B样条曲线小波分解的快速算法

在多分辨率曲线和曲面造型中，基数Ｂ样条小波已经得到广泛应用。为了进行小波分解和重构，通常要解一个线性方程组或者求矩阵的逆。如果曲线比较复杂，控制点较多（例如：数千个以上），则矩阵的阶数就会很大，所需的内存将难以容忍；小波分解与重构的速度也会受到很大影响。该文根据Ｂ样条小波的综合滤波器的特点，给出了３种Ｂ样条小波的快速分解和重构算法，并对它们的优缺点进行了比较。结果表明，带宽解法效率最高

Algorithms for quick curve decomposition using B-spline wavelets

Cardinal B spline wavelets have been widely used in multiresolution modeling for curves and surfaces. The size of coefficient matrix for the orthogonal decomposition is usually too large to solve and to allocate enough memory in a computer if the B spline curve has a huge number of control vertices. Three algorithms for the quick decomposition of such a B spline curve were introduced using B spline wavelets in the paper. It has been shown that the algorithm with a band matrix is the best one in both efficiently computing and saving memory among the three algorithms.