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Geometric Fitting of Parametric Curves and Surfaces
Sung Joon Ahn
Page: 153~158, Vol. 4, No.4, 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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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.