Geometric Fitting of Parametric Curves and Surfaces

Sung Joon Ahn
Volume: 4, No: 4, Page: 153 ~ 158, Year: 2008
10.3745/JIPS.2008.4.4.153
Keywords: Parametric Curve, Parametric Surface, Space Curve, Curve Fitting, Surface Fitting, Geometric Fitting, Geometric Distance, Least-Squares Approximation, Minimization, Parametric Model Recovery, Object Reconstruction
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Abstract
This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting. As their general implementation we describe a new algorithm for geometric fitting of parametric curves and surfaces. The curve/surface parameters are estimated in terms of form, position, and rotation parameters. We test and evaluate the performances of the algorithms with fitting examples.

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Cite this article
IEEE Style
Sung Joon Ahn, "Geometric Fitting of Parametric Curves and Surfaces," Journal of Information Processing Systems, vol. 4, no. 4, pp. 153~158, 2008. DOI: 10.3745/JIPS.2008.4.4.153.

ACM Style
Sung Joon Ahn, "Geometric Fitting of Parametric Curves and Surfaces," Journal of Information Processing Systems, 4, 4, (2008), 153~158. DOI: 10.3745/JIPS.2008.4.4.153.