Skip to main content
SpringerLink
Log in

Computational Design and Construction of Notch-Free Reciprocal Frame Structures

  • Conference paper
  • First Online:
Advances in Architectural Geometry 2014

Abstract

A reciprocal frame (RF) is a self-standing 3D structure typically formed by a complex grillage created as an assembly of simple atomic RF-units, which are in turn made up of three or more sloping rods forming individual units. While RF-structures are attractive given their simplicity, beauty, and ease of deployment; creating such structures, however, is difficult and cumbersome. In this work, we present an interactive computational framework for designing and assembling RF-structures around a 3D reference surface. Targeting notch-free assemblies, wherein individual rods or sticks are simply tied together, we focus on simplifying both the process of exploring the space of aesthetic designs and also the actual assembly process. By providing computational support to simplify the design and assembly process, our tool enables novice users to interactivity explore a range of design variations, and assists them to construct the final RF-structure design. We use the proposed framework to design a range of RF-structures of varying complexity and also physically construct a selection of the models.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The supplementary video can be accessed on the project page: http://geometry.cs.ucl.ac.uk/projects/2014/rf-aag/

References

  • Baverel, O., Nooshin, H., Kuroiwa, Y.: Configuration processing of nexorades using genetic algorithms. J. Int. Assoc. Shell Spat. Struct. 45(2), 99–108 (2004)

    Google Scholar 

  • Brocato, M., Mondardini, L.: Geometric methods and computational mechanics for the design of stone domes based on Abeille’s bond. In: Advances in Architectural Geometry, pp. 149–162. Springer, Wien/New York (2010)

    Google Scholar 

  • Chilton, J.: History of timber structures, lecture E1. In STEP 2, timber engineering. STEP 2, Timber Eng. 2, E1–E13 (1995)

    Google Scholar 

  • Chilton, J.: Development of timber reciprocal frame structures in the UK. In: Proceedings of IASS Symposium 2009: Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures, pp. 1877–1884, 2009

    Google Scholar 

  • Cignoni, P., Pietroni, N., Malomo, L., Scopigno, R.: Field-aligned mesh joinery. ACM Trans. Graph. 33(1), art.11 (2014)

    Google Scholar 

  • Douthe, C., Baverel, O.: Design of nexorades or reciprocal frame systems with the dynamic relaxation method. Comput. Struct. 87(21), 1296–1307 (2009)

    Article  Google Scholar 

  • Eigensatz, M., Kilian, M., Schiftner, A., Mitra, N., Pottmann, H., Pauly, M.: Paneling architectural freeform surfaces. ACM Trans Graph. (SIGGRAPH) 29(4), 45:1–45:10 (2010)

    Google Scholar 

  • Fu, C.-W., Lai, C.-F., He, Y., Cohen-Or, D.: K-set tileable surfaces. ACM Trans. Graph. (SIGGRAPH) 29(4), 44:1–44:6 (2010).

    Google Scholar 

  • Gelez, S., Saby, V.: Nexorades, facing an emergency situation. Int. J. Space Struct. 26(4), 359–362 (2011)

    Article  Google Scholar 

  • Grünbaum, B., Shephard, G.C.: Tilings and Patterns. W. H. Freeman, New York (1986)

    Google Scholar 

  • Kohlhammer, T., Kotnik, T.: Systemic behaviour of plane reciprocal frame structures. Struct. Eng. Int. 21(1), 80–86 (2010)

    Article  Google Scholar 

  • Larsen, O.P.: Reciprocal Frame Structures. Elsevier Science and Technology (2008)

    Google Scholar 

  • Li, X.-Y., Shen, C.-H., Huang, S.-S., Ju, T., Hu, S.-M.: Popup: automatic paper architectures from 3D models. ACM Trans. Graph. (SIGGRAPH) 29(4), 111:1–111:9 (2010)

    Google Scholar 

  • Mitani, J., Suzuki, H.: Making papercraft toys from meshes using strip-based approximate unfolding. ACM Trans. Graph. (SIGGRAPH) 23(3), 259–263 (2004)

    Google Scholar 

  • Panozzo, D., Block, P., Sorkine-Hornung, O.: Designing unreinforced masonry models. ACM Trans. Graph. (Proc. ACM SIGGRAPH) 32(4), 91:1–91:12 (2013)

    Google Scholar 

  • Parigi, D., KirkeGaard, P.H., Sassone, M.: Hybrid optimization in the design of reciprocal structures. In: Proceedings of the IASS Symposium 2012: From Spatial Structures to Spaces Structures, 8p, 2012

    Google Scholar 

  • Pugnale, A., Parigi, D., Kirkegaard, P.H., Sassone, M.: The principle of structural reciprocity: history, properties and design issues. In: IASS: Internationl Conference on Space Structures, pp. 414–421, 2011

    Google Scholar 

  • Schwartzburg, Y., Pauly, M.: Fabrication-aware design with intersecting planar pieces. Comput. Graph. Forum (Proc. Eurograph. 2013) 32(2) (2013)

    Google Scholar 

  • Sheffer, A., Lévy, B., Mogilnitsky, M., Bogomyakov, A.: ABF++: Fast and robust angle based flattening. ACM Trans. Graph. 24(2), 311–330 (2005)

    Article  Google Scholar 

  • Singh, M., Schaefer, S.: Triangle surfaces with discrete equivalence classes. ACM Trans. Graph. (SIGGRAPH) 29, 46:1–46:7 (2010)

    Google Scholar 

  • Song∗, P., Fu∗, C.-W., Goswami, P., Zheng, J., Mitra, N.J., Cohen-Or, D.: Reciprocal frame structures made easy. ACM Trans. Graph. (SIGGRAPH) 29(4), Article 94 (2013). (∗ joint first authors)

    Google Scholar 

  • Thönnissen, U., Werenfels, N.: Reciprocal frames - teaching experiences. Int. J. Space Struct. 26(4), 369–372 (2011). (Rhino-script developed by Prof. Annette Spiro)

    Google Scholar 

  • Umetani, N., Igarashi, T., Mitra, N.: Guided exploration of physically valid shapes for furniture design. ACM Trans. Graph. (SIGGRAPH) 31(4), 86:1–86:11 (2012)

    Google Scholar 

  • Whiting, E., Ochsendorf, J., Durand, F.: Procedural modeling of structurally-sound masonry buildings. ACM Trans. Graph. (SIGGRAPH ASIA) 28(5), 112:1–112:9 (2009)

    Google Scholar 

  • Whiting, E., Shin, H., Wang, R., Ochsendorf, J., Durand, F.: Structural optimization of 3D masonry buildings. ACM Trans. Graph. (SIGGRAPH ASIA) 31(6), 159:1–159:11 (2012)

    Google Scholar 

  • Xin, S.-Q., Lai, C.-F., Fu, C.-W., Wong, T.-T., He, Y., Cohen-Or, D.: Making burr puzzles from 3D models. ACM Trans. Graph. (SIGGRAPH) 30(4), 97:1–97:8 (2011)

    Google Scholar 

  • Yang, Y.-L., Yang, Y.-J., Pottmann, H., Mitra, N.J.: Shape space exploration of constrained meshes. ACM Trans. Graph. (SIGGRAPH ASIA) 30(6), 124:1–124:10 (2011)

    Google Scholar 

Download references

Acknowledgements

We thank the reviewers for their comments and suggestions for improving the paper. We thank Moos Hueting, James Hennessey and Aron Monszpart for their help on physical construction and discussions. This work was supported in part by the Marie Curie Career Integration Grant 303541, the ERC Starting Grant SmartGeometry (StG-2013-335373), the MOE Tier-2 grant (MOE2011-T2-2-041 (ARC 5/12)), and gifts from Adobe Research.

Author information

Authors and Affiliations

  1. University College London, London, UK

    Nicolas Mellado & Niloy J. Mitra

  2. University of Science and Technology of China, Anhui, China

    Peng Song

  3. Nanyang Technological University, Singapore, Singapore

    Xiaoqi Yan & Chi-Wing Fu

Authors
  1. Nicolas Mellado
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xiaoqi Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chi-Wing Fu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Niloy J. Mitra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nicolas Mellado .

Editor information

Editors and Affiliations

  1. BLOCK Research Group, ETH Zürich, Institute for Technology in Architecture, Zürich, Switzerland

    Philippe Block

  2. University of Stuttgart, Inst. of Building Structures and Structural Design, Stuttgart, Germany

    Jan Knippers

  3. University College London, Dept. of Computer Science, London, United Kingdom

    Niloy J. Mitra

  4. The University of Hong Kong, Dept. of Computer Science, Hong Kong, Hong Kong SAR

    Wenping Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Mellado, N., Song, P., Yan, X., Fu, CW., Mitra, N.J. (2015). Computational Design and Construction of Notch-Free Reciprocal Frame Structures. In: Block, P., Knippers, J., Mitra, N., Wang, W. (eds) Advances in Architectural Geometry 2014. Springer, Cham. https://doi.org/10.1007/978-3-319-11418-7_12

Download citation

Publish with us

Policies and ethics

Search

Navigation