Shortest circuits with given homotopy in a constellation

Abstract

A polynomial method is described for computing the shortest circuit with a prescribed homotopy on a surface. The surface is not described by a mesh but by a constellation: a set of sampling points. Points close enough (their distance is less than a prescribed threshold) are linked with an edge: the induced graph is not a triangulation but still permits to compute homologic and homotopic properties. Advantages of constellations over meshes are their simplicity and robustness.