Wydział Geodezji i Gospodarki Przestrzennej Olsztyn, 18.03.2009 r.
Uniwersytet Warmińsko-Mazurski
w Olsztynie
Transformacja pomiędzy układami współrzędnych
Piotr Biedrzycki
GiG III gr. 2, nr 1
Dane:
Δ X=
ΔY=
Δ Z= 82,5 m
δω = 0”,1
δψ = 2”,0
δε = -2”,5
Δ = 0”,0000021
Punkty w układzie WGRS 84:
| x | y | z | |
|---|---|---|---|
| 1 | 3524533.6793 | 1329703.7456 | 5129856.4049 |
| 2 | 3592285.2039 | 1326529.8154 | 5083797.0189 |
| 3 | 3648855.9694 | 1359150.2015 | 5034929.7360 |
TRANSFORMACJA HELMERTA
Obliczenia:
| -23 | 1.0000021000 | 0.0000004848 | -0.0000096963 | 3524533.6793 | ||
|---|---|---|---|---|---|---|
| 124.5 | + | -0.0000004848 | 1.0000021000 | -0.0000121203 | * | 1329703.7456 |
| 82.5 | 0.0000096963 | 0.0000121203 | 1.0000021000 | 5129856.4049 | ||
| -23 | 1.0000021000 | 0.0000004848 | -0.0000096963 | 3592285.2039 | ||
| 124.5 | + | -0.0000004848 | 1.0000021000 | -0.0000121203 | * | 1326529.8154 |
| 82.5 | 0.0000096963 | 0.0000121203 | 1.0000021000 | 5083797.0189 | ||
| -23 | 1.0000021000 | 0.0000004848 | -0.0000096963 | 3648855.9694 | ||
| 124.5 | + | -0.0000004848 | 1.0000021000 | -0.0000121203 | * | 1359150.2015 |
| 82.5 | 0.0000096963 | 0.0000121203 | 1.0000021000 | 5034929.7360 |
Wynik:
Punkty w układzie Krasowskiego ‘42
| x | y | z | ||
|---|---|---|---|---|
| 1 | 3524491.9850 | 1329642.6536 | 5129917.4689 | |
| 2 | 3592244.0969 | 1326469.2422 | 5083858.6046 | |
| 3 | 3648815.4709 | 1359090.2616 | 5034992.1630 |
TRANSFORMACJA MOŁODEŃSKIEGO-BADEKASA
Obliczenia:
| -23 | 3588558.284 | 1.0000021000 | 0.0000004848 | -0.0000096963 | -64024.6049 | |||
|---|---|---|---|---|---|---|---|---|
| 124.5 | + | 1338461.254 | + | -0.0000004848 | 1.0000021000 | -0.0000121203 | * | -8757.5085 |
| 82.5 | 5082861.053 | 0.0000096963 | 0.0000121203 | 1.0000021000 | 46995.3516 |
| -23 | 3588558.284 | 1.0000021000 | 0.0000004848 | -0.0000096963 | 3726.9197 | |||
|---|---|---|---|---|---|---|---|---|
| 124.5 | + | 1338461.254 | + | -0.0000004848 | 1.0000021000 | -0.0000121203 | * | -11931.4387 |
| 82.5 | 5082861.053 | 0.0000096963 | 0.0000121203 | 1.0000021000 | 935.9656 |
| -23 | 3588558.284 | 1.0000021000 | 0.0000004848 | -0.0000096963 | 60297.6852 | |||
|---|---|---|---|---|---|---|---|---|
| 124.5 | + | 1338461.254 | + | -0.0000004848 | 1.0000021000 | -0.0000121203 | * | 20688.9473 |
| 82.5 | 5082861.053 | 0.0000096963 | 0.0000121203 | 1.0000021000 | -47931.3173 |
Wynik:
| x | y | z | |
|---|---|---|---|
| 1 | 3524510.0849 | 1329827.6886 | 5129938.2766 |
| 2 | 3592262.1969 | 1326654.2772 | 5083879.4124 |
| 3 | 3648833.5708 | 1359275.2966 | 5035012.9708 |
Różnice pomiędzy transformacjami
| nr pt | x1 | x2 | różnica | y1 | y2 | różnica | z1 | z2 | różnica |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 3524468.9850 | 3524510.0849 | 41.0999 | 1329767.1536 | 1329827.6886 | 60.5350 | 5129999.969 | 5129938.2766 | -61.6923 |
| 2 | 3592221.0969 | 3592262.1969 | 41.0999 | 1326593.7422 | 1326654.2772 | 60.5350 | 5083941.105 | 5083879.4124 | -61.6923 |
| 3 | 3648792.4709 | 3648833.571 | 41.0999 | 1359214.7616 | 1359275.297 | 60.5350 | 5035074.663 | 5035012.971 | -61.6923 |
[m]
nr punktu