Exact Degree Reduction Algorithm for Multi-Degree Spline Curves Based on Bernstein Basis Representation

To enhance the exact degree reduction theory for multi-degree splines and expedite the reduction process, an exact degree reduction algorithm for multi-degree spline curves is proposed based on the Bernstein basis representation. Initially, adhering to the rule that the values of the curve remain invariant before and after degree reduction without parameter transformation, a necessary and sufficient condition for exact degree reduction of a segment is established using high-order right derivatives at a single point. Subsequently, leveraging the linear representation of the Bernstein basis, explicit expressions of the control points after degree reduction in relation to those before degree reduction are provided. Finally, an exact degree reduction algorithm is presented, enabling a priori determination for the minimum degree that each segment of a multi-degree spline curve can be precisely reduced to. Within the range of degree, the reduced degree for each segment can be chosen, and the control points after degree reduction can be calculated. Compared with dual basis method for exact degree reduction by two self-constructed simple examples, the results indicate that, in the same environment, the computation time of the proposed algorithm is about 30% of that using the dual basis method.