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Best-Fit of Parametric Curves and Surfaces

: Ahn, S.J.; Westkämper, E.; Rauh, W.

Gruen, A. ; TU Wien, Institut für Geodäsie und Geophysik; TH Zürich -ETH-, Institut für Geodäsie und Photogrammetrie:
Optical 3-D Measurement Techniques V : Applications in manufacturing, quality control, robotics, navigation, mobile mapping, medical imaging, animation. Papers presented at the Conference organized at Vienna, Oktober 1-4, 2001
Wien, 2001
ISBN: 3-9501492-0-1
Conference "Optical 3-D Measurement Techniques" <5, 2001, Wien>
Fraunhofer IPA ()
parametric curve; parametric surface; curve fitting; Surface Fitting; Orthogonal Distance Fitting; geometric distance; Object reconstruction; Gauss-Newton-Method

Fitting of parametric curve or surface to a set of given data points is a relevant subject in various fields of science and engineering. In this paper, we review the current orthogonal distance fitting algorithms for parametric curves and surfaces in a well-organized fashion, and present a new algorithm, which minimizes the square sum of the orthogonal error distances between the model feature and the given data points. By the algorithms, the model feature parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters. The form parameters determine the shape of the model feature, and the position/rotation parameters describe the rigid body motion of the model feature. The new algorithm is applicable to any kind of parametric surface and plane curve. We give fitting examples for circle, cylinder and helix in space.