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Geodesic Patterns

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Discrete Voss surfaces: Designing geodesic gridshells with planar cladding panels

Corentin Jean Dominique Fivet, Nicolas Robin Montagne, Olivier Baverel

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

Voss surfaces: A design space for geodesic gridshells

Corentin Jean Dominique Fivet, Nicolas Robin Montagne, Olivier Baverel

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

Integrity of rhythmic spatial gene expression patterns in the vertebrate segmentation clock requires local synchronization between neighboring cells by Delta-Notch signaling and its inhibition causes defective segment boundaries. Whether deformation of the ...

ELIFE SCIENCES PUBLICATIONS LTD2021

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2020

Energy distribution of harmonic 1-forms and Jacobians of Riemann surfaces with a short closed geodesic

Jürgpeter Buser, Robert Silhol

We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that split ...

2020

Vegetation Pattern Formation in Drylands

Sara Bonetti

This chapter aims to (1) provide background for conceptual mathematical models of spontaneous pattern formation, in the context of dryland vegetation patterns, and (2) review observational studies of the phenomenon. The chapter also highlights challenges a ...

Springer2019

On a Lagrangian Formulation of the Incompressible Euler Equation

Hasan Inci

In this paper we show that the incompressible Euler equation on the Sobolev space H-s(R-n), s> n/2+1, can be expressed in Lagrangian coordinates as a geodesic equation on an infinite dimensional manifold. Moreover the Christoffel map describing the geodesi ...

Global Science Press2016

Real-Time High-Accuracy 2D Localization with Structured Patterns

Pierre Dillenbourg, Francesco Mondada, Séverin Lemaignan, Ayberk Özgür, Lukas Oliver Hostettler

Building over algorithms previously developed for digital pens, this article introduces a novel 2D localization technique for mobile robots, based on simple printed patterns. This method combines high absolute accuracy (below 0.3mm), unlimited scalability, ...

IEEE2016

Pattern formation with voluminous processes

Alexandre David Olivier Maurer

When a shoal of small fishes notices a predator, they typically change their collective shape and form a specific pattern. They do so efficiently (in parallel) and without collision. This motivates us to design algorithms with similar properties. In this p ...

EPFL2016

We report results from a systematic numerical investigation of the nonlinear patterns that emerge when a slender elastic rod is deployed onto a moving substrate; a system also known as the elastic sewing machine (ESM). The discrete elastic rods (DER) metho ...

American Society of Mechanical Engineers2015