Construction of Bezier surface patches with Bezier curves as geodesic boundaries
Given four polynomial or rational Bezier curves defining a curvilinear rectangle, we consider the problem of constructing polynomial or rational tensor-product Bezier patches bounded by these curves, such that they are geodesics of the constructed surface. The existence conditions and interpolation scheme, developed in a general context in earlier studies, are adapted herein to ensure that the geodesic-bounded surface patches are compatible with the usual polynomial/rational representation schemes of CAD systems. Precise conditions for four Bezier curves to constitute geodesic boundaries of a polynomial or rational surface patch are identified, and an interpolation scheme for the construction of such surfaces is presented when these conditions are satisfied. The method is illustrated with several computed examples. (C) 2009 Elsevier Ltd. All rights reserved.
geodesic curves surface reconstruction hermite/coons interpolation bezier curves and surfaces