The Approximate Combined Of Two Adjacent Curves With Shape Parameter In CAGD

The curve of shape parameter has become a hot issue in computer-aided geometric design(CAGD). Curves with shape parameter was widely used in the description of curves and surfaces play a very important role, and there is shape parameter choice for designers. However, we often encounter similar problems of approximate merger of the curve,and reduced merging similar product design and development process of data traffic in the CAD/CAM curve, so as to effectively realize the network environment between the different systems of data transmission and exchange. Therefore, the curve is similar to the merger has been an important research topic in the CAGD.This research is mainly focus on Bezier curves and B-spline of approximation merger issues, we main research on the method of the approximate merger of CE-Bezier curve, QE-Bezier curves and three extended uniform B-spline curve with shape parameter. The main contents include:1.Briefly introduce the meaning and development of Bezier curves and B-spline, analyzing and summarize the types of curves with shape parameter definition, nature and shape parameters geometric meaning.2.1n order to further enrich and develop the theory of the CE-Bezier, QE-Bezier curve, we give a method that two adjacent CE-Bezier (or QE-Bezier) curves merge into one CE-Bezier (or QE-Bezier) curves. This methods direct access to the combined CE-Bezier (or QE-Bezier) curves show that the expression control points by fitting curves with the generalized inverse matrix theory, in the same time, experimental results illustrate that the proposed method not only has a good merging effect, but also is easy to implement and simple for error estimation.3.Research approximate merger of a band uniform B-spline parameters. By combining the theory of generalized inverse matrix, gives a reference uniform with the two adjacent B-spline curve with parameters combined into a uniform B-spline curve algorithm. This method not only gives the control point of the combined curve, but also gives the combined error. Finally, the examples are presented, which show the effectiveness of the presented method.