球面大圆上最优点的算法与几何特征

The Algorithm and the Geometric Character of the Optimum Point on the Sphere

运用球面几何理论,将平面规划中的一类经典问题推广到球面,建立了在球面大圆上寻求一点,到已知两点的距离之和最短的模型和算法,并得到了最优点坐标的计算公式以及最优点的几何求法,其结果在球面规划中有一定的应用。

We generalize a kind of classical programming problems on the plane to the sphere, establish a model and the algorithm of finding the point on the major circle which make the sum of distances from it to the two known points is minimum, and obtain a coordinate calculation formula of the optimum point and the geometric method for finding this point. The results in this paper will be used in the spherical programming.