Dual evolution of planar parametric spline curves and TT-spline level sets

By simultaneously considering evolution processes for parametric spline curves and implicitly defined curves, we formulate the framework of dual evolution. This allows us to combine the advantages of both representations. On the one hand, the implicit representation is used to guide the topology of the parametric curve and to formulate additional constraints, such as range constraints. On the other hand, the parametric representation helps to detect and to eliminate unwanted branches of the implicitly defined curves. Moreover, it is required for many applications, e.g., in Computer Aided Design.