arXiv subjects

Daniele Panozzo

Publications and source records attributed to Daniele Panozzo.

43 records · Page 3Linked to original sources

arXiv2019

Half-Space Power Diagrams and Discrete Surface Offsets

We present an efficient, trivially parallelizable algorithm to compute offset surfaces of shapes discretized using a dexel data structure. Our algorithm is based on a two-stage sweeping procedure that is simple to implement and efficient, entirely avoiding volumetric distance field computations typical of existing methods. Our construction is based on properties of half-space power diagrams, where each seed is only visible by a half-space, which were never used before for the computation of surface offsets. The primary application of our method is interactive modeling for digital fabrication. Our technique enables a user to interactively process high-resolution models. It is also useful in a plethora of other geometry processing tasks requiring fast, approximate offsets, such as topology optimization, collision detection, and skeleton extraction. We present experimental timings, comparisons with previous approaches, and provide a reference implementation in the supplemental material.

cs.GR↗

arXiv2019

Deep Geometric Prior for Surface Reconstruction

The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for surface reconstruction. Specifically, we overfit a neural network representing a local chart parameterization to part of an input point cloud using the Wasserstein distance as a measure of approximation. By jointly fitting many such networks to overlapping parts of the point cloud, while enforcing a consistency condition, we compute a manifold atlas. By sampling this atlas, we can produce a dense reconstruction of the surface approximating the input cloud. The entire procedure does not require any training data or explicit regularization, yet, we show that it is able to perform remarkably well: not introducing typical overfitting artifacts, and approximating sharp features closely at the same time. We experimentally show that this geometric prior produces good results for both man-made objects containing sharp features and smoother organic objects, as well as noisy inputs. We compare our method with a number of well-known reconstruction methods on a standard surface reconstruction benchmark.

cs.CV↗

arXiv2019

Deformation Capture via Soft and Stretchable Sensor Arrays

We propose a hardware and software pipeline to fabricate flexible wearable sensors and use them to capture deformations without line of sight. Our first contribution is a low-cost fabrication pipeline to embed multiple aligned conductive layers with complex geometries into silicone compounds. Overlapping conductive areas from separate layers form local capacitors that measure dense area changes. Contrary to existing fabrication methods, the proposed technique only requires hardware that is readily available in modern fablabs. While area measurements alone are not enough to reconstruct the full 3D deformation of a surface, they become sufficient when paired with a data-driven prior. A novel semi-automatic tracking algorithm, based on an elastic surface geometry deformation, allows to capture ground-truth data with an optical mocap system, even under heavy occlusions or partially unobservable markers. The resulting dataset is used to train a regressor based on deep neural networks, directly mapping the area readings to global positions of surface vertices. We demonstrate the flexibility and accuracy of the proposed hardware and software in a series of controlled experiments, and design a prototype of wearable wrist, elbow and biceps sensors, which do not require line-of-sight and can be worn below regular clothing.

cs.GR↗

arXiv2019

Poly-Spline Finite Element Method

We introduce an integrated meshing and finite element method pipeline enabling black-box solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of high-order basis on its elements, combining triquadratic B-splines, triquadratic hexahedra (27 degrees of freedom), and harmonic elements. We demonstrate that our approach converges cubically under refinement, while requiring around 50% of the degrees of freedom than a similarly dense hexahedral mesh composed of triquadratic hexahedra. We validate our approach solving Poisson's equation on a large collection of models, which are automatically processed by our algorithm, only requiring the user to provide boundary conditions on their surface.

math.NA↗

arXiv2018

Surface Networks

We study data-driven representations for three-dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants, which learn from the local metric tensor via the Laplacian operator. Despite offering excellent sample complexity and built-in invariances, intrinsic geometry alone is invariant to isometric deformations, making it unsuitable for many applications. To overcome this limitation, we propose several upgrades to GNNs to leverage extrinsic differential geometry properties of three-dimensional surfaces, increasing its modeling power. In particular, we propose to exploit the Dirac operator, whose spectrum detects principal curvature directions --- this is in stark contrast with the classical Laplace operator, which directly measures mean curvature. We coin the resulting models \emph{Surface Networks (SN)}. We prove that these models define shape representations that are stable to deformation and to discretization, and we demonstrate the efficiency and versatility of SNs on two challenging tasks: temporal prediction of mesh deformations under non-linear dynamics and generative models using a variational autoencoder framework with encoders/decoders given by SNs.

stat.ML↗

arXiv2017

Spline surfaces with T-junctions

This paper develops a new way to create smooth piecewise polynomial free-form spline surfaces from quad- meshes that include T-junctions, where surface strips start or terminate. All mesh nodes can be interpreted as control points of geometrically-smooth, piecewise polynomials that we call GT-splines. GT-splines are B-spline-like and cover T-junctions by two or four patches of degree bi-4. They complement multi-sided surface constructions in generating free-form surfaces with adaptive layout. Since GT-splines do not require a global coordination of knot intervals, GT-constructions are easy to deploy and can provide smooth surfaces with T-junctions where T-splines can not have a smooth parameterization. GT-constructions display a uniform highlight line distribution on input meshes where alternatives, such as Catmull-Clark subdivision, exhibit oscillations.

math.NA↗

arXiv2010

Simplification of cross-field topology

We present an innovative algorithm that simplifies the topology of a cross-field. Our algorithm works through macro-operations that allow us editing the graph of separatrices, which is extracted from a cross-field, while maintaining it topologically consistent. We present preliminary results of our implementation.

cs.CG↗