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Non-linear least squares fitting of Bézier surfaces to unstructured point clouds

Non-linear least squares fitting of Bézier surfaces to unstructured point clouds
Non-linear least squares fitting of Bézier surfaces to unstructured point clouds
Algorithms for linear and non-linear least squares fitting of Bézier surfaces to unstructured point clouds are derived from first principles. The presented derivation includes the analytical form of the partial derivatives that are required for minimising the objective functions, these have been computed numerically in previous work concerning Bézier curve fitting, not surface fitting. Results of fitting fourth degree Bézier surfaces to complex simulated and measured surfaces are presented, a quantitative comparison is made between fitting Bézier surfaces and fitting polynomial surfaces. The developed fitting algorithm is used to remove the geometric form of a complex engineered surface such that the surface roughness can be evaluated.
Bézier surfaces, Least squares fitting, surface metrology
2473-6988
3142-3159
Lifton, Joseph J.
e4b170b4-165c-4ae0-9e7d-9d53ab54247f
Liu, Tong
17f1a70b-449d-4078-af64-957a5b374698
McBride, John
d9429c29-9361-4747-9ba3-376297cb8770
Lifton, Joseph J.
e4b170b4-165c-4ae0-9e7d-9d53ab54247f
Liu, Tong
17f1a70b-449d-4078-af64-957a5b374698
McBride, John
d9429c29-9361-4747-9ba3-376297cb8770

Lifton, Joseph J., Liu, Tong and McBride, John (2021) Non-linear least squares fitting of Bézier surfaces to unstructured point clouds. AIMS Mathematics, 6 (4), 3142-3159. (doi:10.3934/math.2021190).

Record type: Article

Abstract

Algorithms for linear and non-linear least squares fitting of Bézier surfaces to unstructured point clouds are derived from first principles. The presented derivation includes the analytical form of the partial derivatives that are required for minimising the objective functions, these have been computed numerically in previous work concerning Bézier curve fitting, not surface fitting. Results of fitting fourth degree Bézier surfaces to complex simulated and measured surfaces are presented, a quantitative comparison is made between fitting Bézier surfaces and fitting polynomial surfaces. The developed fitting algorithm is used to remove the geometric form of a complex engineered surface such that the surface roughness can be evaluated.

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Accepted/In Press date: 29 December 2020
e-pub ahead of print date: 14 January 2021
Published date: 2021
Keywords: Bézier surfaces, Least squares fitting, surface metrology

Identifiers

Local EPrints ID: 446994
URI: http://eprints.soton.ac.uk/id/eprint/446994
ISSN: 2473-6988
PURE UUID: 7c2c82fd-097a-4cf3-9e36-596be95c8da4

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Date deposited: 01 Mar 2021 17:33
Last modified: 01 Mar 2021 17:33

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Contributors

Author: Joseph J. Lifton
Author: Tong Liu
Author: John McBride

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