Blending techniques based on variational principles

摘要

ent the foundations of a method to generate blend surfaces. The idea of this method is to consider functionals depending on parametrized surfaces and their partial derivatives up to order two. The blend surface then is the surface which minimizes the functional. In section 2 we briefly describe the mathematical foundation. We discuss the variational problem associated to certain bilinear functionals in the Sobolov space of order 2. In section 2 we outline in detail the procedure how to generate blend surfaces by this method. Starting with a primary parameter space and a primary bilinear functional, one has to determine the final bilinear functional. The blend surface then is chosen as the tensor spline surface which minimizes the quadratic form corresponding to this bilinear functional.