Curve Reconstruction Algorithm Based on Discrete Data Points and Normal Vectors
Received:June 17, 2019  Revised:October 26, 2019
Key Word: curve reconstruction   curve fitting   normal vector   B-spline   dominant point  
Fund ProjectL:Supported by the National Natural Science Foundation of China (Nos.11871137; 11572081) and the Program for Liaoning Innovation Talents in University (No.LCR2018001).
Author NameAffiliation
Mingyao GUO Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China 
Chongjun LI Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China 
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      This paper presents a curve reconstruction algorithm based on discrete data points and normal vectors using B-splines. The proposed algorithm has been improved in three steps: parameterization of the discrete data points with tangent vectors, the B-spline knot vector determination by the selected dominant points based on normal vectors, and the determination of the weight to balancing the two errors of the data points and normal vectors in fitting model. Therefore, we transform the B-spline fitting problem into three sub-problems, and can obtain the B-spline curve adaptively. Compared with the usual fitting method which is based on dominant points selected only by data points, the B-spline curves reconstructed by our approach can retain better geometric shape of the original curves when the given data set contains high strength noises.
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