The Research Of Bézier Curve Shape Adjusted Through Control Point Method

In the field of function approximation theory and application, the curve design andshape adjustment for the computer aided geometric design is very important topic. But theBézier curve and B-spline curve is important and most basic method in the computer aidedgeometric design. The generation of these two curve are both based on two key elements:one is the basic function, another is control point. Sometimes it is necessary to adjust thecurve shape, and then got the changing basic function through setting parameters, thenthrough adjusting the parameters to adjust the curve shape. For example the rational Béziercurve. Another way is by adding control point of changeable parameters, then throughadjusting the number and position of control points to achieve the goal of adjusting thecurve shape. The paper is studying a couple of questions in adjusting curve shape throughchanging the control point by parameters.Firstly, we will analyze the feature of the curve generated by rational Bézier curvemethod and control point with parameters method. In approaching the control polygonand inserting a data in any points of the control of the convex polygon, the former one isbetter. But in the diversity and flexibility of generating curve, it’s opposite.Secondly, studied with parameters of the control point in two smooth curve connectingapplications.Finally, we discussed shape changing question of several kinds of Bézier curve withthree adjustable parameters.The curves generated by the rational Bézier curve method and the control point withparameter method have respective feature. From our research we know, if we want thecurve approaching to control polygon, the rational Bézier curve method is better option;if we want the curve shift or deformation, then the control point with parameter method is better option. In addition, we can also connect the two curves smoothly by using thecontrol point with parameter. The new curve can also approach to the control polygon.