On the minimal length curve that densifies the square

Abstract

This paper deals with the existence of a curve of minimal length, expressed in parametric coordinates, which densifies the square J²=≤ft [ −1,1\right ] × ≤ft [ −1,1\right ] \ with a given degree of density α. Nevertheless, the same problem has no solution if we consider the family of curves defined by means of the graphics of continuous and rectifiable functions f: J→ J. Their consequences on the approximation method to the global optimization are also derived.

Citation

Mora, G. and Cherruault, Y. (1999), "On the minimal length curve that densifies the square", Kybernetes, Vol. 28 No. 9, pp. 1054-1064. https://doi.org/10.1108/03684929910300277