Based On The Best Square Approximation B-spline Curve Price

In the field of computer aided geometric design, the B-spline curve is one of basal modeling tools and has wide applications. Degree reduction of B-spline curves is an important technique in curve and surface modeling. To exchange data among different CAD systems, it is widely used. Therefore, degree reduction of B-spline curves has been a research hotspot and drawing more and more attention.In general, degree reduction of Bezier curves is relatively well understood. So Pigel and Tiller decompose a B-spline curve into piecewise Bezier curve segments via knot insertion. Then reduce the degree of each segment respectively. Finally, the desired B-spline curve is obtained by knot removal. In the algorithm of Wolters et al., the blossoming principle and the least squares method are used to reduce the degree of each polynomial segment of a B-spline curve directly. A similar method is to reduce the degree by applying the explicit coefficient matrix of B-spline curves and the best uniform approximation theories. And then, the control points of the degree reduced B-spline curve are obtained by applying the weight scheme for merging multiple copies of the control points produced by the first step. In these methods, there are two steps that may increase the total error. Another method is based on constrained optimization. Qin Kaihuai and Yong Junhai disturb control points by a constrained optimization method to get a degenerate B-spline curve that can be represented by a B-spline curve of a lower degree, and the perturbations between the new control points and the old ones are minimized. The control points of the desired B-spline curve are obtained by solving the system of linear equations deduced by each segment of the degenerate curve.The paper discusses the degree reduction method based on the constrained optimization method and proves theoretically that the degree reduced curve obtained by the method is actually a global polynomial curve. Generally, it is reasonable to approximate a global curve with piecewise curve segments. But this method is just...