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Finetuning Discrete Architectural Surfaces by use of Circle Packing

Finetuning Discrete Architectural Surfaces by use of Circle Packing This paper presents an algorithmic approach for the conceptual design of architectural surfaces represented by triangulated meshes. Specifically, we propose a method to optimise a surface according to user-specified geometric properties including the distribution of the Gaussian curvature and preferable boundary location. Designing a surface manually with specific Gaussian curvatures can be a time-consuming task, and the proposed method automates this task. Also, in the proposed approach, the resulting mesh could be encouraged to form a regular tessellation or kept close to those of the initial one. Our method relies on the idea in computational conformal geometry called circle packing and the discrete Ricch energy, which have been used for surface modelling. We develop a least-squares-based optimisation scheme by introducing a variant of the Ricci energy to accommodate flexibility in specifying design constraints such as boundary locations and convexity of the spanned surface, which are essential to architectural applications. We provide an open-source implementation of our method in Python. 1 1 Our codes are publicly available at https://github.com/shizuo-kaji/ricci_flow http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Asian Architecture and Building Engineering Taylor & Francis

Finetuning Discrete Architectural Surfaces by use of Circle Packing

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Publisher
Taylor & Francis
Copyright
© 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group on behalf of the Architectural Institute of Japan, Architectural Institute of Korea and Architectural Society of China.
ISSN
1347-2852
eISSN
1346-7581
DOI
10.1080/13467581.2023.2229407
Publisher site
See Article on Publisher Site

Abstract

This paper presents an algorithmic approach for the conceptual design of architectural surfaces represented by triangulated meshes. Specifically, we propose a method to optimise a surface according to user-specified geometric properties including the distribution of the Gaussian curvature and preferable boundary location. Designing a surface manually with specific Gaussian curvatures can be a time-consuming task, and the proposed method automates this task. Also, in the proposed approach, the resulting mesh could be encouraged to form a regular tessellation or kept close to those of the initial one. Our method relies on the idea in computational conformal geometry called circle packing and the discrete Ricch energy, which have been used for surface modelling. We develop a least-squares-based optimisation scheme by introducing a variant of the Ricci energy to accommodate flexibility in specifying design constraints such as boundary locations and convexity of the spanned surface, which are essential to architectural applications. We provide an open-source implementation of our method in Python. 1 1 Our codes are publicly available at https://github.com/shizuo-kaji/ricci_flow

Journal

Journal of Asian Architecture and Building Engineering – Taylor & Francis

Published: Jun 29, 2023

Keywords: Surface modelling; computational conformal geometry; architectural surfaces; Gaussian curvature

References

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  • Innovations at Beijing Daxing International: The World ’ S Biggest Airport Terminal