Multi-degree B-spline curves

Multi-degree B-spline (MD-spline) curves are special B-spline curves with various degrees on different intervals, thus adapted to the development of CAD modeling system. MD-spline curves whose maximal variational degree was lower than three were investigated. This kind of MD-splines inherit most properties of polynomial B-splines, such as variation diminishing property, convexity preserving property, etc, and enjoy other advantageous properties for modeling, such as degeneration property, knot insertion property. Also the whole MD-spline curve is at least Cn-1, where n is the smallest degree of whole curve segments. In addition, the relation between MD-spline and B-spline was presented. MD-spline can be transformed into B-spline through knot insertion, simultaneously the degree elevation of B-spline can be interpreted as corner cutting process through MD-spline. MD-splines can effectively reduce the numbers of spline curves control points and knot vectors while keeping the desired accuracy, which are very good for geometric design and data transmission of CAD system.