为了对任意NUBS曲线进行精确的分解和重构，提出了半正交B样条小波分解和重构的新算法，同时给出了处理非均匀B样条曲线的非整数阶分辨率的小波分解和重构算法，并实现了任意非均匀B样条曲线的多分辨率表示，对于任意非均匀B样条或NUBS曲线，无论它有多少个控制点，均可以对它进行半正交分解和重构，而不受控制点数必须等于2＋3的限制，从这个意义上讲，该方法不仅可以实现连续分辨率水平（continuous-resolutionlevel)的非均匀B样条曲线造型，还可以对非均匀B样条和NURBS曲线进行精确的分解和重构，这对于B样条曲线曲面的多分辨率造型与显示具有重大应用价值。

B-spline wavelets have been widely used in multi-resolution modeling for curves and surfaces, but there are some defects in such modeling using semi-orthogonal B-spline wavelets. First, some existing algorithms for multi-resolution curves use uniform B-spline curves to approximate non-uniform B-spline(NUBS) curves. This will result in an error between the new curve and the original one. Second, the constraints in the existing algorithms specify the shape at a continuous-resolution level by interpolating those at integer-resolution levels. If the control point number of a B-spline curve does not match that of a curve at an integer-resolution, that is, 2 i 3

Keywords

Wavelet  B-spline curve  Multi-resolution modeling