Next Article in Journal
Next Generation Wireless Technologies for Internet of Things
Previous Article in Journal
AuNPs Hybrid Black ZnO Nanorods Made by a Sol-Gel Method for Highly Sensitive Humidity Sensing
Article Menu
Issue 1 (January) cover image

Export Article

Open AccessArticle
Sensors 2018, 18(1), 214;

Surface Fitting for Quasi Scattered Data from Coordinate Measuring Systems

State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China
School of Engineering and Computer Science, University of Hull, Hull HU6 7RX, UK
Author to whom correspondence should be addressed.
Received: 21 October 2017 / Revised: 10 January 2018 / Accepted: 10 January 2018 / Published: 13 January 2018
(This article belongs to the Section Physical Sensors)
Full-Text   |   PDF [7913 KB, uploaded 15 January 2018]   |  


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

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Mao, Q.; Liu, S.; Wang, S.; Ma, X. Surface Fitting for Quasi Scattered Data from Coordinate Measuring Systems. Sensors 2018, 18, 214.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Sensors EISSN 1424-8220 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top