arXiv subjects

Daniele Panozzo

Publications and source records attributed to Daniele Panozzo.

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↗

arXiv2026

Topology-First B-Rep Meshing

Parametric boundary representation models (B-Reps) are the de facto standard in CAD, graphics, and robotics, yet converting them into valid meshes remains fragile. The difficulty originates from the unavoidable approximation of high-order surface and curve intersections to low-order primitives: the resulting geometric realization often fails to respect the exact topology encoded in the B-Rep, producing meshes with incorrect or missing adjacencies. Existing meshing pipelines address these inconsistencies through heuristic feature-merging and repair strategies that offer no topological guarantees and frequently fail on complex models. We propose a fundamentally different approach: the B-Rep topology is treated as an invariant of the meshing process. Our algorithm enforces the exact B-Rep topology while allowing a single user-defined tolerance to control the deviation of the mesh from the underlying parametric surfaces. Consequently, for any admissible tolerance, the output mesh is topologically correct; only its geometric fidelity degrades as the tolerance increases. This decoupling eliminates the need for post-hoc repairs and yields robust meshes even when the underlying geometry is inconsistent or highly approximated. We evaluate our method on thousands of real-world CAD models from the ABC and Fusion 360 repositories, including instances that fail with standard meshing tools. The results demonstrate that topological guarantees at the algorithmic level enable reliable mesh generation suitable for downstream applications.

cs.GR↗

arXiv2025

LookUp3D: Data-Driven 3D Scanning

High speed, high-resolution, and accurate 3D scanning would open doors to many new applications in graphics, robotics, science, and medicine by enabling the accurate scanning of deformable objects during interactions. Past attempts to use structured light, time-of-flight, and stereo in high-speed settings have usually required tradeoffs in resolution or inaccuracy. In this paper, we introduce a method that enables, for the first time, 3D scanning at 450 frames per second at 1~Megapixel, or 1,450 frames per second at 0.4~Megapixel in an environment with controlled lighting. The key idea is to use a per-pixel lookup table that maps colors to depths, which is built using a linear stage. Imperfections, such as lens-distortion and sensor defects are baked into the calibration. We describe our method and test it on a novel hardware prototype. We compare the system with both ground-truth geometry as well as commercially available dynamic sensors like the Microsoft Kinect and Intel Realsense. Our results show the system acquiring geometry of objects undergoing high-speed deformations and oscillations and demonstrate the ability to recover physical properties from the reconstructions.

cs.CV↗

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

Time of Impact Dataset for Continuous Collision Detection and a Scalable Conservative Algorithm

We introduce a large-scale benchmark for broad- and narrow-phase continuous collision detection (CCD) over linearized trajectories with exact time of impacts and use it to evaluate the accuracy, correctness, and efficiency of 13 state-of-the-art CCD algorithms. Our analysis shows that several methods exhibit problems either in efficiency or accuracy. To overcome these limitations, we introduce an algorithm for CCD designed to be scalable on modern parallel architectures and provably correct when implemented using floating point arithmetic. We integrate our algorithm within the Incremental Potential Contact solver [24] and evaluate its impact on various simulation scenarios. Our approach includes a broad-phase CCD to quickly filter out primitives having disjoint bounding boxes and a narrow-phase CCD that establishes whether the remaining primitive pairs indeed collide. Our broad-phase algorithm is efficient and scalable thanks to the experimental observation that sweeping along a coordinate axis performs surprisingly well on modern parallel architectures. For narrow-phase CCD, we re-design the recently proposed interval-based algorithm of Wang et al. [45] to work on massively parallel hardware. To foster the adoption and development of future linear CCD algorithms, and to evaluate their correctness, scalability, and overall performance, we release the dataset with analytic ground truth, the implementation of all the algorithms tested, and our testing framework.

cs.GR↗

arXiv2025

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↗

arXiv2025

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↗

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

Polyhedral Discretizations for Elliptic PDEs

We study the use of polyhedral discretizations for the solution of heat diffusion and elastodynamic problems in computer graphics. Polyhedral meshes are more natural for certain applications than pure triangular or quadrilateral meshes, which thus received significant interest as an alternative representation. We consider finite element methods using barycentric coordinates as basis functions and the modern virtual finite element approach. We evaluate them on a suite of classical graphics problems to understand their benefits and limitations compared to standard techniques on simplicial discretizations. Our analysis provides recommendations and a benchmark for developing polyhedral meshing techniques and corresponding analysis techniques.

cs.GR↗

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 Bézier 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

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↗

arXiv2024

Evaluating Deep Clustering Algorithms on Non-Categorical 3D CAD Models

We introduce the first work on benchmarking and evaluating deep clustering algorithms on large-scale non-categorical 3D CAD models. We first propose a workflow to allow expert mechanical engineers to efficiently annotate 252,648 carefully sampled pairwise CAD model similarities, from a subset of the ABC dataset with 22,968 shapes. Using seven baseline deep clustering methods, we then investigate the fundamental challenges of evaluating clustering methods for non-categorical data. Based on these challenges, we propose a novel and viable ensemble-based clustering comparison approach. This work is the first to directly target the underexplored area of deep clustering algorithms for 3D shapes, and we believe it will be an important building block to analyze and utilize the massive 3D shape collections that are starting to appear in deep geometric computing.

cs.CV↗

arXiv2024

Image Sculpting: Precise Object Editing with 3D Geometry Control

We present Image Sculpting, a new framework for editing 2D images by incorporating tools from 3D geometry and graphics. This approach differs markedly from existing methods, which are confined to 2D spaces and typically rely on textual instructions, leading to ambiguity and limited control. Image Sculpting converts 2D objects into 3D, enabling direct interaction with their 3D geometry. Post-editing, these objects are re-rendered into 2D, merging into the original image to produce high-fidelity results through a coarse-to-fine enhancement process. The framework supports precise, quantifiable, and physically-plausible editing options such as pose editing, rotation, translation, 3D composition, carving, and serial addition. It marks an initial step towards combining the creative freedom of generative models with the precision of graphics pipelines.

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

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

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

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

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↗