Generating Bézier points for curves and surfaces from boundary information

This paper presents efficient methods for directly generating Bézier points of curves and surfaces explicitly from the given compatible arbitrary order boundary information of Hermite curves, Coons-Hermite Cartesian sum patches and Coons-Boolean sum patches. The explicit expressions for the generalized Hermite functions are also developed. Furthermore, a method for determining the twist control points and higher level sets of interior control points from their boundary and lower level sets of control points by using the Coons-Boolean sum schema presented. Many interesting and useful examples are also given in this paper.