Construction of rational quadrilateral Bézier geodesics

In terms of given data of four corners (i.e., the surface tangent plane at each corner, the osculating planes and curvatures of the boundaries at each corner), we study constructing rational quadrilateral Bézier curves by these data and the constraints for crossing geodesics on a smooth surface, such that they are four geodesic boundaries of a rational Bézier surface. The control points and weights of the geodesics are obtained by a geometric and optimized method, and the degree 4 is required for rational Bézier curve, which is lower than that in [8]. The computational examples show that the method is feasible.