Digital images of geometric pictures

Abstract Digital geometric pictures, which are the digital images of real geometric pictures, are introduced. Especially, rectangles, equilateral triangles, and isosceles right triangles are treated here. Characterizations of sets of lattice points constructing parallel lines and right angles are investigated first. A necessary and sufficient condition for a given finite set of lattice points to be the digital image of a rectangle is given by making use of these characterizations. Then, characterizations of angles of 60° and 45° are investigated from a point of view of digital geometry. Finally, necessary and sufficient conditions for digitized equilateral triangles and isosceles right triangles are shown.