Skip to Main content Skip to Navigation
Theses

Existence and construction of Chebyshev nets and application to gridshells

Abstract : Chebyshev nets are coordinate systems on surfaces obtained by pure shearing of a planar domain.These nets are used in particular to model gridshells, an architectural construction which is well-known for its low environmental impact. The main issue when designing a gridshell is the lack of diversityof the accessible shapes. Indeed, although any surface admits locally a Chebyshev net at any point, the global existence for these coordinate systems is only possible for a restricted set of surfaces. The research for sufficient conditions ensuring the global existence of Chebyshev nets is still ongoing. A result achieved in this thesis is an improvement on these conditions. Since the improvement in this direction seems to be rather limited, we broaden the perspective by introducing Chebyshev nets with singularities. Our main result is the existence of a global Chebyshev net with conical singularities on any surface with total positive curvature less than "2pi" and with finite total negative curvature. Our proof is constructive, so that this method can be applied to practical cases. We have implemented a special instance of this algorithm in the software Rhinoceros and some discrete Chebyshev nets constructed using this method are presented
Document type :
Theses
Complete list of metadatas

Cited literature [42 references]  Display  Hide  Download

https://tel.archives-ouvertes.fr/tel-01676984
Contributor : Abes Star :  Contact
Submitted on : Monday, April 9, 2018 - 6:40:08 PM
Last modification on : Tuesday, October 13, 2020 - 1:26:06 PM

File

TH2017PESC1144_complete.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01676984, version 2

Collections

Citation

Yannick Masson. Existence and construction of Chebyshev nets and application to gridshells. Mathematical Physics [math-ph]. Université Paris-Est, 2017. English. ⟨NNT : 2017PESC1144⟩. ⟨tel-01676984v2⟩

Share

Metrics

Record views

356

Files downloads

115