Free-form Architectural Design with Repetitive Elements

Free-form surfaces are highly valued in architecture for their expressive aesthetics; however, their double-curved geometries pose significant construction challenges. In particular, the fabrication of building elements, such as beams, panels, and joints, often involves a large number of unique shapes, leading to extensive mould customisation and high manufacturing costs. To address these challenges, this thesis proposes a set of computational methods for designing free-form architectural structures using repetitive elements, enabling cost-effective fabrication across diverse application scenarios. First, a general clustering–optimisation framework is introduced to reduce the number of distinct beams, panels, or joints in an input mesh. Element-specific similarity metrics based on best-fit mapping are employed to group geometrically similar components, while optimisation drives each cluster towards congruent shapes. The framework adaptively determines the number of clusters required to satisfy a user-specified error threshold and is validated through various numerical examples. Second, a mesh-growth algorithm is presented to approximate free-form surfaces using equivalent regular or near-regular triangles. Starting from an initial seed, the mesh grows incrementally by assigning locally optimal vertex valence and updating vertex positions through localised optimisation. The method produces uniform meshes for complex geometries, including surfaces with open boundaries. Via best-fit mapping, all faces can be replaced by congruent panels to enable efficient manufacturing and assembly. Third, a method is proposed for approximating free-form surfaces using assemblies of rotational patches, enabling the simultaneous repetition of multiple element types, such as beams, panels, and joints. A patch layout creation approach segments the input surface into patches that resemble untrimmed rotational patches within a prescribed error threshold. A B-spline-based optimisation framework then refines the fitted patches for smooth connections and faithful surface approximation. To facilitate practical applications, a post-processing step converts the discrete patch assembly into a seamless, smooth quad mesh composed of locally repeated elements. The method is demonstrated on a range of free-form surfaces and is shown to accommodate diverse practical requirements. Overall, this thesis presents a toolkit of computational methods for the design and rationalisation of free-form architectural structures using repetitive elements. Academically, it advances the fields of architectural geometry and computational design by offering new insights into the general topic of free-form surface approximation using discrete elements with prescribed geometric constraints. Practically, it enables cost-effective fabrication by reducing shape variety in beams, panels, and joints, thereby lowering manufacturing complexity and costs. For future work, the proposed methods support further exploration of new element types, structural systems, and design objectives, as well as integration with emerging digital fabrication technologies and AI-empowered design approaches.