Construction of Rational Bézier Surface with Rational Bézier curves as boundary Geodesics

摘要

This paper studies constructing rational Bézier surface that interpolates a curvilinear quadrilateral as boundary geodesics. The construction consists of two parts. First, from the given corner data, four quartic rational Bézier curvilinear quadrilateral with minimum strain energy is constructed to satisfy the constraints of the quadrilateral geodesics on a surface. Second, a rational Bézier surface is designed to interpolate the quadrilateral as boundary geodesics of the surface. The control points and weights of the surfaces are computed by explicit and optimization methods. And the interpolation surface patch adheres to the Non-Uniform Rational B-Splines (NURBS) standard and employs geometric shape handles, such as control points, which is compatible with Computer Aided Design (CAD) systems. The method is illustrated by several computational examples.