C10(3): The Ten Parameter Conformal Group as a Datum Transformation in Three-Dimensional Euclidean Space - Map Projections: Cartographic Information Systems - page 661

E 3 , 3D-Dodoc coordinates Y T Table 24.2 Forty-five Cartesian coordinates of 15 points in := [ Y 1 ,Y 2 ,Y 3 ]in

ED50 datum ( G. Heindl 1986 , p. 27)

No. Station name Y 1 (m) Y 2 (m) Y 3 (m)

1 Kampen 3,632,686.990 532,593.010 5,198,012.640

2 Panker 3,664,733.760 682,227.900 5,158,266.250

3 Norderney 3,753,308.960 476,104.940 5,117,693.680

4 Hohenbunstorf 3,778,209.390 698,622.340 5,074,060.810

5 Damme 3,846,544.210 555,341.820 5,040,584.750

6 Koterberg 3,895,805.000 639,625.330 4,993,304.590

7 Xanten 3,940,527.590 447,142.550 4,978,687.730

8 Kloppenheim 4,041,880.600 620,639.170 4,878,634.660

9 Coburg 4,010,557.230 779,018.460 4,882,109.740

10 Furth 4,125,946.040 526,022.640 4,819,873.340

11 Wettzell 4,075,581.160 931,816.740 4,801,566.920

12 Oberkochen 4,145,299.150 737,359.630 4,775,962.220

13 Feldberg 4,245,428.710 596,955.340 4,708,601.670

14 HohenpeiBenberg 4,213,798.740 819,772.580 4,702,852.110

15 Pfander 4,254,280.390 733,304.990 4,680,867.550

Table 24.3 Residual from a Least Squares fit (LESS)

No. ry 1 (m) ry 2 (m) ry 3 (m)

1 − 0.0544794 +0.0595810 − 0.1096904

2 +0.2130919 − 0.1376099 − 0.2249260

3 − 0.3047065 − 0.4146594 +0.3687087

4 − 0.1872968 +0.1997817 − 0.2769617

5 +0.2774115 +0.1048472 − 0.0096014

6 − 0.2840765 − 0.1386945 +0.0536313

7 +0.6138416 +0.1560176 +0.5031966

8 − 0.3269076 +0.3560758 +0.0884104

9 +0.2442226 − 1.1811614 − 0.0849201

10 − 0.4213069 +0.0674973 − 0.0091904

11 +0.6067057 +0.1580762 − 0.3751288

12 − 0.4084629 +0.3434649 +0.0917456

13 − 0.4585229 − 0.1509711 − 0.3150742

14 +0.2921690 +0.6282125 +0.5677063

15 +0.1983173 − 0.0507579 − 0.2679058

The reader might get the impression that the parameters 7, 8, 9 (“special conformal transfor-
mation”) are not significant because of their vanishing size. Actually the effect arises from the
large extension of the origin and the target system. Its width of about 800km is large. Finally we
have computed the same data with reduced width of submeter as it occurs when using industrial
coordinate measurements. In order to generate a sub-meter extension all coordinates of origin
and target system have been divided by 10 7 . This reduces the original distance between point