A new constructive approach to constraint-based geometric design

In the paper, a new constructive approach to solving geometric constraints in 2-D space is presented. Constraints are employed on lines and points only, but more sophisticated geometric elements like Bézier curves and ellipses can also be constrained by mapping them onto auxiliary lines and points. The algorithm is based on local propagation, but first, the problem is transformed into a form that guarantees success of employing this simple technique. The most important steps are substitution of complex constraints with sets of simpler ones and insertion of redundant constraints by solving triangles and determining sums and differences of adjacent angles. In this way, various well-constrained problems with a few exceptions are solved, over-constrained scenes and input data contradictory to some well-known mathematical theorems are detected, and the algorithm is proved successful in many under-constrained cases as well.