Construction of Rational Bézier Surface Interpolating Asymptotic Quadrilateral

Conditions for construction of rational Bézier surface interpolating a closed quadrilateral as its asymptotic boundary are presented.Firstly,from the given corner data,an optimized rational Bézier asymptotic quadrilateral of degree n is constructed.Secondly,two arrays of control points and weights along the boundary curves are obtained from the quadrilateral and the tangent vectors of the surface.Finally,minimizing the plate spline energy determines the other free control points and then a smooth rational Bézier surface of bi-（5n–7） degree is constructed.Some representative examples show the construction of surfaces interpolating the cubic,quartic or quintic rational Bézier asymptotic quadrilaterals and verify the effectiveness of the method.