Variational Design with Boundary Conditions and Parameter Optimized Surface Fitting

Abstract

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. A major topic is the generation of smooth curves and surfaces which can be immediately supplied to the NC-Process. The fundamental idea of the so called variational design methods is the use of modeling tools (curves or surfaces) which minimize certain functionals which can be interpreted in the sense of physics or geometry. The purpose of this paper is to present a method to include the parametrization as an additional parameter in the variational design process and to include boundary conditions (given curves and neighbouring surfaces) in the design process.