Research For Knot Inserted Based On MD-spline

B-Spline is a common tool in curve and surface design and modeling system, however B-Spline exist some intrinsic defaults. For the constrain of keeping the degree of the curve equal everywhere, it is necessary to use higher-order polynomial to represent curve instead of lower-order polynomial, which result to redundant information and more calculation. In order to avoid this disadvantage, some people give a new conception, multi-degree B-spline. The multi-degree B-spline (MD-spline),as a new method for B-spline modeling, is a particular B-spline which permits the different degree in the different interval. The theory of MD-spline is ongoing development and improvement.Most importantly, MD-spline maintains similar properties as well as traditional B-spline which include not only numerous ordinary properties, such as Local support, Piecewise segmented polynomial, convex hull property, but also some particular properties including Degeneration, and so on. The continuous of the entire MD-splines is at last Cmin{m,n},there m,n is the degree of adjacent polynomial intervals. When the degree of every interval is equal, MD-splines curve degenerates to B-spline curve.Knots inserted in B-spline is the highly basic and important skill in B-spline.As a new spline modeling,MD-spline also have the property. In this paper, we mainly present the theorem of knot inserted given by recursive algorithm founded on primary function of MD-spline. Thus,obtain total positive property of MD-spline and two important properties of MD-splines, Variation diminishing property and Convexity preserving property.We first review the history of development of Computer aided geometric design, enumerate some important modeling curves, and introduce the development of MD-spline briefly.Secondly the algorithm of constructing MD-spline will be mentioned in chapter 2, additionally some property. Then we present the theorem of knot inserted of MD-spline in chapter 3.In chapter 4, we give all positive of MD-spline and two important properties of MD-splines, Variation diminishing property and Convexity preserving property. At the same time, we introduce the application of MD-splines.At the last, conclusion and future work are given.