Highly accurate approximation of ellipsoid surface patch by bicubic Bezier polynomials

Abstract In this paper, the approximation of a Effipsoid surface patch using bicubic Bezier poly-nomials is considered. The approximation is sixth order accurate. Furthermore the adjacentapproximation surface patches have the same tangent plane at their common boundary. Keywords: Approximation, Ellipsoid, Accurate, Patch. 1 Introduction Bezier curves and surfaces are widely used in the geometric modelling, but they could not denotecircle, sphere and the like exactly. Hence in practice, the requirement of approximation of sphereand the like arises when conic sections or rational curves are not available or are not recommended.Many authors have worked with the approximation of circle by Bezier polynomials [1, 2, 3], andin [4] we give a perfect approximation for a octant of ellipsoid surface. This paper we consider theapproximation of a ellipsoid surface patch by bicubic polynomials. The approximation turns outto have sixth order accuracy, giving a very small error.In the following, we introduce the error functions