A design tool for globally developable discrete architectural surfaces using Ricci flow

This paper presents an approach for the design of discrete architectural surfaces that are globally developable; that is, having zero Gaussian curvature at every interior node. This kind of architectural surface is particularly suitable for fast fabrication at a low cost, since their curved geometry can be developed into a plane. This highly non-linear design problem is broken down into two sub-problems: (1) find the member lengths of a triangular mesh that lead to zero Gaussian curvature, by employing the discrete surface Ricci flow developed in the field of discrete differential geometry; (2) realize the final geometry by solving an optimization problem, subject to the constraints on member lengths as well as the given boundary. It is demonstrated by the numerical examples that both of these two sub-problems can be solved with small computational costs and sufficient accuracy. In addition, the Ricci flow algorithm has an attractive feature-the final design is conformal to the initial one. Conformality could result in higher structural performance, because the shape of each panel is kept as close as possible to its initial design, suppressing possible distortion of the panels. This paper further presents an improved circle packing scheme implemented in the discrete surface Ricci flow to achieve better conformality, while keeping its simplicity in algorithm implementation as in the existing Thurston's scheme

A Survey of Developable Surfaces: From Shape Modeling to Manufacturing

Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, and mechanical materials, as well as in the development of tangible interaction and deformable robots, with the characteristics of easy-to-product, low-cost, transport-friendly, and deformable. Transforming shapes into developable surfaces is a complex and comprehensive task, which forms a variety of methods of segmentation, unfolding, and manufacturing for shapes with different geometry and topology, resulting in the complexity of developable surfaces. In this paper, we reviewed relevant methods and techniques for the study of developable surfaces, characterize them with our proposed pipeline, and categorize them based on digital modeling, physical modeling, interaction, and application. Through the analysis to the relevant literature, we also discussed some of the research challenges and future research opportunities.Comment: 20 pages, 24 figures, Author submitted manuscrip

Dr. KID: Direct Remeshing and K-set Isometric Decomposition for Scalable Physicalization of Organic Shapes

Dr. KID is an algorithm that uses isometric decomposition for the physicalization of potato-shaped organic models in a puzzle fashion. The algorithm begins with creating a simple, regular triangular surface mesh of organic shapes, followed by iterative k-means clustering and remeshing. For clustering, we need similarity between triangles (segments) which is defined as a distance function. The distance function maps each triangle's shape to a single point in the virtual 3D space. Thus, the distance between the triangles indicates their degree of dissimilarity. K-means clustering uses this distance and sorts of segments into k classes. After this, remeshing is applied to minimize the distance between triangles within the same cluster by making their shapes identical. Clustering and remeshing are repeated until the distance between triangles in the same cluster reaches an acceptable threshold. We adopt a curvature-aware strategy to determine the surface thickness and finalize puzzle pieces for 3D printing. Identical hinges and holes are created for assembling the puzzle components. For smoother outcomes, we use triangle subdivision along with curvature-aware clustering, generating curved triangular patches for 3D printing. Our algorithm was evaluated using various models, and the 3D-printed results were analyzed. Findings indicate that our algorithm performs reliably on target organic shapes with minimal loss of input geometry

Integrated computational framework for the design and fabrication of bending-active structures made from flat sheet material

This paper introduces an integrated computational design framework for the design and realization of arbitrarily-curved bending-active architectural structures. The developed framework consists of a series of methods that enable the production of a complex 3D structures composed of a set of flat 2D panels whose mechanical properties are locally tuned by varying the shape of embedded spiraling patterns. The resulting panels perform as variable stiffness elements, and they are optimized to match a desired target shape once assembled together. The presented framework includes all the steps for the physical delivery of architectural objects, including conception, static assessment, and digital fabrication. The developed framework has been applied to an architectural scale prototype, which demonstrates the potential of integrating architectural design, computational simulation, structural engineering, and digital fabrication, opening up several possible novel applications in the building sector.</p

Discrete Triangulated Meshes for Architectural Design and Fabrication

Recent innovations in design and construction of architectural buildings has led us to revisit the metrics for discretizing smooth freeform shapes in context with both aesthetics and fabrication. Inspired by the examples of the British Museum Court Roof in Britain and the Beijing Aquatic Centre in China, we propose solutions for generating aesthetic as well as economically viable solutions for tessellating smooth, freeform shapes. For the purpose of generating an aesthetic tessellation, we propose a simple linearized strain based metric to minimize dissimilarity amongst triangles in a local neighborhood. We do so by defining an error function that measures deformation required to map a pair of triangles onto each other. We minimize the error using a global non-linear optimization based framework. We also reduce the complexity associated with prefabricating triangulated panels for a given shape. To do so, we propose a global optimization based framework to approximate any given shape using significantly reduced numbers of unique triangles. By doing so, we leverage the economies of scale as well as simplify the process of physical placement of panels by manual labor

Computational Architecture: development, design and optimization. Case study of a glass and steel roof for the Scuola Normale Superiore's courtyard in Pisa

This thesis is built around the conception, development and optimization of complex architecture, also known as free form. The project consists in a steel and glass roof over the inner courtyard of the Scuola Normale Superiore, with the aim to make the living space accessible at every moment of day life. The shape was conceived such that it would suit well the architecture of the Scuola Normale and the spirit it emobdies, with a special regard to energetics and fabrication, true weakness of architectures of this kind. The structure was modelled entirely on Grasshopper, a Rhino3D plug-in which allows to parametrically design objects. This programming environment allowed to interface add-ons, both proprietary and made on purpose by the author. With those tools, the author was able to develop algorithms for structural and geometric optimization. The former consisted in the process at the end of which the best structural performance is found, at constant weight: in the case studym genetic algorithms and iterative processes were used. Geometric optimization consisted in seeking the fabricability of the architecture, in the reduction of overall panel curvatures and eventually in the panelization of the surface. Finally, thanks to the code so created, it was possible to easily export all data and run required analysis exploiting the software more suited for each needing