Computational design and fabrication of tileable patterns: from geometry to mechanical properties

With the increasing availability of CNC machines and 3D printers, the fabrication of physical artifacts and their visual appearance has become trending research topics in the Computer Graphics community. In recent years, several workflows have been developed to streamline the Digital Fabrication process, overcome material, size, and geometric limitations, and speed up the reproduction and the prototyping phase. In addition to high-resolution reproductions, new approaches which realize objects in an artistic manner instead, have acquired attention. It quickly became apparent that these techniques could also be directed towards the production of objects that look and perform in a desired way, e.g. when subject to a particular external or internal stimulus. In this context, a common theme is the design of ornamental patterns and their use as structural building blocks of complex pattern assemblies bringing into the spotlight the interplay between aesthetics and mechanical properties. In this thesis, we investigate and propose a novel pipeline for designing and efficiently simulating complex pattern tessellations. The thesis presents 3 main contributions. The first one targets the scarcity of open and efficient simulation tools by proposing a computational tool for predicting the static-equilibrium of general bending-active structures which is accompanied by an efficient open-source implementation. Our second contribution is a novel approach for generating a wide range of flat patterns with favorable fabrication-related properties. The third is a computational method for calibrating a reduced mechanical model for each generated pattern enabling the interactive simulation of complex pattern assemblies.