Inter-diagrammatic reasoning and digital geometry

In this paper we examine inter-diagrammatic reasoning (IDR) as a framework for digital geometry. We show how IDR can be used to represent digital geometry in two dimensions, as well as providing a concise language for specifying algorithms. As an example, we specify algorithms and examine the algorithmic complexity of using IDR for reasoning about the relationships between planar regions. Finally, we discuss the circumstance under which the algorithmic abstractions in IDR can produce efficient algorithms under realistic computational assumptions.