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A Design Model for a (Grid)shell Based on a Triply Orthogonal System of Surfaces

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Towards Radical Regeneration (DMS 2022)

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Abstract

We present a design model for a (grid)shell that is an assembly of 3D components (‘rational-voxels’) fabricated from planar/developable faces. This rationalization was achieved thanks to the geometric properties of principal patches arising from a Triply Orthogonal system of Surfaces (TOS). By using such a system we were able to generate a curvilinear coordinate system where the coordinate lines are principal curves on the respective surfaces in the TOS. Next, generate 3D components (voxels) where each voxel is a curvilinear cube where its sides are principal patches, and its edges are principal curves obtained by intersecting two neighboring surfaces from each of the three families in the TOS. These voxels are then rationalized into rational-voxels having planar/developable faces and straight/planar edges. The design model allows for five degrees of design freedom for choosing: (1) the shell-slice type in the TOS, (2) the shell-slice thickness, (3) the voxel-assembly method, (4) the rational-voxel type and (5) being either a solid or a hollow voxel-assembly. A design to build process of a large scale pavilion is presented as a demonstration of the proposed design model.

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References

  1. Bobenko, A., Matthes, D., Suris, Y.: Discrete and smooth orthogonal systems: C∞-approximation. Available from ar**v:math/0303333 (2003)

  2. Bobenko, A., Suris, Y.: Discrete differential geometry. Consistency as integrability. Available from ar**v:math/0504358 (2005)

  3. Bobenko, A., Tsarev, S.: Curvature line parameterization from circle patterns. Available from ar**v: 0706.3221 (2007)

    Google Scholar 

  4. DoCarmo, M.: Differential Geometry of Curves and Surfaces. Prentice-Hall Inc, Englewood Cliffs, New Jersey (1976)

    Google Scholar 

  5. Eisenhart, L.: A Treatise on Differential Geometry of Curves and Surfaces. Ginn and Company, Boston (1909)

    Google Scholar 

  6. Gray, A., Abbena, E., Salamon, S.: Modern differential geometry of curves and surfaces with Mathematica, 3rd edn. Chapman & Hall/CRC (2006)

    Google Scholar 

  7. Liu, Y., Pottmann, H., Wallner, J., Yang, Y., Wang, W.: Geometric modeling with conical meshes and developable surfaces. ACM Tr., Proc. SIGGRAPH 25(3), 681–689 (2006)

    Google Scholar 

  8. Pottmann, H., Liu, Y., Bobenko, A., Wallner, J., Wang, W.: Geometry of multi-layer freeform structures for architecture. ACM Tr., Proc. SIGGRAPH 26(65), 1–11 (2007)

    Google Scholar 

  9. Pottmann, H., et al.: Freeform surfaces from single curved panels. ACM Tr. 27(3), 1–10 (2008)

    Google Scholar 

  10. Filz, G., Schiefer, S.: Rapid assembly of planar quadrangular, self-interlocking modules to anticlastically curved forms. Available on researchgate.net/publication/ 271436191 (2014)

    Google Scholar 

  11. Kilian, A.: Fabrication of partially double-curved surfaces out of flat sheet material through a 3D puzzle approach. Available on researchgate.net/publication/30871581 (2003)

    Google Scholar 

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Acknowledgement

The realized prototype was the result of work done within the framework of a workshop for the master students at the national school of architecture and landscape in Lille. The supply of materials, production, and transportation of the pavilion was funded by the school. The pavilion was exhibited the 11th of June 2022 at Bazaar St-So during the 10th edition of the “braderie de l’architecture”.

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Authors and Affiliations

  1. Laboratoire GSA – Géométrie Structure Architecture (École nationale supérieure d’architecture Paris-Malaquais), 14 rue Bonaparte, 75006, Paris, France

    Aly Abdelmagid, Ahmed Elshafei & Ahmed Hussein

  2. Laboratoire LATCH- Conception, Territoire Histoire et Matérialité (École nationale supérieure d’architecture et de paysage de Lille), 2 Rue Verte, 59650, Villeneuve-d’Ascq, France

    Mohammad Mansouri

Authors
  1. Aly Abdelmagid
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  2. Ahmed Elshafei
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  3. Mohammad Mansouri
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  4. Ahmed Hussein
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Corresponding author

Correspondence to Ahmed Elshafei .

Editor information

Editors and Affiliations

  1. Institute of Architecture and Urban Planning, Department for Structural Design and Engineering, KET, Berlin University of the Arts, Berlin, Berlin, Germany

    Christoph Gengnagel

  2. Laboratoire Navier/GSA, School of Architecture of Grenoble and Ecole des Ponts Paristech, Grenoble, France

    Olivier Baverel

  3. Architectural Design for Building Performance, University of California, Berkeley, Berkeley, CA, USA

    Giovanni Betti

  4. Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands

    Mariana Popescu

  5. CITA, The Royal Danish Academy of Fine Arts, Copenhagen, Denmark

    Mette Ramsgaard Thomsen

  6. Faculty of Architecture, Regenerative Architecture and Biofabrication, KU Leuven, Leuven, Belgium

    Jan Wurm

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Abdelmagid, A., Elshafei, A., Mansouri, M., Hussein, A. (2023). A Design Model for a (Grid)shell Based on a Triply Orthogonal System of Surfaces. In: Gengnagel, C., Baverel, O., Betti, G., Popescu, M., Thomsen, M.R., Wurm, J. (eds) Towards Radical Regeneration. DMS 2022. Springer, Cham. https://doi.org/10.1007/978-3-031-13249-0_5

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  • DOI: https://doi.org/10.1007/978-3-031-13249-0_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-13248-3

  • Online ISBN: 978-3-031-13249-0

  • eBook Packages: EngineeringEngineering (R0)

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