Algorithm for determining whether m given demand points are on a hemisphere or not

Location problems on a sphere can be solved easily by mathematical programming or geometrical methods if it is known that all the demand points are located on a hemisphere. This paper presents an algorithm for determining whether m given demand points are on a hemisphere or not. In this algorithm, the great circle is rotated successively until the hemisphere which contains the m given demand points is found or it becomes known using our criteria that the m given demand points are not on a hemisphere. The convergence of this algorithm is proved, and two illustrative examples are presented.