Domain-Specific Languages for Efficient Composition of Paths in 3D

We explore some domain-specific languages to describe (families of related) paths in 3D space. In particular, we explain the syntax, semantics, and implementation of Anton’s Path Language. The syntax resembles that of file paths with wildcards, and the semantics of a path expression is the set of all paths that satisfy the constraints imposed by that expression. Anton’s Path Language incorporates a mechanism to define patterns, based on repeated and transformed motifs. Through these patterns, various symmetries can be enforced. The implementation is an efficient engine running in Rhinoceros with GrassHopper, that quickly finds paths satisfying a given path expression and some global constraints. Anton’s Path Language underlies a powerful toolbox for artists, who can express their ideas in a path expression, feed it into the engine, and then post-process this through some beauty filters or by visual inspection. We provide three example artworks and how they were discovered using this toolbox.