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Open AccessArticle

Surface Fitting for Quasi Scattered Data from Coordinate Measuring Systems

by Qing Mao 1, Shugui Liu 1,*, Sen Wang 1 and Xinhui Ma 2
1
State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China
2
School of Engineering and Computer Science, University of Hull, Hull HU6 7RX, UK
*
Author to whom correspondence should be addressed.
Sensors 2018, 18(1), 214; https://doi.org/10.3390/s18010214
Received: 21 October 2017 / Revised: 10 January 2018 / Accepted: 10 January 2018 / Published: 13 January 2018
(This article belongs to the Section Physical Sensors)
Non-uniform rational B-spline (NURBS) surface fitting from data points is wildly used in the fields of computer aided design (CAD), medical imaging, cultural relic representation and object-shape detection. Usually, the measured data acquired from coordinate measuring systems is neither gridded nor completely scattered. The distribution of this kind of data is scattered in physical space, but the data points are stored in a way consistent with the order of measurement, so it is named quasi scattered data in this paper. Therefore they can be organized into rows easily but the number of points in each row is random. In order to overcome the difficulty of surface fitting from this kind of data, a new method based on resampling is proposed. It consists of three major steps: (1) NURBS curve fitting for each row, (2) resampling on the fitted curve and (3) surface fitting from the resampled data. Iterative projection optimization scheme is applied in the first and third step to yield advisable parameterization and reduce the time cost of projection. A resampling approach based on parameters, local peaks and contour curvature is proposed to overcome the problems of nodes redundancy and high time consumption in the fitting of this kind of scattered data. Numerical experiments are conducted with both simulation and practical data, and the results show that the proposed method is fast, effective and robust. What’s more, by analyzing the fitting results acquired form data with different degrees of scatterness it can be demonstrated that the error introduced by resampling is negligible and therefore it is feasible. View Full-Text
Keywords: scattered data; NURBS fitting; resampling; iterative projection optimization; hierarchical fitting scattered data; NURBS fitting; resampling; iterative projection optimization; hierarchical fitting
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Mao, Q.; Liu, S.; Wang, S.; Ma, X. Surface Fitting for Quasi Scattered Data from Coordinate Measuring Systems. Sensors 2018, 18, 214.

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