Fitting Data with Quadric Surfaces Based on Orthogonal Distance Regression

Xiangqian Jiang, Paul J. Scott, Xiangchao Zhang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Quadric surfaces commonly exist in natural objects and artificial components. It is widely needed to recognise the actual surface shape from a set of measured data points. In this paper a shape recognition approach is presented to determine the surface type and shape parameters from the general implicit quadratic function. A new method is introduced to fit quadric surfaces by implicit functions in the sense of orthogonal distance regression. The fitting accuracy and stability can be greatly improved. This method has no requirement on the surface type or initial position of the data. Finally some numerical examples are given to compare the proposed algorithm with the linear least squares method and the specific geometric modelling and to demonstrate its superiority on accuracy, stability and wide applicability.

Original languageEnglish
Title of host publicationENBIS - IMEKO TC21 Workshop on Measurement Systems and Process Improvement 2010
Pages711-724
Number of pages14
Publication statusPublished - 1 Dec 2010

Cite this

Jiang, X., Scott, P. J., & Zhang, X. (2010). Fitting Data with Quadric Surfaces Based on Orthogonal Distance Regression. In ENBIS - IMEKO TC21 Workshop on Measurement Systems and Process Improvement 2010 (pp. 711-724)
Jiang, Xiangqian ; Scott, Paul J. ; Zhang, Xiangchao. / Fitting Data with Quadric Surfaces Based on Orthogonal Distance Regression. ENBIS - IMEKO TC21 Workshop on Measurement Systems and Process Improvement 2010. 2010. pp. 711-724
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Jiang, X, Scott, PJ & Zhang, X 2010, Fitting Data with Quadric Surfaces Based on Orthogonal Distance Regression. in ENBIS - IMEKO TC21 Workshop on Measurement Systems and Process Improvement 2010. pp. 711-724.

Fitting Data with Quadric Surfaces Based on Orthogonal Distance Regression. / Jiang, Xiangqian; Scott, Paul J.; Zhang, Xiangchao.

ENBIS - IMEKO TC21 Workshop on Measurement Systems and Process Improvement 2010. 2010. p. 711-724.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - Quadric surfaces commonly exist in natural objects and artificial components. It is widely needed to recognise the actual surface shape from a set of measured data points. In this paper a shape recognition approach is presented to determine the surface type and shape parameters from the general implicit quadratic function. A new method is introduced to fit quadric surfaces by implicit functions in the sense of orthogonal distance regression. The fitting accuracy and stability can be greatly improved. This method has no requirement on the surface type or initial position of the data. Finally some numerical examples are given to compare the proposed algorithm with the linear least squares method and the specific geometric modelling and to demonstrate its superiority on accuracy, stability and wide applicability.

AB - Quadric surfaces commonly exist in natural objects and artificial components. It is widely needed to recognise the actual surface shape from a set of measured data points. In this paper a shape recognition approach is presented to determine the surface type and shape parameters from the general implicit quadratic function. A new method is introduced to fit quadric surfaces by implicit functions in the sense of orthogonal distance regression. The fitting accuracy and stability can be greatly improved. This method has no requirement on the surface type or initial position of the data. Finally some numerical examples are given to compare the proposed algorithm with the linear least squares method and the specific geometric modelling and to demonstrate its superiority on accuracy, stability and wide applicability.

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Jiang X, Scott PJ, Zhang X. Fitting Data with Quadric Surfaces Based on Orthogonal Distance Regression. In ENBIS - IMEKO TC21 Workshop on Measurement Systems and Process Improvement 2010. 2010. p. 711-724