Elimination of corners in the mapping of a closed curve

Summary

A transformation, which maps the exterior or the interior of a simple closed curve with corners into the exterior or interior respectively of a simple smooth (corner-free) closed curve, is introduced. Symmetry properties are shown to be preserved by the transformation and a numerical procedure for applying the proposed transformation to an arbitrary curve is presented.

Smooth curves, resulting from the application of the corner-eliminating transformation to a square and to a sixcornered double ship section are also given.