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Best-Fit of Implicit Surfaces and Plane Curves

: Ahn, S.J.; Rauh, W.; Warnecke, H.-J.

Mathematical methods for curves and surfaces
Nashville: Vanderbilt University Press, 2001 (Innovations in Applied Mathematics)
ISBN: 0-8265-1378-6
International Conference on Mathematical Methods for Curves and Surfaces <5, 2000, Oslo>
Conference Paper
Fraunhofer IPA ()
mathematical method; surface; curve; Oberfläche; Mathematisches Verfahren

Dimensional model fitting to a set of given points is a relevant subject in various disciplines of science and engineering. In this paper, we present a universal, and very efficient, best-fit algorithm for implicit surfaces and plane curves, by which the square sum of the orthogonal error distances of the given points to the model feature will be minimized. The estimation parameters are grouped in form, position, and rotation parameters, and are simultaneously estimated. 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 mathematical frame of the proposed algorithm is applicable to any kind of implicit surface and plane curve.