曲线曲面小波变换的边界连续性保持

现有的小波分解边界连续性保持方法由于将去除的节点全部插回,摒弃了数据压缩特性.为此在曲线小波分解边界处理方面提出2种基于数据压缩的连续性保持方法:一是插入与Cr连续相关的节点,然后调整相应的控制顶点与高分辨曲线的控制顶点保持一致；二是不插入节点,直接调整与Cr连续相关的控制顶点.在曲面方面,提出了曲面分裂法和T曲面法:通过插入重节点把曲面分裂成边界部分和中心部分并对边界部分插入节点,再调整相应的控制顶点与高分辨曲面的重合；构造了T网格,使其边界部分与高分辨曲面一致,中心部分与低分辨曲面一致.最后把T曲面方法推广到周期曲面小波变换边界处理上.实验结果表明,文中方法既保证了小波分解后模型的边界连续,又保留了数据压缩特性.

Boundaries Continuity Preserving of Curve and Surface in Wavelet Transform

The existing method of boundaries continuity preserving loses the data compression property due to inserting all deleted knots.In this paper,two methods to preserve the curve boundary continuity during wavelet transform are presented.One is inserting knots related with Crcontinuity and then adjusting the corresponding control points to be consistent with high resolution curve;the other is directly adjusting the control points related with Crcontinuity.In terms of surface,the surface splitting method and the T surface method are presented: the surface is divided into the parts of boundary and center,inserting knots in the part of boundary and then adjusting the corresponding control points to be consistent with high resolution surface;T-mesh is constructed,which part of boundary and center is consistent with high resolution and low resolution surface respectively.The T-surface boundary preserving method is extended to the closed B-spline surface wavelet transform.The experimental results demonstrate that the methods in this paper are not only preserving the boundaries continuity in the wavelet transform,but also retaining the data compression property.