of the geometric constraints. They may have strong resolution dependence, requiring careful adaptation of the potential parameters to the object discretizations. We present a systematic derivation of a continuum potential defined for smooth and piecewise smooth surfaces, starting from identifying a set of natural requirements for contact potentials, including the barrier property, locality, differentiable dependence on shape, and absence of forces in rest configurations. Our potential is formulated independently of surface discretization and addresses the shortcomings of existing potential-based methods while retaining their advantages. We present a discretization of our potential that is a drop-in replacement for the potential used in the Incremental Potential Contact (IPC) formulation, and compare its behavior to other potential formulations, demonstrating that it has the expected behavior. The presented formulation connects existing barrier approaches, as all recent existing methods can be viewed as a variation of the presented potential, and lays a foundation for developing alternative (e.g., higher-order) versions.

cs.GR↗

arXiv2023

PRS: Sharp Feature Priors for Resolution-Free Surface Remeshing

Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased, perceptually distorted surfaces and lack scalability to high-resolution 3D shapes. We present a data-driven approach for automatic feature detection and remeshing that requires only a coarse, aliased mesh as input and scales to arbitrary resolution reconstructions. We define and learn a collection of surface-based fields to (1) capture sharp geometric features in the shape with an implicit vertexwise model and (2) approximate improvements in normals alignment obtained by applying edge-flips with an edgewise model. To support scaling to arbitrary complexity shapes, we learn our fields using local triangulated patches, fusing estimates on complete surface meshes. Our feature remeshing algorithm integrates the learned fields as sharp feature priors and optimizes vertex placement and mesh connectivity for maximum expected surface improvement. On a challenging collection of high-resolution shape reconstructions in the ABC dataset, our algorithm improves over state-of-the-art by 26% normals F-score and 42% perceptual $\text{RMSE}_{\text{v}}$.

cs.CV↗

arXiv2023

Cut-Cell Microstructures for Two-scale Structural Optimization

Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is increasingly widely used in many fabrication applications to achieve a target deformation behavior for a variety of objects. The main idea of this approach is to optimize the distribution of material properties in the object partitioned into relatively coarse cells, and then replace each cell with microstructure geometry that mimics these material properties. In this paper, we focus on adapting this approach to complex shapes in situations when preserving the shape's surface is important. Our approach extends any regular (i.e. defined on a regular lattice grid) microstructure family to complex shapes, by enriching it with individually optimized cut-cell tiles adapted to the geometry of the cut-cell. We propose an automated and robust pipeline based on this approach, and we show that the performance of the regular microstructure family is only minimally affected by our extension while allowing its use on 2D and 3D shapes of high complexity.

cs.GR↗

arXiv2023

Optimized shock-protecting microstructures

Mechanical shock is a common occurrence in various settings, there are two different scenarios for shock protection: catastrophic protection (e.g. car collisions and falls) and routine protection (e.g. shoe soles and shock absorbers for car seats). The former protects against one-time events, the latter against periodic shocks and loads. Common shock absorbers based on plasticity and fracturing materials are suitable for the former, while our focus is on the latter, where elastic structures are useful. Improved elastic materials protecting against shock can be used in applications such as automotive suspension, furniture like sofas and mattresses, landing gear systems, etc. Materials offering optimal protection against shock have a highly non-linear elastic response: their reaction force needs to be as close as possible to constant with respect to deformation. In this paper, we use shape optimization and topology search to design 2D families of microstructures approximating the ideal behavior across a range of deformations, leading to superior shock protection. We present an algorithmic pipeline for the optimal design of such families combining differentiable nonlinear homogenization with self-contact and an optimization algorithm. These advanced 2D designs can be extruded and fabricated with existing 3D printing technologies. We validate their effectiveness through experimental testing.

math.OC↗

arXiv2023

Convergent Incremental Potential Contact

Recent advances in the simulation of frictionally contacting elastodynamics with the Incremental Potential Contact (IPC) model have enabled inversion and intersection-free simulation via the application of mollified barriers, filtered line-search, and optimization-based solvers for time integration. In its current formulation the IPC model is constructed via a discrete constraint model, replacing non-interpenetration constraints with barrier potentials on an already spatially discretized domain. However, while effective, this purely discrete formulation prohibits convergence under refinement. To enable a convergent IPC model we reformulate IPC potentials in the continuous setting and provide a first, convergent discretization thereof. We demonstrate and analyze the convergence behavior of this new model and discretization on a range of elastostatic and dynamic contact problems, and evaluate its accuracy on both analytical benchmarks and application-driven examples.

math.NA↗

arXiv2023

Algebraic Smooth Occluding Contours

Computing occluding contours is a key building block of non-photorealistic rendering, but producing contours with consistent visibility has been notoriously challenging. This paper describes the first general-purpose smooth surface construction for which the occluding contours can be computed in closed form. For a given input mesh and camera viewpoint, we produce a $G^1$ piecewise-quadratic surface approximating the mesh. We show how the image-space occluding contours of this representation may then be described as piecewise rational curves. We show that this method produces smooth contours with consistent visibility much more efficiently than the state-of-the-art.

cs.GR↗

arXiv2022

Metric Optimization in Penner Coordinates

Many parametrization and mapping-related problems in geometry processing can be viewed as metric optimization problems, i.e., computing a metric minimizing a functional and satisfying a set of constraints, such as flatness. Penner coordinates are global coordinates on the space of metrics on meshes with a fixed vertex set and topology, but varying connectivity, making it homeomorphic to the Euclidean space of dimension equal to the number of edges in the mesh, without any additional constraints imposed. These coordinates play an important role in the theory of discrete conformal maps, enabling recent development of highly robust algorithms with convergence and solution existence guarantees for computing such maps. We demonstrate how Penner coordinates can be used to solve a general class of optimization problems involving metrics, including optimization and interpolation, while retaining the key solution existence guarantees available for discrete conformal maps.

cs.CG↗

arXiv2022

High-Order Incremental Potential Contact for Elastodynamic Simulation on Curved Meshes

High-order bases provide major advantages over linear ones in terms of efficiency, as they provide (for the same physical model) higher accuracy for the same running time, and reliability, as they are less affected by locking artifacts and mesh quality. Thus, we introduce a high-order finite element (FE) formulation (high-order bases) for elastodynamic simulation on high-order (curved) meshes with contact handling based on the recently proposed Incremental Potential Contact (IPC) model. Our approach is based on the observation that each IPC optimization step used to minimize the elasticity, contact, and friction potentials leads to linear trajectories even in the presence of nonlinear meshes or nonlinear FE bases. It is thus possible to retain the strong non-penetration guarantees and large time steps of the original formulation while benefiting from the high-order bases and high-order geometry. We accomplish this by mapping displacements and resulting contact forces between a linear collision proxy and the underlying high-order representation. We demonstrate the effectiveness of our approach in a selection of problems from graphics, computational fabrication, and scientific computing.

cs.GR↗

arXiv2022

DEF: Deep Estimation of Sharp Geometric Features in 3D Shapes

We propose Deep Estimators of Features (DEFs), a learning-based framework for predicting sharp geometric features in sampled 3D shapes. Differently from existing data-driven methods, which reduce this problem to feature classification, we propose to regress a scalar field representing the distance from point samples to the closest feature line on local patches. Our approach is the first that scales to massive point clouds by fusing distance-to-feature estimates obtained on individual patches. We extensively evaluate our approach against related state-of-the-art methods on newly proposed synthetic and real-world 3D CAD model benchmarks. Our approach not only outperforms these (with improvements in Recall and False Positives Rates), but generalizes to real-world scans after training our model on synthetic data and fine-tuning it on a small dataset of scanned data. We demonstrate a downstream application, where we reconstruct an explicit representation of straight and curved sharp feature lines from range scan data.

cs.CV↗

arXiv2022

Differentiable solver for time-dependent deformation problems with contact

We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed incremental potential contact method for handling contact and friction forces to solve ODE- and PDE-constrained optimization problems on scenes with complex geometry. It supports static and dynamic problems and differentiation with respect to all physical parameters involved in the physical problem description, which include shape, material parameters, friction parameters, and initial conditions. Our analytically derived adjoint formulation is efficient, with a small overhead (typically less than 10% for nonlinear problems) over the forward simulation, and shares many similarities with the forward problem, allowing the reuse of large parts of existing forward simulator code. We implement our approach on top of the open-source PolyFEM library and demonstrate the applicability of our solver to shape design, initial condition optimization, and material estimation on both simulated results and physical validations.

cs.GR↗

arXiv2022

3D Parametric Wireframe Extraction Based on Distance Fields

We present a pipeline for parametric wireframe extraction from densely sampled point clouds. Our approach processes a scalar distance field that represents proximity to the nearest sharp feature curve. In intermediate stages, it detects corners, constructs curve segmentation, and builds a topological graph fitted to the wireframe. As an output, we produce parametric spline curves that can be edited and sampled arbitrarily. We evaluate our method on 50 complex 3D shapes and compare it to the novel deep learning-based technique, demonstrating superior quality.

cs.CV↗

arXiv2022

Multi-sensor large-scale dataset for multi-view 3D reconstruction

We present a new multi-sensor dataset for multi-view 3D surface reconstruction. It includes registered RGB and depth data from sensors of different resolutions and modalities: smartphones, Intel RealSense, Microsoft Kinect, industrial cameras, and structured-light scanner. The scenes are selected to emphasize a diverse set of material properties challenging for existing algorithms. We provide around 1.4 million images of 107 different scenes acquired from 100 viewing directions under 14 lighting conditions. We expect our dataset will be useful for evaluation and training of 3D reconstruction algorithms and for related tasks. The dataset is available at skoltech3d.appliedai.tech.

cs.CV↗