CoordTrans - Report
free Similarity Transformation Software

General

CoordTrans:v2.2.20131124
Transformation type: 3D-Transformation
Date of calculation:03.01.2014 - 10:58:01
Adjustment type: Least square adjustment (Gauß-Helmert modell)
Flaw dislocation: No scheme
Probability value α [%]:0.1
Test power β [%]:80.0
Sum of squares of errors Ω:0.882721604192
Degree of freedom f = n-u+d = spur(R):20
σ2a-priori : σ2a-posteriori:1 : 0.044
Global test TGlobalFf,∞,1-α'|H0:H0 not rejected, because 0.044 ≤ 1.595 (α'G = 4.4%)
Critical value for point test Kprio (F3,∞,1-α):5.422 (αprio = 0.1%)
Critical value for point test Kpost (F3,f-3,1-α):5.121 (αpost = 1.0%)

Form parameters – 3D-Transformation

Name Value σPar Significant
Tx -0.145334747 0.149147850
Ty -0.052013679 0.211664391
Tz 0.335127451 0.212112048
q0 0.002398663 0.033209781
q1 0.087904952 0.032362183
q2 -0.668809428 0.020681907
q3 -0.738214681 0.017345392
a11 -0.032153004 0.000975601
a12 0.008596213 0.002484141
a13 -0.032085006 0.000977790
a22 -0.030982588 0.001320319
a23 -0.001820760 0.001556582
a33 -0.001026082 0.001578029
Mx 0.032153004 0.000975601
My 0.032153004 0.000975601
Mz 0.032153004 0.000975601
Rx 1.479931956 0.052344263
Ry 0.133389156 0.067952681
Rz 3.256912077 0.065224357
Sx 2.083979896 0.755301445
Sy 1.505749424 0.048437535
Sz 0.270645338 0.082065005

Variance component analysis

System rG ΩG 1 : σ2G KG (Ff,∞,1-αG) TG ≤ KG
Source 0.0224 0.0017 0.0753 604.8209
Target 19.9776 0.8810 0.0441 1.5960

Source System

Point-ID X0 Y0 Z0 X Y Z σX σY σZ rX rY rZ εX εY εZ X Y Z Ω Tprio Tpost T ≤ K
1 4.364689 11.568557 5.784753 4.360854 11.569091 5.780889 0.210032 0.210083 0.210032 0.000511 0.000024 0.000516 0.003835 -0.000534 0.003864 1298.592747 70.536506 -1288.305214 0.000030 0.011758 0.235878
2 -163.912003 -35.090801 224.192001 -163.898762 -35.096240 224.205063 0.209999 0.210039 0.209999 0.000829 0.000448 0.000827 -0.013241 0.005439 -0.013062 102.710320 0.318284 -86.877639 0.000376 0.074482 1.920569
3 -121.995003 -33.177700 231.994995 -121.994603 -33.177747 231.995514 0.209990 0.209997 0.209991 0.000908 0.000847 0.000908 -0.000400 0.000047 -0.000519 -138.468150 -7.979331 137.067428 0.000000 0.005379 0.105513
4 -121.580002 -65.910202 228.684006 -121.581588 -65.908719 228.682513 0.209990 0.209996 0.209990 0.000912 0.000852 0.000911 0.001586 -0.001483 0.001493 -34.183575 -0.569213 32.377204 0.000007 0.001679 0.032523
5 -102.737000 -8.429520 248.977005 -102.743536 -8.425525 248.970538 0.209999 0.209997 0.210000 0.000825 0.000849 0.000818 0.006536 -0.003995 0.006467 94.675940 8.256090 -100.426209 0.000101 0.021225 0.440533
6 -78.809898 -6.169780 248.264999 -78.811697 -6.166041 248.263440 0.210004 0.210003 0.210006 0.000775 0.000793 0.000763 0.001799 -0.003739 0.001559 -69.775257 0.500797 68.314561 0.000020 0.006965 0.137388
7 -78.642899 -65.747398 247.242004 -78.651317 -65.751969 247.233046 0.209993 0.209996 0.209993 0.000883 0.000853 0.000883 0.008418 0.004571 0.008958 171.768699 2.016333 -181.141620 0.000172 0.055849 1.327559
8 -53.557899 -65.885002 248.800003 -53.540135 -65.890522 248.817757 0.210000 0.210015 0.210000 0.000818 0.000679 0.000816 -0.017764 0.005520 -0.017754 -89.204913 -7.304589 109.187378 0.000661 0.131406 4.572920
9 -80.709602 -114.245003 229.559006 -80.721576 -114.240519 229.547177 0.210006 0.209999 0.210007 0.000757 0.000828 0.000755 0.011974 -0.004484 0.011829 -74.573201 -2.194593 58.337439 0.000303 0.064339 1.585848
10 -76.934097 -145.630005 207.016006 -76.931354 -145.628662 207.018841 0.210028 0.210009 0.210030 0.000548 0.000729 0.000535 -0.002743 -0.001343 -0.002835 60.330231 7.516718 -52.465794 0.000017 0.008950 0.177764

Target System

Point-ID X0 Y0 Z0 X Y Z σX σY σZ rX rY rZ εX εY εZ X Y Z Ω Tprio Tpost T ≤ K
1 0.000000 0.000000 0.000000 0.120277 0.008416 -0.001260 0.149209 0.209127 0.208823 0.495572 0.009104 0.011988 -0.120277 -0.008416 0.001260 0.379149 -1.265100 -0.253438 0.014539 0.011758 0.235878
2 2.392252 0.000000 1.383163 1.998868 -0.081088 1.267044 0.096671 0.161551 0.161340 0.788263 0.408678 0.410222 0.393384 0.081088 0.116119 -0.475547 -0.134402 -0.219378 0.174810 0.074482 1.920569
3 3.592250 0.000000 1.383163 3.564688 0.110256 1.393688 0.073916 0.092099 0.090202 0.876211 0.807816 0.815652 0.027562 -0.110256 -0.010525 -0.032986 0.136847 0.013165 0.013027 0.005379 0.105513
4 3.592250 0.000000 2.383163 3.633331 0.028927 2.425583 0.073492 0.091582 0.089842 0.877628 0.809969 0.817119 -0.041081 -0.028927 -0.042420 0.045402 0.035146 0.050813 0.004324 0.001679 0.032523
5 4.392252 0.349643 0.633729 4.594129 0.292304 0.724357 0.097675 0.110260 0.092879 0.783841 0.724551 0.804547 -0.201877 0.057339 -0.090628 0.250565 -0.079231 0.094313 0.052256 0.021225 0.440533
6 5.280683 0.349643 0.633729 5.317990 0.388364 0.748607 0.110237 0.128085 0.107741 0.724666 0.628293 0.736993 -0.037307 -0.038721 -0.114878 0.029774 0.061218 0.151585 0.016088 0.006965 0.137388
7 5.280683 0.349643 2.833729 5.583919 0.253333 2.635594 0.080478 0.088114 0.088261 0.853257 0.824089 0.823499 -0.303236 0.096310 0.198135 0.356852 -0.118173 -0.242036 0.140485 0.055849 1.327559
8 6.980683 0.349643 2.833729 6.430119 0.355679 2.745623 0.097591 0.125528 0.125026 0.784213 0.642985 0.645836 0.550564 -0.006036 0.088106 -0.698833 0.028952 -0.105435 0.310920 0.131406 4.572920
9 4.836467 0.000000 4.033729 5.192669 0.083237 4.125625 0.109494 0.111244 0.094482 0.728362 0.719609 0.797741 -0.356202 -0.083237 -0.091896 0.486967 0.116481 0.107335 0.142253 0.064339 1.585848
10 4.836467 0.000000 5.033729 4.747998 -0.040855 5.087002 0.147933 0.156662 0.119065 0.504166 0.443927 0.678801 0.088469 0.040855 -0.053273 -0.197356 -0.090844 0.106573 0.012334 0.008950 0.177764

Transformed Points

Point-ID XS YS ZS XT YT ZT σX σY σZ
1 4.364689 11.568557 5.784753 0.120524 0.008441 -0.001219 0.149505 0.209129 0.209034
2 -163.912003 -35.090801 224.192001 1.998005 -0.081167 1.266789 0.096873 0.161586 0.161534
3 -121.995003 -33.177700 231.994995 3.564659 0.110253 1.393683 0.074063 0.092102 0.090293
4 -121.580002 -65.910202 228.684006 3.633436 0.028935 2.425640 0.073635 0.091581 0.089929
5 -102.737000 -8.429520 248.977005 4.594562 0.292340 0.724525 0.097865 0.110264 0.092966
6 -78.809898 -6.169780 248.264999 5.318115 0.388367 0.748736 0.110445 0.128087 0.107837
7 -78.642899 -65.747398 247.242004 5.584449 0.253404 2.635503 0.080648 0.088132 0.088367
8 -53.557899 -65.885002 248.800003 6.428962 0.355568 2.745337 0.097757 0.125484 0.125105
9 -80.709602 -114.245003 229.559006 5.193448 0.083310 4.125841 0.109722 0.111256 0.094588
10 -76.934097 -145.630005 207.016006 4.747827 -0.040878 5.087027 0.148227 0.156670 0.119175

Covariance matrix

# Tx Ty Tz q0 q1 q2 q3 a11 a12 a13 a22 a23 a33 Mx My Mz Rx Ry Rz Sx Sy Sz
Tx +2.2245e-02 -2.2513e-03 -1.1090e-03 -1.8139e-04 -2.6705e-05 -7.2253e-05 +6.1691e-05 +1.0563e-04 -7.8319e-05 +1.0326e-04 +8.7889e-05 +3.0732e-05 +2.6522e-05 +1.0563e-04 -1.0563e-04 -1.0563e-04 +1.8993e-04 -2.9519e-04 +2.4436e-04 -3.8361e-03 +1.0263e-03 -1.6164e-03
Ty -2.2513e-03 +4.4802e-02 -1.1196e-04 +1.2817e-04 +1.1196e-04 +1.7222e-04 -1.4228e-04 +9.6904e-06 -9.1000e-06 +1.4645e-05 +7.5317e-06 +2.1915e-05 -1.9316e-04 +9.6904e-06 -9.6904e-06 -9.6904e-06 -4.3137e-04 +3.6417e-04 -6.5882e-05 +8.5663e-02 -2.3802e-03 -2.1009e-04
Tz -1.1090e-03 -1.1196e-04 +4.4992e-02 -1.0938e-04 +1.1369e-04 +2.7459e-05 -1.1695e-05 +1.2505e-05 +6.9268e-06 +2.4023e-05 +1.4899e-05 -1.9259e-04 -1.7580e-05 +1.2505e-05 -1.2505e-05 -1.2505e-05 -3.4213e-05 +2.3677e-05 +3.1390e-04 -3.7914e-02 -5.5238e-03 +3.3148e-04
q0 -1.8139e-04 +1.2817e-04 -1.0938e-04 +1.1029e-03 +3.1218e-05 +1.9496e-04 -1.6933e-04 -2.9539e-06 -4.9681e-05 -3.7477e-06 -1.6849e-05 +2.9533e-05 -2.7778e-05 -2.9539e-06 +2.9539e-06 +2.9539e-06 -5.3643e-04 +1.5641e-03 -1.6228e-03 +1.8517e-02 +3.8283e-04 -1.6290e-03
q1 -2.6705e-05 +1.1196e-04 +1.1369e-04 +3.1218e-05 +1.0473e-03 +2.9647e-04 -1.4378e-04 +3.4266e-06 +4.4551e-05 +5.8231e-06 +1.5917e-05 -2.5388e-05 -2.9662e-05 +3.4266e-06 -3.4266e-06 -3.4266e-06 -4.5034e-04 +1.6263e-03 +1.3477e-03 +6.4002e-03 -1.1502e-03 +1.4675e-03
q2 -7.2253e-05 +1.7222e-04 +2.7459e-05 +1.9496e-04 +2.9647e-04 +4.2774e-04 -3.5159e-04 +6.7252e-07 +5.7205e-06 +1.0425e-06 +2.2851e-06 -2.2389e-06 -7.5524e-06 +6.7252e-07 -6.7252e-07 -6.7252e-07 -1.0631e-03 +7.6506e-04 +4.4218e-05 +2.6222e-03 -1.7772e-04 +1.9044e-04
q3 +6.1691e-05 -1.4228e-04 -1.1695e-05 -1.6933e-04 -1.4378e-04 -3.5159e-04 +3.0086e-04 -2.1086e-07 -3.9034e-08 -2.6328e-07 -2.2966e-07 -8.9879e-07 +3.2200e-06 -2.1086e-07 +2.1086e-07 +2.1086e-07 +9.0777e-04 -4.9438e-04 +1.1515e-04 -1.5534e-03 +2.5295e-05 -3.0794e-06
a11 +1.0563e-04 +9.6904e-06 +1.2505e-05 -2.9539e-06 +3.4266e-06 +6.7252e-07 -2.1086e-07 +9.5180e-07 +4.2220e-07 +9.4881e-07 +1.1049e-06 +8.9562e-08 -2.3181e-09 +9.5180e-07 -9.5180e-07 -9.5180e-07 -6.1620e-07 +1.1520e-06 +8.9819e-06 +2.2005e-05 +4.6811e-07 +2.1840e-05
a12 -7.8319e-05 -9.1000e-06 +6.9268e-06 -4.9681e-05 +4.4551e-05 +5.7205e-06 -3.9034e-08 +4.2220e-07 +6.1710e-06 +5.5652e-07 +2.1503e-06 -2.3519e-06 +1.4063e-09 +4.2220e-07 -4.2220e-07 -4.2220e-07 +3.7476e-07 -7.0380e-07 +1.3400e-04 -5.5307e-04 -6.4693e-05 +2.0282e-04
a13 +1.0326e-04 +1.4645e-05 +2.4023e-05 -3.7477e-06 +5.8231e-06 +1.0425e-06 -2.6328e-07 +9.4881e-07 +5.5652e-07 +9.5607e-07 +1.1391e-06 -4.7077e-08 -8.0772e-08 +9.4881e-07 -9.4881e-07 -9.4881e-07 -7.9594e-07 +3.6582e-06 +1.3401e-05 +2.2610e-05 -4.4364e-06 +2.6150e-05
a22 +8.7889e-05 +7.5317e-06 +1.4899e-05 -1.6849e-05 +1.5917e-05 +2.2851e-06 -2.2966e-07 +1.1049e-06 +2.1503e-06 +1.1391e-06 +1.7432e-06 -5.5959e-07 -2.0155e-09 +1.1049e-06 -1.1049e-06 -1.1049e-06 -5.3550e-07 +1.0003e-06 +4.6499e-05 -1.3061e-04 -1.7464e-05 +7.8938e-05
a23 +3.0732e-05 +2.1915e-05 -1.9259e-04 +2.9533e-05 -2.5388e-05 -2.2389e-06 -8.9879e-07 +8.9562e-08 -2.3519e-06 -4.7077e-08 -5.5959e-07 +2.4229e-06 -2.0917e-08 +8.9562e-08 -8.9562e-08 -8.9562e-08 -3.0030e-06 +2.2087e-06 -7.8352e-05 +5.7789e-04 +6.5287e-05 -7.5137e-05
a33 +2.6522e-05 -1.9316e-04 -1.7580e-05 -2.7778e-05 -2.9662e-05 -7.5524e-06 +3.2200e-06 -2.3181e-09 +1.4063e-09 -8.0772e-08 -2.0155e-09 -2.0917e-08 +2.4902e-06 -2.3181e-09 +2.3181e-09 +2.3181e-09 +1.0908e-05 -8.2210e-05 +1.4444e-06 -1.0429e-03 +3.7541e-05 +2.5386e-08
Mx +1.0563e-04 +9.6904e-06 +1.2505e-05 -2.9539e-06 +3.4266e-06 +6.7252e-07 -2.1086e-07 +9.5180e-07 +4.2220e-07 +9.4881e-07 +1.1049e-06 +8.9562e-08 -2.3181e-09 +9.5180e-07 -9.5180e-07 -9.5180e-07 -6.1620e-07 +1.1520e-06 +8.9819e-06 +2.2005e-05 +4.6811e-07 +2.1840e-05
My -1.0563e-04 -9.6904e-06 -1.2505e-05 +2.9539e-06 -3.4266e-06 -6.7252e-07 +2.1086e-07 -9.5180e-07 -4.2220e-07 -9.4881e-07 -1.1049e-06 -8.9562e-08 +2.3181e-09 -9.5180e-07 +9.5180e-07 +9.5180e-07 +6.1620e-07 -1.1520e-06 -8.9819e-06 -2.2005e-05 -4.6811e-07 -2.1840e-05
Mz -1.0563e-04 -9.6904e-06 -1.2505e-05 +2.9539e-06 -3.4266e-06 -6.7252e-07 +2.1086e-07 -9.5180e-07 -4.2220e-07 -9.4881e-07 -1.1049e-06 -8.9562e-08 +2.3181e-09 -9.5180e-07 +9.5180e-07 +9.5180e-07 +6.1620e-07 -1.1520e-06 -8.9819e-06 -2.2005e-05 -4.6811e-07 -2.1840e-05
Rx +1.8993e-04 -4.3137e-04 -3.4213e-05 -5.3643e-04 -4.5034e-04 -1.0631e-03 +9.0777e-04 -6.1620e-07 +3.7476e-07 -7.9594e-07 -5.3550e-07 -3.0030e-06 +1.0908e-05 -6.1620e-07 +6.1620e-07 +6.1620e-07 +2.7399e-03 -1.5507e-03 +3.6275e-04 -5.2525e-03 +8.6628e-05 +6.7786e-06
Ry -2.9519e-04 +3.6417e-04 +2.3677e-05 +1.5641e-03 +1.6263e-03 +7.6506e-04 -4.9438e-04 +1.1520e-06 -7.0380e-07 +3.6582e-06 +1.0003e-06 +2.2087e-06 -8.2210e-05 +1.1520e-06 -1.1520e-06 -1.1520e-06 -1.5507e-03 +4.6176e-03 -2.0316e-04 +3.4787e-02 -1.2003e-03 -1.2775e-05
Rz +2.4436e-04 -6.5882e-05 +3.1390e-04 -1.6228e-03 +1.3477e-03 +4.4218e-05 +1.1515e-04 +8.9819e-06 +1.3400e-04 +1.3401e-05 +4.6499e-05 -7.8352e-05 +1.4444e-06 +8.9819e-06 -8.9819e-06 -8.9819e-06 +3.6275e-04 -2.0316e-04 +4.2542e-03 -1.9008e-02 -2.1235e-03 +4.4025e-03
Sx -3.8361e-03 +8.5663e-02 -3.7914e-02 +1.8517e-02 +6.4002e-03 +2.6222e-03 -1.5534e-03 +2.2005e-05 -5.5307e-04 +2.2610e-05 -1.3061e-04 +5.7789e-04 -1.0429e-03 +2.2005e-05 -2.2005e-05 -2.2005e-05 -5.2525e-03 +3.4787e-02 -1.9008e-02 +5.7048e-01 -3.1184e-04 -1.7661e-02
Sy +1.0263e-03 -2.3802e-03 -5.5238e-03 +3.8283e-04 -1.1502e-03 -1.7772e-04 +2.5295e-05 +4.6811e-07 -6.4693e-05 -4.4364e-06 -1.7464e-05 +6.5287e-05 +3.7541e-05 +4.6811e-07 -4.6811e-07 -4.6811e-07 +8.6628e-05 -1.2003e-03 -2.1235e-03 -3.1184e-04 +2.3462e-03 -2.0840e-03
Sz -1.6164e-03 -2.1009e-04 +3.3148e-04 -1.6290e-03 +1.4675e-03 +1.9044e-04 -3.0794e-06 +2.1840e-05 +2.0282e-04 +2.6150e-05 +7.8938e-05 -7.5137e-05 +2.5386e-08 +2.1840e-05 -2.1840e-05 -2.1840e-05 +6.7786e-06 -1.2775e-05 +4.4025e-03 -1.7661e-02 -2.0840e-03 +6.7347e-03

Rotation matrix

-9.8453393153390900e-01 -1.1404186542110843e-01 -1.3299394944755144e-01
-1.2112477823759328e-01 -1.0537639057549741e-01 +9.8702816799024220e-01
-1.2657695586194956e-01 +9.8787158539992110e-01 +8.9933336445213840e-02

Transformation matrix

+3.1655723030480344e-02 -4.9299510989183270e-03 +3.1932882928315750e-02 -1.4533474722907070e-01
+3.8945254289445960e-03 +2.2236189266724960e-03 +3.0653827848046600e-03 -5.2013679486615560e-02
+4.0698293156483320e-03 -3.1694900861004570e-02 +2.1702663031973684e-03 +3.3512745109760256e-01
+0.0000000000000000e+00 +0.0000000000000000e+00 +0.0000000000000000e+00 +1.0000000000000000e+00