Discrete Triangulated Meshes for Architectural Design and Fabrication

Abstract

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.