Variable-radius circles of cluster merging in geometric constraints: I. Translational clusters

Variable-radius circles are common constructs in planar constraint solving and are usually not handled fully by algebraic constraint solvers. We give a complete treatment of variable-radius circles when such a circle must be determined simultaneously with placing two groups of geometric entities. The problem arises for instance in solvers using triangle decomposition to reduce the complexity of the constraint problem. Part I sets up the problem statement and considers clusters where the relative motion is translational. Part I also reviews past work on the subject. Part II treats rotational clusters motion.