均匀B样条曲线曲面的小波表示

摘要

Wavelets-based representation provides a more flexible method for expressing curves and surfaces in different resolution levels. For uniform B-spline curves and surfaces, a unified expression can be adopted after decomposition to describe the wavelets for the interior and boundaries of the domain defined, and hence the multiplication is the only operation be needed to wavelets reconstruction. This results in high efficiency for the computation. The paper describes, from the point of geometry view, the principles and methods of realizing wavelets-based multiresolution representation of uniform cubic B-spline curves and surfaces.%小波基为曲线曲面带来了更为灵活的表达方式。均匀B样条曲线曲面在经过小波分解以后所得到的小波在定义域边界与内部可以采用统一的表达式，在进行小波重构时仅需作乘法运算，计算效率高。本文试图从几何概念出发由浅入深地论述基于小波的均匀三次B样条曲线曲面多分辨表示的原理及其实现。