Numerical solving of geometric constraints

In computer-aided design, geometric modeling by constraints enables users to describe shapes by relationships, called constraints between geometric elements. The problem is to derive automatically these geometric elements. Many resolution methods have been proposed for solving systems of geometric constraints. Geometric methods can be very efficient but are only applicable to particular kinds of problems (typically rule and compass constructive problems). Some schemes cannot be solved by any geometric method. A numerical method is then necessary. We use the bisection method to solve these "difficult" cases. The bisection method enables users to reliably find all solutions to a system of nonlinear equations within a region defined by bounds on each individual coordinate of the geometric objects.