Arrangements Containing Shapes: Mathematical Features and their Use in Visual Calculating

Abstract

Construction lines and registration marks in shape grammars ground the appearance of shapes to provide an algorithmic approach to visual calculating. Here, the two concepts are studied in unity as a new object called point-line arrangement. This chapter develops such topics as the comparison and classification of shapes by their arrangements, the characterization of the “geometries” that arrangements give rise to, the algebra of arrangements, and others. In this way, it provides a more holistic view of construction lines and registration marks, beyond the usual roles they receive in algorithmic implementations of shape grammars.