66 D.-M. Chen and W.D. Zhu Fig. 6.8 (a) A 3D structure scanned by three SLDVs placed at three different locations, and (b) frames made up by two different sets of reference points Table 6.1 Rotation angles and initial distances corresponding to different reference points Coordinate (mm) Location1 Location2 Location3 x y z ˛ (ı) ˇ(ı) r 0 (mm) ˛ ( ı) ˇ(ı) r 0 (mm) ˛ ( ı) ˇ(ı) r 0 (mm) 150 150 0 1.121 1.381 1600 6.669 3.107 1370 2.844 5.132 1600 150 150 0 4.168 1.443 1590 1.463 3.012 1520 7.786 5.059 1470 150 150 0 4.215 3.712 1620 1.381 2.403 1540 7.551 0.502 1500 150 150 0 1.072 3.755 1630 6.538 2.806 1410 2.765 0.019 1630 5 35 80 1.409 0.610 1520 3.257 0.892 1370 4.355 3.015 1460 5 35 150 1.578 1.967 1450 2.349 0.546 1320 3.825 1.587 1410 5 35 80 1.590 0.610 1520 3.082 0.902 1370 4.523 3.000 1460 5 35 150 1.384 1.967 1450 2.530 0.556 1320 3.825 1.587 1410 Once the coordinates of the scan points in the SMCS are obtained by Eq. (6.27), they can further be transformed to rotation angles of two mirrors and distances r by Eq. (6.28). Comparison of measured and calculated rotation angles is shown in Tables 6.4, 6.5 and 6.6. At location 1 the maximum relative errors of rotation angles are 2.5 % in Set 1 and 3.5 % in Set 2. For most scan points, the relative errors are less than 1 %. The rotation matrix and translation vector provide good estimates of the orientation and position of the SLDV at location 1. The same conclusion can be obtained from Tables 6.5 and 6.6, where the relative errors for most scan points are less than 0.5 %. In Table 6.6 there are two large relative errors of over 30 % in both sets because the rotation angles of Y mirror are very small and close to zero. It is seen from Tables 6.4, 6.5 and 6.6 that relative errors between measured and calculated rotation angles are less than 2 % for most scan points at the three locations. One can find that the distance r in Eq. (6.26) also plays an important role in
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