|Abstract as per original application
Symmetry is fundamental in nature, science, engineering, and art. Perception and recognition of symmetries influence not only our understanding of the world but also our design processes. Symmetry is also ubiquitous and continuous in architecture, appearing in all places over the world and at all times throughout history, for example, the Great Wall of China, the Parthenon of Greece, the Taj Mahal of India, ‘The Gherkin’ in London, and the Sydney Opera House in Australia. The ubiquity of symmetry in architecture is far from accidental, rather it is the result of considerations relating to function, economics, mechanics, manufacturing, and aesthetics.
Recent advances in sensing technology, such as laser scanning and photogrammetry, provide increasingly available 3D point clouds of architectures and cities. Detection of architectural symmetries from 3D point clouds is not only an intriguing inquiry in its own right, but also an effective and essential step in creating accurate and informative digital building/city models for various applications such as architectural design, computer vision, construction management, heritage conservation, and smart and resilient city development. However, as it is too time-consuming, tedious, and costly to manually recognize and segment architectural symmetries from 3D point clouds, the challenge is to devise an automated detection of architectural symmetries.
To meet this challenge, the proposed research project aims to apply modern derivative-free optimization (DFO) algorithms, which have been successfully used to solve many science and engineering problems, to automated architectural symmetry detection from 3D point clouds. Extending the mathematical definition of symmetry, this research proposes a general formulation of detecting symmetry in architecture. The major innovation here is an elegant means of detecting all types of architectural symmetries, including reflection, translation, rotation, uniform scaling, or combinations thereof, as a unified nonlinear optimization problem which is solvable by modern DFO methods. Our recent pilot study, involving a dense cloud of over one million points from a neoclassical building, has confirmed the technological feasibility of this proposed DFO approach.
The project offers both academic insights and practical benefits. The findings will extend knowledge of how modern mathematical methods can be used to discover symmetry in architecture or related areas. The outcomes may lead to a breakthrough in theoretical explanation of the challenges in architectural symmetry detection. Practically, the research will offer a useful methodological tool for the creation of accurate and informative building/city models from inexpensive point clouds for industries related to architecture, construction, engineering, automobiles, and robotics.