A spatial constraint template problem

Three-dimensional geometric constraint solving is a rapidly developing field, with applications in areas such as kinematics, molecular, modeling, surveying, and geometric theorem proving. While two-dimensional constraint solving has been studied extensively, there still remain many open questions in the arena of three-dimensional problems. We first introduce some techniques presented by (Hoffmann and Vermeer, 1995). The constraint system Hoffmann has studied consists of six geometric elements and pairwise constraints between triples of the elements. The core idea is to solve the geometric constraint template problems. Based on this, we continue to demonstrate how to solve a special template system composed of three points and three planes. This constraint system includes the angle constraints between two planes that are not discussed before.