An Edge Vector Representation for the Construction of Two-Dimensional Shapes

This paper is concerned with the construction of polygonal shapes using an approach based on vector geometry. Starting with the concept of an atomic polygon cell, configurations of planar animals are constructed. A vector approach for the representation of polygons in which they are represented as a sequence of edge vectors is proposed as a general representation for abstract concepts without the need for situation within a coordinate system. A rule is postulated for joining two shapes in edge-to-edge contact by the addition of edge vectors of equal magnitude but opposite direction. Examples of various animals generated from the application of this rule to various atomic polygonal shapes are given. The rule is shown to be applicable for joining any two polygonal shapes but the principle can be generalised to curved shapes. It is shown that this representation allows a simple recording of the history of the generation of a complex shape through a hierarchical record of the joining of two shapes.