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Published in:
2021 | OriginalPaper | Chapter
B-Spline Curve Fitting with Normal Constrains in Computer Aided Geometric Designed
Authors : Zizhi Lin, Yun Ding
Published in: Big Data Analytics for Cyber-Physical System in Smart City
Publisher: Springer Singapore
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Abstract
We present an algorithm for fitting data points with normal constrains in Computer Aided Geometric Designed. Different from previous methods which interpolate the normal vectors accurately, the purpose of our method is to approximate these normal vectors. We make the normal vectors on the fitting curve are close to the normal constrains with their corresponding parameters. According to approximate the normal vectors constrains, we can control the shape of fitting curve. Our purpose is to minimize the square sum of inner products of normal vectors on fitting curve and normal constrain vectors. In interpolation, we need to minimize the square sum of the inner products and interpolate these data points, so we use Lagrange multiplier method to solve the control points. In approximation, the inner product terms is made as the fair terms, we minimize the weighted sum of the distance term and fair term to get the control points of the fitting curve. Finally, an example of this algorithm is demonstrated.