基于特征点自动识别的B样条曲线逼近技术

提出一种实用的用三次B样条曲线逼近稠密且带噪声的二维断面数据点列的算法。剔除数据点列中的重合点并对其进行均匀弧长重采样处理后，利用相邻点拟合圆弧的方法来近似计算各数据点的离散曲率值，并根据相邻点之间的离散曲率符号变化情况及相近点之间的曲率值和曲率差分关系自动识别出断面数据中绝大多数的特征点(拐点、折痕点、曲率极值点)。构造插值于特征点的B样条曲线，并在逼近误差最大处插入新的插值点。重复这一过程，直到逼近误差小于预先给定值，从而得到最终插值点列并构造相应的B样条曲线。试验结果表明，所构造的曲线节点数目及其分布合理，能够很好地反映原始断面数据点列中的细小特征部分。该算法具有速度快、逼近精度高等特点，可广泛应用于二维断面数据的曲线重建。

B-spline Curve Approximation Based on Feature Points Automatic Recognition

A practical algorithm for B-spline curve approximation to a dense and noisy sectional data point set is proposed. The redundant points are eliminated and the point set is resampled by using the equal-arc-length method. The discrete curvature and the first-order difference of each point are calculated. Almost all the feature points, including crease points, inflection points and curvature extrema value points, are identified automatically. A B-spline curve is constructed to interpolate all the feature points and one new interpolation point is inserted at the place where the maximum fitting error occurs. This process is repeated until the maximum fitting error is less than the given error bound. A few examples are presented to show that the curve can reconstruct the small features of the sectional profile well, and both the number and the location of the knots are reasonable. The algorithm is feasible and efficient, and it can be widely used to deal with sectional profile fitting problems.