A 4-degree Bézier Shape Adjusting Of Study

Bernstein polynomial plays an immeasurable role in the theory and application of function approximation. Especially in the 70’s of the last century, it is used to construct Bézier curves and surfaces, provides support for important mathematics for computer aided geometric design. This paper studies 4-degree by the Bernstein polynomial basis functions structure of the Bézier curve of the problem of shape adjusting. Mainly decomposition analysis of the shape with some extensions to adjust the parameters of Bézier curve, adjustable parameters which control the geometric sense, then proposed does not change the basic function but by adjusting the parameters of adjustment the control points, and then to adjust the shape of the curve method purposes.Firstly, a comprehensive analysis of overview on the status of Bézier curve shape adjustment study and a brief analysis of its features.Secondly, for some four B curve constructed with local shape parameter adjustment in-depth analysis. The method of adjusting the shape of the curve control points transformation matrix with adjustment parameters are given on this basis. Research on the curve shape wherein the variation parameter.Again, given by adding independent adjustable parameters, And a Bézier curve is divided into two the same the number of Bézier curves of smooth stitching of curve, discusses the impact parameter selection curve stitching continuity.By using control points with shape adjusting parameters and the main advantage of a standard Bernstein basis function is constructed to generate curves, to avoid the discussed nature of the new basis function step, also greatly expanded the range of parameter selection, so that the shape of the curve changes with greater ?exibility, and geometric meaning of the parameters is obvious.