C10(3): The Ten Parameter Conformal Group as a Datum Transformation in Three-Dimensional Euclidean Space - Map Projections: Cartographic Information Systems - page 664

Table 24.9 Estimated parameters for LESS, BLAVE, MINIMAX without centered reduction for reduced data

No. Least squares BLAVE MINIMAX

1 − 0.00001032 − 0.00000879 − 0.00000863

2 − 0.00000364 − 0.00000261 − 0.00003243

3 − 0.00001503 − 0.00002249 − 0.00000845

4 − 0.00001627 − 0.00001812 +0.00003923

5 +0.00000119 +0.00001925 +0.00000677

6 +0.00001392 +0.00001876 − 0.00005707

7 +0.00000382 +0.00002151 − 0.00000280

8 +0.00001443 +0.00001953 − 0.00005548

9 +0.00000335 +0.00000289 +0.00000437

10 +0.00000932 +0.00002388 − 0.00000238

Table 24.10 Estimated parameters for LESS, BLAVE, MINIMAX including centered reduction for reduced
data

No. Least squares BLAVE MINIMAX

1 +0.00000000 +0.00000003 − 0.00000003

2 − 0.00000001 − 0.00000001 +0.00000005

3 − 0.00000001 − 0.00000001 − 0.00000002

4 − 0.00000530 − 0.00000540 − 0.00000341

5 +0.00000008 +0.00000038 +0.00000088

6 +0.00000015 − 0.00000008 − 0.00000109

7 +0.00000382 +0.00002151 +0.00008381

8 +0.00001443 +0.00001953 − 0.00000325

9 +0.00000335 +0.00000289 +0.00000987

10 +0.00000111 +0.00000139 +0.00000125

Appendix 1

In order to transmit more familiarity with the special conformal transformation ( 1.4 ) we introduce
in more detail the composite transformation RT c R .
1st transformation: inversion with respect to the unit sphere

S

2

Rx μ = x μ

x 2 =: x μ

(24.8)

2nd transformation : translation T c

T c x μ = x μ + c μ = x μ (24.9)

( 24.8 )

→ x μ = x μ

x 2 + c μ = x μ + x 2 c μ

(24.10)

x 2

3rd transformation :inversion with respect to the unit sphere S

2

x 3 =: x μ A ( 24.9 )

Rx μ = x μ

x μ + c μ
( x v + c v )( x v + c v ) =

x μ + c μ
x 2 +2 x v c v + c 2

x μ =

−→ (24.11)