B\'ezier Surfaces with Special Coordinate Curve Nets

Abstract:

      B\'ezier surfaces play an important role in Computer-aided Geometric Design (CAGD), and coordinate curve nets are widely discussed in differential geometry. In this paper, we study the B\'ezier surfaces with special coordinate curve nets, such as orthogonal coordinate net, curvature coordinate net and asymptotic coordinate net. In addition, we develop the B\'ezier surfaces which satisfy some shape constraints with the help of energy terms. Moreover, some applicable sufficient conditions based on geometrical structure of control nets are deduced and several representative examples are given.