带法向约束的隐式B样条曲线重构PIA方法

Implicit Curve Reconstruction with Normal Constraint Using Progressive and Iterative Approximation

为使隐式曲线能够更好地拟合散乱数据点及其几何特征,提出一种带法向约束的隐式曲线重构渐进迭代(progressive and iterative approximation,PIA)方法.首先,基于隐式B样条函数提出有效的曲线拟合模型;其次,通过加入偏移数据点来消除额外零水平集,同时加入法向项来控制曲线的法向误差;最后,经多次优化迭代得到高精度的拟合曲线.在配置为2.6 GHz英特尔处理器,内存为16 GB的电脑上采用MATLAB实现编程.经多条不同形态封闭曲线拟合的实验结果表明,与隐式PIA(implicit PIA,I-PIA)方法和T样条曲线重构方法相比,从数据点精度和法向误差以及收敛速度3个评价指标进行评估,该方法能够在保证数据点精度的前提下,有效地降低法向误差,并具有更快的收敛速度.此外,实例结果也表明该方法具备鲁棒性.

In order to make the implicit curve fit the scattered data points and their geometric characteristics better,an implicit curve reconstruction with normal constraints using PIA method is proposed.Firstly,an effective curve fitting model is proposed based on the implicit B-spline function.Secondly,eliminate the extra zero level set by adding offset data points,and add a normal term to control the normal error of the curve.Finally,obtain a high-precision fitting curve after multiple optimization iterations.All the experiments were performed in MATLAB on a PC with a 2.6 GHz processor and 16 GB of RAM.Compared with the I-PIA method and T-spline method,the experimental results of multiple closed curve fittings with different shapes demonstrate that,in respect of the data point accuracy,normal error and convergence speed,this method can effectively reduce the normal error while ensuring the accuracy of data points and has faster convergence speed.In addition,the test results also show that this method is robust.