Researches On Quasi-bezier Curves And Surfaces Modeling

The reason why the Bezier curve shows so powerful vitality in practice is that it has excellent control properties and geometric intuition which enables designers to mimic the design process of the curve and surface. In addition, the method is amazing simpleness which has a stable and efficient matching algorithm. But we must note that the Bezier method also has some shortcomings. It does not have local modification properties and its adjusting methods for the curve are single. Besides it lacks adequate freedom to achieve the partial modification for the composite curve. The defects of the Bezier method affect its application to some extent. So, it is hot to study the extension of the Bezier curve and surface, which makes the extended Bezier curve and curved surface not only retain the original properties, but also have more flexible regulation methods when we design spline curve and surface in the CAGD study.The paper includes the following there aspects:First, the paper discusses the issue of expansion of the quartic Bezier curves with three parameters and extends the representation of quartic Bezier curve called quasi quartic Bezier curve by introducing Bernstein basi s function with three shape parameters and discusses a series of basis properties of the curve. Taking different values of the shape parameters, shape of the curves can be modified easily. Without adjusting the control points, we can realize C1 and G2 merging of the quasi-quartic Bezier curves by changing the values of the shape parameters locally which can better meet the practical applications.Second, we introduce a set of basis functions with n shape parameters Based on these basis functions the n orde r Quasi-Bezier curve is defined. Then we discuss how to realize smooth merging of the curve segments and surface patches by modifying the value of the shape parameters without changing the control points in detail. As long as the order of curve is not less than four, we can modify locally the C1, G2 and C2 Quasi-Bezier spline curves without affecting the overall continuity of the spline which has a good local property.Thirdly, by discussing the effect of shape parameters on the definition of the m×n Quasi-Bezier surface, we present the method of how to realize C1 smooth merging of the surface patches by modifying the value of the shape parameters without changing the control points.