Masonry Shell Structures with Discrete Equivalence Classes

This paper proposes a method to model masonry shell structures where the shell elements fall into a set of discrete equivalence classes. Such shell structure can reduce the fabrication cost and simplify the physical construction due to reuse of a few template shell elements. Given a freeform surface, our goal is to generate a small set of template shell elements that can be reused to produce a seamless and buildable structure that closely resembles the surface. The major technical challenge in this process is balancing the desire for high reusability of template elements with the need for a seamless and buildable final structure. To address the challenge, we define three error metrics to measure the seamlessness and buildability of shell structures made from discrete equivalence classes and develop a hierarchical cluster-and-optimize approach to generate a small set of template elements that produce a structure closely approximating the surface with low error metrics. We demonstrate the feasibility of our approach on various freeform surfaces and geometric patterns, and validate buildability of our results with four physical prototypes. Code and data of this paper are at https://github.com/Linsanity81/TileableShell.