The complexity of shape grammars being produced continues to surpass the technology behind implementing them. One step towards implementing more useful shape grammars is the creation of a subshape matching technique for shapes composed of curved lines that lie in a plane. An interpreter with this ability allows for the practical implementation in general of two-dimensional grammars as well as opening the door for new applications of shape grammars. Our method for matching shapes consisting of curved lines is outlined and some examples from the Buick brand shape grammar, which was implemented by our interpreter, are shown. The emergent properties of shape grammars are also explored and considered using the new technique.