The paper researches some applications of secure multi-party computation in space geometry problems. First, private-preserving determination protocol of distance relation of two-point in space based on threshold and private-preserving determination protocol of distance relation of point-line in space based on threshold are presented. Second, a private-preserving determination protocol of position relation of point and two parallel planes in space is presented. Finally, a private-preserving solution for private-preserving determination problem of distance relation of point and line segment in space based on threshold is constructed using the first two protocols. These protocols and solutions have potential application values in engineering, commerce and military field.