Implicit Curve Reconstruction with Normal Constraint Using Progressive and Iterative Approximation

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.