Building Construction Sets by Tiling Grammar Simplification

Authors: Javor Kalojanov, Michael Wand, Philipp Slusallek

Abstract: This paper poses the problem of fabricating physical construction sets from example geometry: A construction set provides a small number of different types of building blocks from which the example model as well as many similar variants can be reassembled. This process is formalized by tiling grammars. Our core contribution is an approach for simplifying tiling grammarssuchthatweobtainphysicallymanufacturablebuildingblocksofcontrollablegranularitywhileretainingvariability, i.e., the ability to construct many different, related shapes. Simpliļ¬cation is performed by sequences of two types of elementary operations: non-local joint edge collapses in the tile graphs reduce the granularity of the decomposition and approximate replacement operations reduce redundancy. We evaluate our method on abstract graph grammars in addition to computing several physical construction sets, which are manufactured using a commodity 3D printer.