关键词: 变次数样条, B 样条, 细分, 连续阶, 线性插值

Abstract: A subdivision scheme of changeable degree spline curves was proposed, in which the degree of each segment and the continuity between different segments can be specified before subdivision. In the algorithm, the degree of each segment can be selected from [1,4], the continuity between different degree segments was optional from C0 or C1 , and the continuity between the same degree segments was the degree minus 1. The scheme was based on the knot insertion of changeable degree spline. The midpoints were inserted into all non-zero knot intervals, and the relation of basis functions before and after the subdivision process were given accurately. At the same time, the length of each knot interval was proportional to its degree, which simplified the interpolation coefficients of different degree segments in the subdivision process. The subdivision process can be expressed in the form of linear interpolation, but it is different from the asymmetric local interpolation method for each segment. Instead, it is a global interpolation method, which is similar to the Lane-Riesenfeld subdivision of uniform B-spline. Therefore, the Lane-Riesenfeld subdivision scheme with degree ≤4 is included. 

Key words: changeable degree spline, B-spline, subdivision, continuity order, linear interpolation