Hardware Assist for Constrained Circle Constructions II: Cluster Merging Problems

In geometric constraint solving, constructing circles with indeterminate radius is an important sub problem. Such constructions are both sequential, meaning that we seek a circle tangent to three known geometric entities, as well as simultaneous, when several sets of entities, among them variable-radius circles, must be determined together. In Part I of our investigation, we considered sequential constructions in which a single circle had to be constructed from required tangencies to known geometric entities. In Part II, we develop hardware-assisted techniques to solve the simultaneous construction problems of variable-radius circles. We utilize the graphics hardware to determine the solutions. For Part I, this could be accomplished relying fundamentally on constructing distance maps. Here, we need to construct and sample surfaces from configuration space.