Implementation of shape embedding in 2D CAD systems

Abstract

The process of shape embedding, that is, the inquiry whether for two shapes u and w there is a transformation f that embeds the shape f(u) in w is the most critical – and elusive – process for all shape grammar interpreters implemented within CAD systems. This paper identifies three major challenges underlying the implementation of shape embedding within a CAD environment and proposes three corresponding solutions. The focus is given here in the calculation of shape embedding for shapes made up of lines in a 2D CAD environment to provide the testbed for the mechanisms proposed. The integration of these three sets of algorithms into one coherent framework produces the blueprint of Shape Machine, a general-purpose shape grammar interpreter implemented in Rhinoceros, a NURBS 2D/3D CAD software. Some preliminary thoughts regarding the impact of the proposed shape-rewrite modeler in CAD industry and more broadly, in design education are given in the end.