Asymptotic Building Envelope

Department: Architecture
Active Dates: August 2020 - ongoing
Principal Investigator: Eike Schling
Academic Partners: Shen Guan Shih, NTUST, Department of Architecture
Industry Partners: Chih-Lin Hsu, GOMORE, Building Envelope Technology
Project Team: Eike Schling, Jachy Chu, Wesley She, Muye Ma, Nuozi Chen, Fai Lam Chung Lee Chun Ki, Yao Dongni, Choi Chung Hei, Chung Bing Tsun, Ma Chun Hon, Ng Sherene Poh Li, So Cheuk Lam, Wang Xiangning, Zhu Xiang, Yang Mei, Chan Ching Yee
Funding Body: Seed Fund for Basic Research for New Staff
A ECS proposal for this project has been submitted for the funding period of 2022-2023


There is an urgent need for innovative building construction methods that combine high structural efficiency with low production cost, offer design freedom and integrate well into the built environment. Great potential lies in double-curved systems, such as gridshells. These form-active structures enable a spatial load transfer via compression and tension, allowing for optimal use of material to create lightweight, transparent building envelopes. Nonetheless, their application in architecture remains rare and specialized, as their free-form geometry creates high costs in the fabrication and assembly of individual and spatially complex parts. To achieve a shell-load-transfer, a consistent double curvature and tangential supports are necessary, which constraints the design and often lacks to integrate with the urban environment.

The research branch of Architectural Geometry (Pottmann et al. 2015) has produced fundamental insights on topology optimization for curved structural grids (Bo et al. 2011; Bartoň et al. 2013; Pellis and Pottmann 2018) as well as curved building skins (Liu et al. 2006; Huard et al. 2015; Eversmann et al. 2016) with the goal to simplify fabrication and allow the use of planar or developable building elements.

Recent research on elastic gridshells has presented asymptotic curves (following the path of vanishing normal curvature), as beneficial network for lamella construction, as they facilitate simple fabrication from straight and flat elements with repetitive orthogonal nodes (Schling 2018). Asymptotic lamella networks allow for a simple, self-forming erection process, where the weak axis of the lamellas is elastically bent and twisted to form the design shape, while the strong axis creates high resilience against external loads (Schikore et al. 2019).

This system thus combines the structural benefits of a gridshell and grillage, offers a versatile design from curved to flat, and allows smooth integration into the urban environment. However, this design method has only been used for free-standing sculptural projects without a cladding solution (Figure 1). The potential for integrated building skins has not been investigated.

This project investigate a construction system for doubly curved curtain wall systems, which combines a structural layout along the asymptotic curves with a cladding layout along the principal curvature lines. Both networks are combined in an isothermal web on a minimal surface (Pottmann et al. 2007, p. 648) bisecting

each other and thus creating reciprocal benefits for structural bracing and façade connections.


  1. Develop a computational workflow for the design of asymptotic structures, that integrates geometric modelling, structural form-finding and analysis within one digital environment for architects and engineers.
  2. Create a robust and sustainable construction system for building envelopes through the systematic development and testing of two full-scale prototypes for (a) a vertical curtain wall module and (b) a horizontal roof structure.
  3. Establish architectural applications by designing urban scenarios for asymptotic building envelopes, investigate their geometric limits and evaluating their functional qualities.
  4. Disseminate our knowledge through peer-reviewed articles as well as conference presentations, exhibitions, workshops and digital media for the academic and professional community.

The overarching, long-term goal of our research is to enhance the design and implementation of repetitive construction systems as a sustainable strategy that embraces simple fabrication and construction without sacrificing the high structural potential of free-form design.


  • Schling, Eike; Hsu, Chih-Lin; Ma, Muye (2021): Asymptotic Building Envelope – Combining the benefits of asymptotic and principal curvature layouts. In: CAADRIA2021, Hong Kong (to be published)
  • Design Build Workshop at HKU and NTUST for a 2.4 x 2.4 x 2.4 prototypical façade module.


By creating the constructive and computational method to design low-cost, light-weight asymptotic building envelopes, this study will become a building block for sustainable and affordable architectural applications for the twenty-first century. It thus offers an alternative to the extravagant and bespoke design solutions currently used for free-form construction.


Bo, P., Pottmann, H., Kilian, M., Wang, W. and Wallner, J.: 2011, Circular arc structures, ACM

Transactions on Graphics, 30 (101)(DOI: 10.1145/1964921.1964996), 1-11.

Bartoň, M., Shi, L., Kilian, M., Wallner, J. and Pottmann, H.: 2013, Circular Arc Snakes and Kinematic Surface Generation, Computer Graphics Forum, 32(2pt1), 1-10.

Eversmann, P., Schling, E., Ihde, A. and Louter, C.: 2016, Low Cost Double Curvature. Geometrical and Structural Potentials of Rectangular, Cold-bent Glass Construction, K. Kawaguchi, M. Ohsaki, T. Takeuchi (Eds.): IASS Annual Symposium 2016, Tokyo.

Huard, M., Eigensatz, M. and Bompas, P.: 2015, Planar Panelization with Extreme Repetition, Philippe Block, Jan Knippers, Niloy J. Mitra, Wenping Wang (Eds.): Advances in Architectural Geometry 2014, London, 259–279.

Liu, Y., Pottmann, H., Wallner, J., Yang, Y.L. and Wang, W.: 2006, Geometric modeling with conical meshes and developable surfaces, ACM Transactions on Graphics, 25 (3)(DOI: 10.1145/1141911.1141941), 681.

Pellis, D. and Pottmann, H.: 2018, Aligning principal stress and curvature directions, Lars Hesselgren, Karl-Gunnar Olsson, Axel Kilian, Samar Malek, Olga Sorkine-Hornung, Chris Williams (Eds.): Advances in Architectural Geometry 2018, Gothenburg, 34-53.

Pottmann, H., Asperl, A., Hofer, M. and Kilian, A.: 2007, Architectural Geometry, Springer & Bentley Institute Press, ISBN: 978-3-211-99765-9.

Pottmann, H., Eigensatz, M., Vaxman, A. and Wallner, J.: 2015, Architectural Geometry, Computers and Graphics, 47(DOI: 10.1016/j.cag.2014.11.002), 145-164.

Schikore, J., Bauer, A.M., Barthel, R. and Bletzinger, K.U.: 2019, Large torsion on elastic lamella grid structures, Carlos Lázaro, K.-U. Bletzinger, Eugenio Oñate (Eds.): FORM and FORCE 2019, Barcelona, 807-814.

Schling, E.: 2018, Repetitive Structures. Design and Construction of Curved Support Structures with Repetitive Parameters, Ph.D. Thesis, Chair of Structural Design, Technical University of Munich (DOI: 10.14459/2018md1449869).


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