带尖锐特征的细分曲线参数化及曲线拟合

Parameterization of Subdivision Curve with Sharp Feature and Their Applications

快速精确地估计曲线曲面参数具有广泛的应用。在前人研究的基础上,通过对细分过程及三次B样条细分矩阵的特征结构进行分析,将细分模式转换到其特征空间,给出了带尖锐特征的B样条细分曲线的参数化形式。并用于处理带尖锐特征的光滑曲线拟合问题。以曲率极大点作为初始拟合点。利用推导的参数化公式构造曲线的尖锐部分并方便误差估计。拟合点为曲线段端点,误差估计时不仅优化计算速度,而且在曲线分支距离过近或自交情况下避免错误匹配。

The rapid and precise evaluation of curve ＆ surface parameterizations has wide application. In the paper we present a parameterization technique for cubic B-spline subdivision curves with sharp feature. The eigenstructure of the subdivision matrix is analyzed. The subdivision matrix and control points are projected into the eigenspace of matrix. The technique can deal with curve fitting with sharp features directly. The vertices with maximal curvature are as the initial fitting vertices. With the parameterization technique given in this paper, the curve segment with sharp feature is constructed; and the distance between the original data and the curve is also calculated. The fitting vertices are located at the extremities of curve segment; during error estimation it can improve computation speed and avoid mismatching when the target curve is self intersection or when two branches are too close.