Most existing finite element formulations are not suited for the geometry description.Methods such as Bezier, B-spline and NURBS curves and surfaces used in CAD systems for the geometry description are point-based methods.Non-Uniform Rational B-Splines and Bezier spline play key roles in isogeometric analysis, we want to use it reform the local cover function in manifold numeric method ,for Bezier curve has the physical meaning connecting the four control points, Up to now, Bezier spline as one tool in manifold numeric method ,there are more problems left to study.