| RIGID BODY TRANSFORMATION | ||||||||||||
| x | y | X | Y | Wi | X' | Y' | ||||||
| A | 1000.00 | 1000.00 | 999.70 | 1000.05 | 100 | 999.2507337 | 999.6407167 | Ao= | -1.3144 | |||
| B | 1000.00 | 1350.00 | 999.90 | 1350.33 | 100 | 999.4485864 | 1349.640661 | Bo= | 0.20617 | |||
| C | 1350.00 | 1350.00 | 1350.22 | 1350.00 | 1 | 1349.44853 | 1349.442808 | Alf= | -0.032388932 | -0.000565294 | ||
| D | 1350.00 | 1000.00 | 1349.90 | 1000.11 | 1 | 1349.250678 | 999.442864 | |||||
| a= | 202 | Wi(Bo-yi) | Wi(xi-Ao) | Wi(Bo-yi)^2 | Wi(xi-Ao)^2 | Wi Vx | Wi Vy | |||||
| b= | -237235.3771 | -99943.45467 | 100056.5134 | 99886941.32 | 100113058.7 | 44.92663029 | 40.92832538 | |||||
| c= | 202834.14 | -134943.4491 | 100076.2986 | 182097344.5 | 100152655.5 | 45.14135865 | 68.93391762 | |||||
| d= | 488717500 | -1349.236638 | 1350.76293 | 1820439.506 | 1824560.494 | 0.771469509 | 0.557191893 | |||||
| f= | 1298622500 | -999.236694 | 1350.565078 | 998473.9707 | 1824026.029 | 0.649322225 | 0.66713597 | |||||
| g= | 91.48878068 | Wi (Bo-yi)*Vx | Wi (xi-Ao)*Vy | |||||||||
| h= | 111.0865709 | -44901.22638 | 40951.45536 | |||||||||
| m= | 4085.359084 | -60915.30633 | 68986.51327 | |||||||||
| -1040.894927 | 752.6341537 | |||||||||||
| Ao= | -0.863774335 | -648.8265938 | 901.0105435 | |||||||||
| Bo= | 0.758060671 | |||||||||||
| Alf= | -0.000111675 | |||||||||||
| Matrix A | Matrix At | |||||||||||
| 1 | 0 | -999.84383 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | ||
| 0 | 1 | 1001.0144 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | ||
| 1 | 0 | -1350.1238 | -999.84383 | 1001.0144 | -1350.12383 | 1001.2144 | -1349.79383 | 1351.5344 | -999.90383 | 1351.2144 | ||
| 0 | 1 | 1001.2144 | ||||||||||
| 1 | 0 | -1349.7938 | Matrix N | Matrix L | ||||||||
| 0 | 1 | 1351.5344 | 4 | 0 | -4699.66532 | 44.92663029 | ||||||
| 1 | 0 | -999.90383 | 0 | 4 | 4704.981745 | 40.92832538 | ||||||
| 0 | 1 | 1351.2144 | -4699.66532 | 4704.981745 | 11301169.28 | 45.14135865 | ||||||
| 68.93391762 | ||||||||||||
| Matrix N-1 | 0.771469509 | |||||||||||
| 5.878831476 | -5.635199006 | 0.004790836 | 0.557191893 | |||||||||
| -5.635199006 | 5.891573739 | -0.004796256 | 0.649322225 | |||||||||
| 0.004790836 | -0.004796256 | 4.0776E-06 | 0.66713597 | |||||||||
| Matrix U | Matrix X | |||||||||||
| -2.325616483 | -0.581404121 | |||||||||||
| -2.323 | -0.5807 | |||||||||||
| 0.0451 | 7.8E-17 | |||||||||||
| EXAMPLES OF 4 PARAMETER TRANSFORMATION | |||||||||
| 1. TWO POINTS | |||||||||
| 2. WITH OVER DETERMINATION | |||||||||
| Transformations (2 points, no weight) | (similarity 4 parameters) | ||||||||
| x | y | X | Y | ||||||
| 1 | 100.69 | 166.39 | 670305 | 224173 | |||||
| 2 | 34.90 | 56.07 | 670764 | 223898 | |||||
| xb | yb | Xb | Yb | xbXb | ybYb | xbYb | ybXb | xb2+yb2 | |
| -65.79 | -110.32 | 459 | -275 | -30197.61 | 30338.00 | 18092.25 | -50636.88 | 16498.83 | |
| a1 = | 0.00850909 | ||||||||
| b1 = | 4.16569809 | ||||||||
| a0 = | 670997.274 | ||||||||
| b0 = | 223752.14 | ||||||||
| Example 1 | X=a0+a1*x -b1*y | 670305 | 670764 | ||||||
| Y=b0+b1*x+a1*y | 224173 | 223898 | |||||||