Extension Of Bézier Curve And Its Connection

The Bézier curve is one of the important components for computer aidedgeometric design and tools for the Curve Surface Modeling Design, its approximationprinciple is used to imitate the design process of curve and surface, at the same timefor the use of programmer. For a given control polygon, the Bézier curve’s position isdetermined, while these curve’s shape is complicated and variable in the practicalapplication it is difficult to describe with a single curve or surface. Therefore, byquoting the shape parameter in the curve’s function in the chapter two, and changingthe parameter value to adjust the curve shape. In addition, through the smoothconnection between the curves to achieve a better expression for the complexcombination curves.First of all, a class of quartic Bernstein basis function with three parameters ispresented as an extension of the quartic Bernstein.Properties are analyzed and thequasi Bézier with three shape parameters is defined based on it. The curve inheritingthe outstanding properties of quartic Bézier curve, and the smooth connectionbetween curves are analyzed. Some examples illustrate that the defined curveprovides an effective method for designing curves and surfaces. Secondly, using theBézier b-spline curve ‘s constructing method and applying the Bézier curve splicingtechnology, the smoothG0、G1、G2connection between uniform B spline curve andBezier curve come true. Thirdly, using the mutual transformation between theNURBS curve and rational Bezier curve, transforming the connection betweenquadratic Bezier curve and cubic non-uniform b-spline curve into a quadratic Beziercurve and cubic Bezier curve’s connection, and connection theorem are obtained.Finally, the work is summarized and some problems should be studied in the futureare given.