The authors proposed an efficient method for determining the distance between an interval and a point on the surface of a spheroid to address some ensuing control problems. The authors described detection of multi extremal situations in the proposed problem and the causes of its occurrence. The authors suggested the algorithm of its solution under such conditions. In the case of multiextremality, the algorithm divides the interval into parts that are analyzed separately. In general case of unimodal intervals the algorithm uses special gnomonic projections with squared degree of convergence. The limits of applicability of the projection method are determined, and the optimal choice of the center of the gnomonic projection is justified. If the method is not applicable the universal minimization method provides the required solution. The method demonstrates high accuracy of the solution and the authors recommend it for use in commercial navigation and geodetic software products. The technique extends to control problems associated with different applications of navigation.