Exact degree reduction algorithm for multi-degree spline curves based on Bernstein basis representation

Multi-degree spline is a direct extension of B-spline and can be used to reduce the number of control points for joint polynomial curves with different degrees. Exact degree reduction of multi-degree spline curves can be used to convert a B-spline into a multi-degree spline or to transform from one multi-degree spline to another losslessly, while reducing the number of control points. Firstly, based on the fact that the values of the curve before and after degree reduction remain unchanged without any parameter transformation, a necessary and sufficient condition for exact degree reduction of each curve segment is given. Secondly, according to the linear representation of Bernstein basis, the explicit expression of the control points after degree reduction is derived with respect to the control points before degree reduction. Thirdly, an exact degree reduction algorithm is presented to check the minimum degree of each segment of a multi-degree spline exactly reduced to. When the multi-degree spline is degree reducible, the reduced degrees can be selected and the control points after degree reduction can be calculated. Lastly, compared with the exact degree reduction method using dual bases, examples show that our algorithm possesses higher calculation efficiency.