Reciprocal projections

Abstract

Transformation by inverse radiiThe reciprocal projections are based on the reciprocal transformation, or the so-called transformation by inverse radii, which follows from the involution of points on a line. In the involution of points on a line, there are two real or two imaginary double points that divide harmonically any pair of corresponding points. The middle point between the double points is called the center of the involution and it corresponds to the infinitely distant point of the line. The product of the distances of two corresponding points to the center of involution is a constant value.