Digital straight segments

It will be proved in this paper that all digital straight segments connecting two given pixels form an area whose lower bound and upper bound are also the digital straight segments. These two bounds will be simply calculated and have the following properties; one is different from the other by unity in the x or y coordinate, and their chain codes of directions reverse from each other. Hence, for practical purposes, these results are used to define general digital straight segments as the digital arcs in this area, and also used to define the convexity and concavity of digital arcs.