A Geometric Constraint Solver with Decomposable Constraint Set

Abstract

In the paper, a new constructive approach to solving geometric constraints in 2D space is presented. The main step of the algorithm is pre-processing, which transforms both, geometric elements and geometric constraints, into simpler forms, and adds redundant constraints of distances and angles by solving triangles and determining sums and differences of adjacent angles. A wide variety of well-constrained problems can then be solved by a simple technique of local propagation, and over-constrained scenes and input data contradictory to some well-known mathematical theorems can also be detected in the same phase. Only with under-constrained problems and some special well-constrained cases, an additional step of merging clusters and/or geometrical relaxation is required.