A class of generalized moving average operators is introduced, and the integral representations of an average function are provided. It has been shown that the average of Dirac δ distribution is just the well kn...A class of generalized moving average operators is introduced, and the integral representations of an average function are provided. It has been shown that the average of Dirac δ distribution is just the well known box spline. Some remarks on box splines, such as their smoothness and the corresponding partition of unity, are made. The factorization of average operators is derived. Then, the subdivision algorithm for efficient computing of box splines and their linear combinations follows.展开更多
基金supported by the Natural Science Foundation of Chongqing (Grant No.cstc2012jjA70004)the National Natural science Foundation of China (Grant No.51275551)
文摘A class of generalized moving average operators is introduced, and the integral representations of an average function are provided. It has been shown that the average of Dirac δ distribution is just the well known box spline. Some remarks on box splines, such as their smoothness and the corresponding partition of unity, are made. The factorization of average operators is derived. Then, the subdivision algorithm for efficient computing of box splines and their linear combinations follows.
