Box－样条级数的单调性

The Monotonicity of the Box Spline Series

研究了Ｂｏｘ－样条级数的控制点与Ｂｏｘ－样条级数单调性之间的关系，给出其必要条件、充分条件。同时，建立了三方向和四方向Ｂｏｘ－样条级数在任意方向上的单调性条件，这些结论推广了Ｗ．Ｄａｈｍｅｎ和Ｃ．Ａ．Ｍｉｃｃｈｅｌｉ给出的单调性结果［１］。

The objective of this paper is to study the relationship between properties of the control points of the box spline series and the monotonicity of the box spline series. The necessary conditions and sufficient conditions for the monotonicity of the box spline series are presented. We give the sufficient conditions of the monotonicity of the box spline series on the three and four directional meshes.