Surface Construction Based on Variational Principles

. Variational principles have become quite popular in the design of surfaces. The idea is to consider a class of surfaces having more degrees of freedom than are necessary to fulfill the constraints (e. g. interpolation or boundary conditions). The remaining degrees of freedom are set by minimizing a fairness functional. The choice of the `right' fairness functional is a crucial step. In this paper we describe a systematic approach for choosing an appropriate fairness functional that produces high quality surfaces and which allows the solution of the optimization problem in a reasonable amount of time. x1. Introduction In different areas in CAGD arises the problem of constructing smooth curves or surfaces satisfying certain constraints. Typical examples are (scattered data) interpolation and the construction of blending surfaces. In scattered data interpolation one has to construct a surface which does not oscillate too much and goes through a sampled set of points in the space. Findi..