Abstract. Geometric constraint solving (GCS) is the central topic in much of the current work of developing intelligent and parametric CAD systems. It also has applications in chemical molecular modeling, linkage design, computer vision and computer aided instruction. GCS algorithms accept the declarative description of geometric diagrams or engineering drawings as the input and output a drawing procedure for the diagram.

A basic idea of geometric constraint solving is to decompose the constraint problem into smaller ones according to some basic configurations. We find all spatial basic configurations involving points, lines, and planes containing up to six geometric primitives in an automated way. Many of these basic configurations still resist effective analytical solutions. We propose the locus intersection method for geometric constraint solving, which is used to solve all these basic configurations.