Solving geometric constraint systems. II. A symbolic approach and decision of Rc-constructibility

This paper reports a geometric constraint solving approach based on symbolic computation. With this approach, we can compute robust numerical solutions for a set of equations. We give complete methods of deciding whether the constraints are independent and whether a constraint system is over-constraint. Also, over-constrainted systems can be handled naturally. Based on symbolic computation, we also give a decision procedure for the problem of deciding whether a constrainted diagram can be constructed with ruler and compass (rc-constructibility).