A Hermite Method On Bezier Surface

A class of Hermite-Bezier fitting surface with condition of tangent vectors is studied in this paper. The method is based on the Kirov approximation theorem. We can find that this curve(surface) possesses all the positive properties exclude convex hull. It can also show huge advantages in modifying and smooth joining.The existing CAD/CAM system methods of surface modeling based on traditional CAGD pure mathematic theory defines surface through control curve and control point with a function of adjusting local shape. However, this flexibility brings a great deal of inconvenience to shape design for typical demand of design is not only qualitative but also quantitative, such as a global smooth and fair surface approximating a group of scattered points and interpolating a section curve .The constraints for both globe and local surface is required, but the existing surface constructing method can hardly meet the requirements.When modifying the surface, the designer is often asked in shape-oriented. Through indirectly adjusting vertices, weight factor and knot vector to modify the shape is fussy, time-consuming and not intuitionist and it is difficult to modify the shape qualitatively and quantitatively, locally adjust control point can hardly retain the globaltraits such as convexity or smoothness.This method can supply the condition of tangent vectors for each control points ,when curve and surface are modified, we only need to adjust the control vector that is the condition just now, to satisfy the requirement.So, compared to the general Bezier curve-fitting, it possesses more degrees of freedom and much intuitivism especially when the high-time continuity which refers to modification to a great deal of control vertices is needed, computing is decreased remarkably, while the degree of the fitted surface is just one time higher than that of Bezier surface. This method help the engineer in CAGD areas to introduce Bezier Scheme to control the shape of the surface.