Abstract
In recent years, voxel-based approaches have been explored to address data distributions related to space and form in diverse design disciplines. While originally used for the digital reconstruction of the human body, they are now widely used in design to represent intensive spatial properties. However, a voxel-based design process can limit design outcomes due to a predetermined voxel size and space resolution. Although variable voxel density subdivision algebras exist, a generalized algebra for volume subdivision of any size and shape as well as computing between individual subdivided parts has not been implemented. This paper presents a generalized volumetric space dividing algebra for closed, convex Polyhedra of any shape, which extends the Ice-Ray Shape Grammar and demonstrates weighted 3D boundary subdivision. Specifically, we present an algebra for subdividing any closed convex polyhedron, we demonstrate a boundary-weight algebra that interrelates properties (weights) with a variably subdivided space and allows for their direct manipulation in space as the design process takes place. We also present rules for extracting isocurves and reconstructing iso-surfaces in a variably subdivided, weighted 3D space. Finally, a use case of The Marching Shape 3D is demonstrated in a renewable energy based design process. Algebras and schemas are shown for a general shape grammar as well as for a digital computing platform.
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Tsamis, A., Varsami, C. (2023). The Marching Shape 3D. In: Turrin, M., Andriotis, C., Rafiee, A. (eds) Computer-Aided Architectural Design. INTERCONNECTIONS: Co-computing Beyond Boundaries. CAAD Futures 2023. Communications in Computer and Information Science, vol 1819. Springer, Cham. https://doi.org/10.1007/978-3-031-37189-9_1
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