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Concept

Differential geometry of surfaces

Related publications (31)

The effect of smooth parametrizations on nonconvex optimization landscapes

Nicolas Boumal

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

Springer Heidelberg2024

Geometric Learning: Leveraging differential geometry for learning and control

Bernardo Fichera

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

EPFL2024

Scalable constrained optimization

Maria-Luiza Vladarean

Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

EPFL2024

Laser-based manufacturing of freeform glass micro-optics through topological transformation

Samuel Youcef Benketaf

Glass has been the material of choice for making optical elements, in large part due to its intrinsic properties: a temperature-dependent viscosity, which enables shaping the material into a broad variety of functional and artistic glassware. Silica glass ...

EPFL2024

A unified framework for Simplicial Kuramoto models

Alexis Arnaudon

Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three ...

2024

Search for narrow resonances in the b-tagged dijet mass spectrum in proton-proton collisions at √s=13 TeV

Jian Wang, Matthias Finger, Qian Wang, Yiming Li, João Miguel das Neves Duarte, Matthias Wolf, Varun Sharma, Yi Zhang, Lei Zhang, Tian Cheng, Yixing Chen, Alexis Kalogeropoulos, Ioannis Papadopoulos, Hua Zhang, Siyuan Wang, Jessica Prisciandaro, Xin Chen, Michele Bianco, Sebastiana Gianì, Sun Hee Kim, Davide Di Croce, Guido Andreassi, Arvind Shah, Jian Zhao, Rakesh Chawla, Jan Steggemann, Konstantin Androsov, Anna Mascellani, Federica Legger, Gabriele Grosso

A search is performed for narrow resonances decaying to final states of two jets, with at least one jet ffiffioriginating from a b quark, in proton-proton collisions at p s = 13 TeV. The data set corresponds to an integrated luminosity of 138 fb-1 collecte ...

American Physical Society2023

Hybrid Quadratic Programming - Pullback Bundle Dynamical Systems Control

Aude Billard, Bernardo Fichera

Dynamical System (DS)-based closed-loop control is a simple and effective way to generate reactive motion policies that well generalize to the robotic workspace, while retaining stability guarantees. Lately the formalism has been expanded in order to handl ...

SPRINGER INTERNATIONAL PUBLISHING AG2023

Continuation Methods For Riemannian Optimization

Daniel Kressner, Axel Elie Joseph Séguin

Numerical continuation in the context of optimization can be used to mitigate convergence issues due to a poor initial guess. In this work, we extend this idea to Riemannian optimization problems, that is, the minimization of a target function on a Riemann ...

SIAM PUBLICATIONS2022

An unrefinement algorithm for planar THB-spline parameterizations

Annalisa Buffa

Unrefinement is a tool that allows to perform faster numerical simulations by controlling the level of precision in the specified area. We introduce an algorithm that creates a coarser geometry from an initial regular geometry, which is represented with re ...

ELSEVIER2022

Fast and accurate decoding of finger movements from ECoG through Riemannian features and modern machine learning techniques

Mahsa Shoaran, Bingzhao Zhu

Objective. Accurate decoding of individual finger movements is crucial for advanced prosthetic control. In this work, we introduce the use of Riemannian-space features and temporal dynamics of electrocorticography (ECoG) signal combined with modern machine ...

IOP Publishing Ltd2022

An experimental validation of the polynomial curvature model: identification and optimal control of a soft underwater tentacle

Josephine Anna Eleanor Hughes, Francesco Stella, Nana Obayashi

The control possibilities for soft robots have long been hindered by the lack of accurate yet computationally treatable dynamic models of soft structures. Polynomial curvature models propose a solution to this quest for continuum slender structures. Nevert ...

Institute of Electrical and Electronics Engineers Inc.2022

Discrete Voss surfaces: Designing geodesic gridshells with planar cladding panels

Corentin Jean Dominique Fivet, Nicolas Robin Montagne

The design and construction of doubly-curved structures often reveals to be challenging and can result in complex manufacturing and assembly. A recent strategy to tackle this difficulty consists in exploiting the connection between discrete differential ge ...

2022

From kirigami to hydrogels: a tutorial on designing conformally transformable surfaces

Yingying Ren, Tian Chen

Elastic surfaces that morph between multiple geometrical configurations are of significant engineering value, with applications ranging from the deployment of space-based PV arrays, the erection of temporary shelters, and the realization of flexible displa ...

2023

Robust numerical integration on curved polyhedra based on folded decompositions

Annalisa Buffa, Pablo Antolin Sanchez, Xiaodong Wei

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the g ...

ELSEVIER SCIENCE SA2022

Computational Design of Weingarten Surfaces

Mark Pauly, Davide Pellis

In this paper we study Weingarten surfaces and explore their potential for fabrication-aware design in freeform architecture. Weingarten surfaces are characterized by a functional relation between their principal curvatures that implicitly defines approxim ...

2021

A method to numerically determine the secondary electron yield considering effects of the surface morphology

Guang-Yu Sun

Secondary electron emission (SEE) of solid materials due to electron bombardment is influenced by numerous properties of materials, where the surface condition plays a critical role in the value of secondary electron yield (SEY). Here, a 3D random microstr ...

2021

Examples of normal, not geometrically normal, projective Gorenstein del Pezzo surfaces with at most Du Val singularities

Ursina Schweizer

While over fields of characteristic at least 5, a normal, projective and Gorenstein del Pezzo surface is geometrically normal, this does not hold for characteristic 2 and 3. There is no characterization of all such non-geometrically normal surfaces, but th ...

EPFL2021

FE analysis and experimental validation of mechanical wedge-barrel anchors for CFRP rods

Alain Nussbaumer, Elyas Ghafoori, Hossein Heydarinouri

This paper presents a comparative study of the geometrical optimization of mechanical wedge-barrel anchors for prestressed carbon fiber-reinforced polymer (CFRP) rods. Various anchor configurations were simulated using three-dimensional finite-element (FE) ...

ELSEVIER SCI LTD2021

Voss surfaces: A design space for geodesic gridshells

Corentin Jean Dominique Fivet, Nicolas Robin Montagne

The design of envelopes with complex geometries often leads to construction challenges. To overcome these difficulties, resorting to discrete differential geometry proved successful by establishing close links between mesh properties and the existence of g ...

2021

Leveraging Spatial and Photometric Context for Calibrated Non-Lambertian Photometric Stereo

Pascal Fua, Engin Türetken, David Honzátko

The problem of estimating a surface shape from its observed reflectance properties still remains a challenging task in computer vision. The presence of global illumination effects such as inter-reflections or cast shadows makes the task particularly diffic ...

IEEE COMPUTER SOC2021