Abstract:  In order to avoid distortions and wrinkles in the surface modeling, the K-2 ring mesh at the inner point of the quad mesh served as the control mesh, a simple and flexible surface construction method was proposed. With a given K-2 ring control mesh, a planar mesh with the same topologyit was constructed. Then the plane mesh was expanded into a spatial quad mesh, and samples were made in the plane mesh. The quad mean value coordinates of the sampling points were later calculated with respect to the vertices of the spatial quad mesh. Finally, the surface was generated using the quad mean value coordinates to ensure that each point on the surface meets C∞ . In this process, a global shape factor h was set to control the degree of approximation between the surface and the initial control mesh. It is proved through examples that the smaller h is, the closer the surface is to the initial control mesh. 

Key words:  , surface modeling, K-2 ring mesh, quad mean value coordinates, shape control, continuity