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Table 7 Six sets of initial values of transformation parameters

From: WTLS iterative algorithm of 3D similarity coordinate transformation based on Gibbs vectors

Parameters

Set 1

Set 2

Set 3 (default)

Set 4

Set 5

Set 6

Scale

 \(\lambda\)

1

1

1

1

1

1

Gibbs vector (from initial rotation angles)

 \(a\)

− 0.0210

− 0.1981

0

0.0688

− 0.2513

− 0.7442

 \(b\)

0.0874

0.0453

0

− 0.2867

− 0.2235

0.2915

 \(c\)

0.2400

0.2565

0

0.2401

− 0.3192

− 0.1960

Rotation angles

 \(\theta_{x}\) (°)

0

20

0

0

20

76

 \(\theta_{y}\) (°)

− 10

− 10

0

32

30

− 10

 \(\theta_{z}\) (°)

− 27

− 27

0

− 27

30

30

Biased angles (from the correct solution)

 For \(\theta_{x}\) (°)

− 1.1

18.9

− 1.1

− 1.1

18.9

74.9

 For \(\theta_{y}\) (°)

2.5

2.5

12.5

44.5

42.5

2.5

 For \(\theta_{z}\) (°)

2.4

2.4

29.4

2.4

59.4

59.4

Number of iterations

5

5

6

6

8

8

  1. The values in italics denote the maximum biased angle from the correct solution for each set of initial values