An Algorithm for Constructing 3D Struts

Abstract

A simple robust “strut algorithm” is presented which, when given a graph embedded in 3D space, thickens its edges into solid struts. Various applications, crystallographic and sculptural, are shown in which smooth high-genus forms are the output. A toolbox of algorithmic techniques allow for a variety of novel, visually engaging forms that express a mathematical aesthetic. In sculptural examples, hyperbolic tessellations in the Poincaré plane are transformed in several ways to three-dimensional networks of edges embodied within a plausibly organic organization. By the use of different transformations and adjustable parameters in the algorithms, a variety of attractive forms result. The techniques produce watertight boundary representations that can be built with solid freeform fabrication equipment. The final physical output satisfies the “coolness criterion,” that passers by will pick them up and say “Wow, that’s cool!”