Original scientific paper
Least squares fitting of spheres and ellipsoids using not orthogonal distances
H. Späth
Abstract
Berman [1] examined the problem of estimating the parameters of a
circle when angular differences between successively measured data points were also measured. Applications were reported. Späth [4] generalized that problem by considering an ellipse. Now we will consider measured data points (x_k,y_k,z_k) in space and also associated measured angles
(u_k,v_k) k=1, ..., n>8, for the canonical parametric representation
of a sphere or an ellipsoid. The center and the radius or the three half
axes, respectively, and two other parameters will be fitted such that some suitable sum of squared not orthogonal distances between the two measurements is minimized. Numerical examples are given. Generalizations are discussed. Another numerical method was proposed by Watson [5].
Keywords
least squares; not orthogonal distances; ellipsoid; sphere
Hrčak ID:
839
URI
Publication date:
20.6.2001.
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