Variational Design and Parameter Optimized Surface Fitting

Computer Aided Geometric Design has emerged from the need for freeform surfaces in CAD/CAM technologies; it has become a major research topic in computer science with direct applications for all engineering sciences. The main task of the so-called variational design is to determine smooth curves or surfaces, which minimizes certain functionals and fulfill special constraints. First we interpret one widely used functional in the sense of physics. This approach naturally extends to a physical-based modification of surfaces. As an optimization step we include the parametrization as an additional parameter in the variational design process.