The Study Of Reduction Approximation Of Rational Bezier Curve

Computer Aided Geometric Design (CAGD) is to study the representation of curves and approximation, calculation in the field of computer, with rapidly developing interdisciplinary subject, involving theoretical knowledge of the mathematical aspects of approximation theory, numerical computation, differential geometry, algebraic geometry, topology, etc. It also has a close relation with engineering disciplines, such as computer graphics, data structures, and computer language because of a wide range of practical applications in CAGD.With the further continuing development and research of computer technology, functions on the development of computers and powerful graphical display for the mathematical model of curves in computer aided geometric design and computer-aided manufacturing applications provide basic and condition for a rapid realization.Because the number of curves in different systems aren’t completely identical, it is very difficult for the data transfer and sharing in different systems. In order to realize data transfer promptly and effectively in the different systems, it usually achieves the expected effect by lift order. However, most systems take the validity first in the practical application, moreover the system becomes unstable after ascend of the curves. Therefore it often makes high curves reduce order. The subject becomes one of the hot issues among many researchers because of a wide range of application and necessity of parameter curves’descend in the actual project.In this paper, it mainly has a discussion on rational Bezier curve with a multi-degree reduction. First it describes the importance of rational Bezier curves and reduced-order approximation in practical applications briefly, then introduce related knowledge of the rational Bezier curve and describes the need to address reduction problem. The core content of this paper is the reduction problem into a homogeneous space, in the nonlinear problem is transformed into a linear problem, and then to adopt the best average approximation method to solve this problem.Then use the least square approximation algorithm to solve this problem whose calculating process is easy and results are stable, being able to quickly solve the unknown coefficients. It achieve a multi-degree reduction quickly and efficiently by the rational Bezier curve conjunction with the calculation. If added security endpoint conditions, it can achieve the effect of the protection endpoint reduction, the error is smaller, the better the approximation effect is. It achieves the desired effect and purpose through an example calculation of the experiment. The application of new algorithm is very meaningful to realization of a multi-degree reduction of rational Bezier curves.