A Few Class Extends The Bezier Curve Of Continuation Method Research

The paper is divided into two parts, one is about the extension problem of some kinds of extended Bezier curve on the CAD system, another is about the extension of Bezier curve to other types of curve.In the application of curves and surfaces design, it is finite to express a single piece of parametric curve or surface, when the shape of the curve and surface are complex, we need to denote the curve or the surface with the segmental technology, then stitch these pieces of curves or surfaces together smoothly, thus we can get the more complex curve or surface.Based on the extension of existing Bezier curve, this paper put forward to a new method of the extended curve extension. First,we discussed with the extension of Bezier curve that with one parameter to the target point, according to the continuity sufficient and necessary conditions of curve at a splice point, the derived control point satisfies a relationship, and then select the object function, search the perfect parameters by minimizing the objective function; Besides analysis the extended curve quantitatively, we also study on the influence of parameters to extension curves by changing the different parameters And then we study on the extension of extended three Bezier curve that take a parameter to the target point, which is still according to continuity conditions of the curve at a splice point,thus we deduced a relationship which the control point satisfies, and study the effect of parameters on extension curve qualitative, quantitative respectively. And then discussed with the extension of the extended three Bezier curve with one parameter to the target curve with two parameter and the three extension Bezier curve to the target point continuation. Finally we proves the effectiveness of the proposed algorithm through the example.Although Bezier curve is an important method for curve construction in computer-aided design, it is convenient to curve surface design staff for its superior geometry and approximation, but just discuss about the extension of Bezier curves between Bezier curves is not enough in practical application, we also need to discuss the extension issue between Bezier curve and other types of Bezier curve (B-spline curve, H-Bezier curve and C-Bezier curve), the fourth chapter of this article emphatically discussed this question, and we show the algorithm is feasible by example.