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.