Skip to main content
Springer Nature Link
Log in

Mathematically Developing Building Facades: An Algorithmic Framework

  • Conference paper
  • First Online:
Formal Methods in Architecture

Part of the book series: Advances in Science, Technology & Innovation ((ASTI))

Abstract

The importance of Algorithmic Design (AD) is growing due to its advantages for the design practice: It empowers the creative process, facilitating design changes and the exploration of larger design spaces in viable time, and supports the search for better-performing solutions that satisfy environmental demands. Still, AD is a complex approach and requires specialized knowledge. To promote its use in architecture, we present a mathematics-based framework to support architects with the algorithmic development of designs by following a continuous workflow embracing the three main design stages: exploration, evaluation, and manufacturing. The proposed framework targets the design of buildings’ facades due to their aesthetical and environmental relevance. In this paper, we explain the framework’s structure and its mathematical implementation, and we describe the predefined algorithms, as well as their combination strategies. We focus on the framework’s algorithms that generate different geometric patterns, exploring their potentialities to create and modify different facade designs. In the end, we evaluate the flexibility of the framework for generating, modifying, and optimizing different geometrical patterns in an architectural design context.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Caetano, I., Santos, L., & Leitão, A. (2020). Computational design in architecture: Defining parametric, generative, and algorithmic design. Frontiers of Architectural Research, 287–300.

    Google Scholar 

  2. Aguiar, R., Cardoso, C., & Leitão, A. (2017). Algorithmic design and analysis fusing disciplines. In Disciplines and disruption—Proceedings of the 37th annual conference of the association for computer aided design in architecture, pp. 28–37. Cambridge, Massachusetts, USA.

    Google Scholar 

  3. Trubiano, F. (2013). Performance based envelopes: A theory of spatialized skins and the emergence of the integrated design professional. Buildings, 3, 689–712.

    Article  Google Scholar 

  4. El Sheikh, M. M. (2011). Intelligent building skins: Parametric-based algorithm for kinetic facades design and daylighting performance integration. PhD thesis. University of Southern California, Los Angeles, USA.

    Google Scholar 

  5. Al-Kodmany, K., & Ali, M. M. (2016). An overview of structural and aesthetic developments in tall buildings using exterior bracing and diagrid systems. International Journal of High-Rise Buildings, 5(4), 271–291.

    Article  Google Scholar 

  6. Schulz, C. N. (1971). Existence, space & architecture. New York: Praeger. Stamps.

    Google Scholar 

  7. Schittich, C. (2006). Building skins. Birkhäuser.

    Google Scholar 

  8. Stojšić, M. (2017). (New) media facades: Architecture and/as a medium in urban context. AM Journal, 12, 135–148.

    Google Scholar 

  9. Venturi, R., Brown, D. S., & Izenour, S. (1972). Learning from Las Vegas. MIT Press.

    Google Scholar 

  10. Moussavi, F., & Kubo, M. (2006). The function of ornament. Actar.

    Google Scholar 

  11. Otani, M., & Kishimoto, T. (2008). Fluctuating patterns of architecture façade and their automatic creation. In: CAADRIA 2008—Proceedings of the 13th international conference on computer aided architectural design research in Asia, pp. 375–382. Chiang mai, Thailand.

    Google Scholar 

  12. Pell, B. (2010). The articulate surface: Ornament and technology in contemporary architecture. Germany: Birkhäuser GmbH.

    Book  Google Scholar 

  13. Caetano, I., Santos, L., & Leitão, A. (2015). From idea to shape, from algorithm to design: A framework for the generation of contemporary facades. In G. Celani, D. Sperling, & J. Franco (Eds.), Computer-aided architectural design: The Next City—New technologies and the future of the built environment 16th international conference, CAAD futures 2015, selected papers (pp. 527–546). Berlin: Springer.

    Google Scholar 

  14. Woodbury, R., Aish, R., & Kilian, A. (2007). Some patterns for parametric modeling. In Expanding bodies: Art • cities• environment—Proceedings of the 27th annual conference of the association for computer aided design in architecture, pp. 222–229. Halifax, Nova Scotia.

    Google Scholar 

  15. Qian, Z. C. (2009). Design patterns: Augmenting design practice in parametric CAD systems. PhD thesis. School of Interactive Arts and Technology: Simon Fraser University. Burnaby, Canada.

    Google Scholar 

  16. Chien, S., Su, H., & Huang, Y. (2015). PARADE: A pattern-based knowledge repository for parametric designs. In Emerging experience in past, present and future of digital architecture—Proceedings of the 20th international conference of the association for computer-aided architectural design research in Asia (CAADRIA), pp. 375–384. Daegu, Korea.

    Google Scholar 

  17. Leitão, A. (2014). Improving generative design by combining abstract geometry and higher-order programming. In Rethinking comprehensive design: Speculative counterculture—Proceedings of the 19th international conference on computer-aided architectural design research in Asia (CAADRIA), pp. 575–584. Kyoto, Japan.

    Google Scholar 

  18. Caetano, I., & Leitão, A. (2019). Weaving architectural façades: Exploring algorithmic stripe-based design patterns. In Hello, culture—Proceeding of the 18th international conference on computer aided architectural design futures, pp. 1023–1043. Daejeon, South Korea.

    Google Scholar 

  19. Grünbaum, G., & Shephard, G. C. (1987). Tilings and patterns. New York, USA: W.H. Freeman.

    Google Scholar 

  20. Caetano, I., & Leitão, A. (2018). Algorithmic patterns for facade design: merging design exploration, optimization and rationalization. In Facade tectonics 2018 world congress conference proceedings (Vol. 1, pp. 413–422). Los Angeles, USA.

    Google Scholar 

  21. Sammer, M., Leitão, A., & Caetano, I. (2019). From visual input to visual output in textual programming. In Intelligent & informed—Proceedings of the 24th international conference of the association for computer-aided architectural design research in Asia (Vol. 1, pp. 645–654). Wellington, New Zeland.

    Google Scholar 

  22. Bezanson, J., Edelman, A., Karpinski, S., & Shah, V. B. (2012). The Julia language. https://julialang.org/, last accessed Mach 28, 2020.

  23. ParaCloud GEM. (2011). https://paracloud-gem.software.informer.com/, last accessed March 29, 2020.

  24. Issa, R. (2013). PanelingTools for rhino and grasshopper. https://www.food4rhino.com/app/panelingtools-rhino-and-grasshopper, last accessed March 27, 2020.

  25. Miller, N. (2011). LUNCHBOX. https://www.food4rhino.com/app/lunchbox, last accessed March 21, 2020.

  26. Weaverbird—Topological Mesh Editor. (2009). http://www.giuliopiacentino.com/weaverbird/, last accessed March 19, 2020.

  27. Esmaeil. (2019). PARAKEET. https://www.food4rhino.com/app/parakeet, last accessed March 23, 2020.

  28. sgaray. (2017). SKINDESIGNER. https://www.food4rhino.com/app/skindesigner, last accessed March 21, 2020.

  29. Zboinska, M. A. (2015). Hybrid CAD/E platform supporting exploratory architectural design. CAD Computer Aided Design, 59, 64–84.

    Article  Google Scholar 

  30. Leitão, A., Santos, L., & Lopes, J. (2012). Programming languages for generative design: A comparative study. International Journal of Architectural Computing, 10(1), 139–162.

    Article  Google Scholar 

  31. Janssen, P. (2014). Visual dataflow modelling: Some thoughts on complexity. In Fusion—Proceedings of the 32nd eCAADe conference (Vol. 2, pp. 305–314). Department of Architecture and Built Environment, Faculty of Engineering and Environment, Newcastle upon Tyne.

    Google Scholar 

  32. Wortmann, T., & Tunçer, B. (2017). Differentiating parametric design: Digital workflows in contemporary architecture and construction. Design Studies, 53, 173–197.

    Article  Google Scholar 

  33. Celani, G., & Vaz, C. (2012). CAD scripting and visual programming languages for implementing computational design concepts: A comparison from a pedagogical point of view. International Journal of Architectural Computing, 10(1), 121–138.

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by national funds through Fundação para a Ciência e a Tecnologia (FCT) with references UIDB/50021/2020 and PTDC/ART-DAQ/31061/2017, and by the Ph.D. grant under contract of FCT with reference SFRH/BD/128628/2017.

Author information

Authors and Affiliations

  1. INESC-ID/Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    Inês Caetano & António Leitão

Authors
  1. Inês Caetano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. António Leitão
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Inês Caetano .

Editor information

Editors and Affiliations

  1. Instituto Universitário de Lisboa (ISCTE-IUL), ISTAR, Lisbon, Portugal

    Sara Eloy

  2. Instituto Universitário de Lisboa (ISCTE-IUL), ISTAR, Lisbon, Portugal

    David Leite Viana

  3. Laboratório de Investigação em Arquitetura e Design (LIAD), Escola Superior Artística do Porto (ESAP), Porto, Portugal

    Franklim Morais

  4. Laboratório de Investigação em Arquitetura e Design (LIAD), Escola Superior Artística do Porto (ESAP), Porto, Portugal

    Jorge Vieira Vaz

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Caetano, I., Leitão, A. (2021). Mathematically Developing Building Facades: An Algorithmic Framework. In: Eloy, S., Leite Viana, D., Morais, F., Vieira Vaz, J. (eds) Formal Methods in Architecture. Advances in Science, Technology & Innovation. Springer, Cham. https://doi.org/10.1007/978-3-030-57509-0_1

Download citation

Publish with us

Policies and ethics

Search

Navigation