| Abstrakt: |
Given the direction cosines ai' = (a1i, a2i, a3i)corresponding to a set of pspherically projected fabric poles, an initial estimate x' = (x1, x2, x3, x4)for the angular radius x4,and direction cosines of the center of the least-squares small circle which minimizes the sum of the squares of the angular residuals $$r = \sum\limits_p {\left[ {x_4 - \cos ^{ - 1} \left( {a_1^i x_1 + a_2^i x_2 + a_3^i x_3 } \right)} \right]} ^2 $$ can be iteratively improved by taking xj+1 = xj + ?xwhere xjis the value of xat the jth iteration and $$\Delta x = - H_j^{ - 1} \left[ {q_j + x_j \left( {x'_j H_j^{ - 1} x_j } \right)\left( {q_j - x'_j H_j^{ - 1} q_j } \right)} \right],$$ whereAs an initial approximation for xwe have found it convenient to ignore the fact that the data are constrained to lie on the surface of the reference sphere and to use the parameters of a least-squares plane through the given poles. |
