30 Years after Sketchpad : relaxation of geometric constraints revisited (I)

The problem of solving sets of coupled geometric constraints in the context of inetractive computer aided sketching is studied. Some criteria for solution methods are given and the applicability of a relaxation method is discussed. Despite its relatively slow convergence, the relaxation method turns out to be sufficiently flexible (it works for a variety of constraint types and it can be implemented to handle both under-and over-constrained systems in a stable way) to be of at least qualitative use in an interactive design environment. Some mathematical aspects of the method are discussed and examples of applications are given.