A Hybrid Parametrization Method for B‐Spline Curve Interpolation via Supervised Learning

B‐spline curve interpolation is a fundamental algorithm in computer‐aided geometric design. Determining suitable parameters based on data points distribution has always been an important issue for high‐quality interpolation curves generation. Various parameterization methods have been proposed. Howe...

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Published in:	Computer graphics forum Vol. 43; no. 7
Main Authors:	Song, Tianyu, Shen, Tong, Ge, Linlin, Feng, Jieqing
Format:	Journal Article
Language:	English
Published:	Oxford Blackwell Publishing Ltd 01.10.2024
Subjects:	Algorithms CCS Concepts Computing methodologies → Parametric curve and surface models Curves Data points Interpolation Machine learning Parameter identification Parameterization Spline functions Statistical methods Supervised learning Supervised learning by classification
ISSN:	0167-7055, 1467-8659
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Abstract	B‐spline curve interpolation is a fundamental algorithm in computer‐aided geometric design. Determining suitable parameters based on data points distribution has always been an important issue for high‐quality interpolation curves generation. Various parameterization methods have been proposed. However, there is no universally satisfactory method that is applicable to data points with diverse distributions. In this work, a hybrid parametrization method is proposed to overcome the problem. For a given set of data points, a classifier via supervised learning identifies an optimal local parameterization method based on the local geometric distribution of four adjacent data points, and the optimal local parameters are computed using the selected optimal local parameterization method for the four adjacent data points. Then a merging method is employed to calculate global parameters which align closely with the local parameters. Experiments demonstrate that the proposed hybrid parameterization method well adapts the different distributions of data points statistically. The proposed method has a flexible and scalable framework, which can includes current and potential new parameterization methods as its components.
AbstractList	B‐spline curve interpolation is a fundamental algorithm in computer‐aided geometric design. Determining suitable parameters based on data points distribution has always been an important issue for high‐quality interpolation curves generation. Various parameterization methods have been proposed. However, there is no universally satisfactory method that is applicable to data points with diverse distributions. In this work, a hybrid parametrization method is proposed to overcome the problem. For a given set of data points, a classifier via supervised learning identifies an optimal local parameterization method based on the local geometric distribution of four adjacent data points, and the optimal local parameters are computed using the selected optimal local parameterization method for the four adjacent data points. Then a merging method is employed to calculate global parameters which align closely with the local parameters. Experiments demonstrate that the proposed hybrid parameterization method well adapts the different distributions of data points statistically. The proposed method has a flexible and scalable framework, which can includes current and potential new parameterization methods as its components.
Author	Feng, Jieqing Shen, Tong Ge, Linlin Song, Tianyu
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Copyright	2024 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd. 2024 The Eurographics Association and John Wiley & Sons Ltd.
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SubjectTerms	Algorithms CCS Concepts Computing methodologies → Parametric curve and surface models Curves Data points Interpolation Machine learning Parameter identification Parameterization Spline functions Statistical methods Supervised learning Supervised learning by classification
Title	A Hybrid Parametrization Method for B‐Spline Curve Interpolation via Supervised Learning
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