Geometry of Arrangements that Determine Shapes

A shape in the universe $U^*$ has an underlying arrangement that consists of construction lines and registration marks. Relations between construction lines and registration marks in an arrangement are represented as an incidence structure, satisfying special incidence laws. Arrangements that determine shapes are distinguished into those that constitute point-line (incidence) geometries and those that do not. Arrangements that constitute point-line geometries give an alternative characterization of determinate rules in shape grammars