Research And Applictaion Of B-spline Curves' Knot Insertion Algorithm

With the changes of actual demand and the emergence of a great deal of the ways of drawing curves, such as parametric cubic curves, Bézier curves, B-spline curves, NURBS curves. B-spline curves and the special case of its cubic uniform B-spline curves have already been widely used in many fields. There are many correlation algorithms and theories of B-spline curves and cubic uniform B-spline curves. This paper research the knot insertion algorithm and the application of the knot insertion technology of B-spline curves and cubic uniform B-spline curves for the need of the important weather map in Civil Aviation.B-spline curves for its own characteristics modify the shape of curves by adjusting the control point. There are many corresponding algorithms, such as knot insertion algorithms, degree elevation, and degree reduction. This article attends the knot insertion algorithms of B-spline curves.The cubic uniform B-spline curves have not only improved the computational efficiency, but also satisfied the required of the general engineering. Therefore, its have become an important curves drawing method. Taking into the practical application of items account, facilitating the control of the shape of curves through inserting knot in order to complete the man-machine combination of curves drawing, also using this knot insertion technology realizes the smooth of curves. The problem of improving the generating efficiency of the cubic uniform B-spline curves becomes an important research aspect. This article begins reasearch based on these.The main contents are as follows:(1) Introducing and analysising the existing B-spline knot insertion algorithms, such as the Boehm algorithm, Oslo algorithm, the algorithm of Qin Kaihuai proposed, as well as in practical applications of these algorithms improved.(2) Refining and realizing the knot insertion algorithm based on Tailor of cubic uniform B-spline curves. This algorithm effectively improved the generation rate of cubic uniform B-spline curve by analysising of Tailor series and combining with its mathematical characteristics.(3)The technology provided by the knot insertion algorithm of Tailor-based series of cubic uniform B-spline curves to achieve local control and curve smoothing. Especially dealing with the smooth of drawing the rapidly changing complexities of rendering curves.(4) And putting these related knot insertion algorithm and the technology provided by the knot insertion algorithm to deal with the specific projects.