基于等式约束最小二乘的B样条曲线拟合

 给出一种B样条曲线拟合有序数据的方法。以曲率为代价对有序数据简化。将简化后的数据插值曲线作为硬约束条件，以原始数据逼近曲线作为软约束条件，建立等式约束的最小二乘方程。利用QR分解技术求解方程确定B样条曲线的控制点。采用平方距离最小化方法计算原始数据到生成的B样条曲线的距离，如果不满足误差要求将误差最大数据加入硬约束条件，对局部受影响的部分重新生成曲线。该方法在满足拟合精度的前提下，具有较快的收敛速度，生成的B样条曲线具有较少的控制点。该方法也可用于解决带约束的曲线拟合问题。

B-spline Curve Fitting Using Equality-constrained Least Squares

The paper gives a method of B-spline curve fitting a series of ordered data. The ordered data are simplified with curvature as cost. The simplified data interpolate the curve, which is treated as hard constraint. The original data approximate the curve, which is treated as soft constraint. Then we build equality constrained least squares equation. The positions of control points are calculated by solving the equation with QR decomposition. By calculating the distance between the ordered data and B-spline curve, the point of maximum error is inserted the simplified data if the error is beyond a pre specified error tolerance. The method gives satisfying results regarding to approximation error, convergence speed and the number of control points. The method can also solve constrained curve fitting.