Privacy-preserving computational geometry is a special secure multi-party computation problem. It can be defined as the problem of several users computing a cooperative task of their geometric input in a distributed network, where no user is willing to disclose his secret inputs to anyone else. This problem may be applied in the field of research and exploitation of the outer space. Private determination of whether two sets of data are proportional correspondingly is a basic problem of secure multi-party computation, and it also plays an important role in the relative position determination for two spatial geometric objects. In this paper, a protocol for determining whether two sets of data are proportional correspondingly is developed, its correctness, security and efficiency are analyzed, and the corresponding algorithms for determining the relative position of spot, line and plane in space are also presented.