Środa
Katedra Geodezji i Astronomii Geodezyjnej
Politechnika Warszawska
Ćwiczenie nr 8
Temat: Wyznaczenie na podstawie 7 punktów
współczynników transformacji afinicznej oraz przez podobieństwo. Obliczenie współrzędnych punktów do układu wtórnego, obliczenie różnic oraz błędu transformacji.
Data oddania: 17.12.2008r.
Rok akademicki: |
2008/2009 |
Imię i nazwisko: |
Semestr: |
III |
Tomasz Blachowicz |
Grupa: |
IIa |
|
Numer: |
42 |
Dane:
Nr |
układ pierwotny |
układ wtórny |
||||
|
X |
Y |
Z |
X |
Y |
Z |
1 |
3 904 633,351 |
1 360 191,915 |
4 840 630,819 |
3 904 609,689 |
1 360 314,850 |
4 840 712,184 |
2 |
3 814 251,039 |
1 410 360,176 |
4 911 504,911 |
3 814 227,433 |
1 410 483,374 |
4 911 586,376 |
3 |
3 628 943,159 |
1 029 356,123 |
5 123 689,022 |
3 628 917,884 |
1 029 479,499 |
5 123 770,087 |
4 |
3 479 651,051 |
1 938 265,261 |
4 747 562,786 |
3 479 629,265 |
1 938 390,556 |
4 747 645,149 |
5 |
3 794 892,363 |
1 568 743,244 |
5 048 963,219 |
3 794 869,429 |
1 568 866,437 |
5 049 045,188 |
6 |
3 548 976,210 |
1 789 540,219 |
4 848 692,130 |
3 548 953,996 |
1 789 664,970 |
4 848 774,155 |
7 |
3 528 741,598 |
1 866 421,399 |
4 947 258,306 |
3 528 719,620 |
1 866 546,186 |
4 947 340,685 |
8 |
3 856 487,268 |
1 568 342,085 |
4 925 984,365 |
3 856 464,354 |
1 568 465,245 |
4 926 066,116 |
9 |
3 764 896,244 |
1 674 236,641 |
5 129 864,010 |
3 764 873,720 |
1 674 359,899 |
5 129 946,164 |
10 |
3 698 124,246 |
1 984 562,305 |
5 020 305,009 |
3 698 102,945 |
1 984 686,402 |
5 020 387,700 |
11 |
3 876 941,064 |
1 509 647,238 |
4 735 687,123 |
3 876 917,865 |
1 509 770,580 |
4 735 768,626 |
Rozwiązanie:
TRANSFORMACJA PRZEZ PODOBIEŃSTWO:
Macierz A: Macierz L:
23,662 |
-122,935 |
-81,365 |
23,606 |
-123,198 |
-81,465 |
25,275 |
-123,376 |
-81,065 |
22,914 |
-123,160 |
-81,751 |
22,524 |
-123,258 |
-82,154 |
21,301 |
-124,097 |
-82,691 |
23,199 |
-123,342 |
-81,503 |
x1 |
3904633,351 |
0 |
-4840630,819 |
1360191,915 |
1 |
0 |
0 |
y1 |
1360191,915 |
4840630,819 |
0 |
-3904633,351 |
0 |
1 |
0 |
z1 |
4840630,819 |
-1360191,915 |
3904633,351 |
0 |
0 |
0 |
1 |
x2 |
3814251,039 |
0 |
-4911504,911 |
1410360,176 |
1 |
0 |
0 |
y2 |
1410360,176 |
4911504,911 |
0 |
-3814251,039 |
0 |
1 |
0 |
z2 |
4911504,911 |
-1410360,176 |
3814251,039 |
0 |
0 |
0 |
1 |
x3 |
3628943,159 |
0 |
-5123689,022 |
1029356,123 |
1 |
0 |
0 |
y3 |
1029356,123 |
5123689,022 |
0 |
-3628943,159 |
0 |
1 |
0 |
z3 |
5123689,022 |
-1029356,123 |
3628943,159 |
0 |
0 |
0 |
1 |
x8 |
3856487,268 |
0 |
-4925984,365 |
1568342,085 |
1 |
0 |
0 |
y8 |
1568342,085 |
4925984,365 |
0 |
-3856487,268 |
0 |
1 |
0 |
z8 |
4925984,365 |
-1568342,085 |
3856487,268 |
0 |
0 |
0 |
1 |
x9 |
3764896,244 |
0 |
-5129864,010 |
1674236,641 |
1 |
0 |
0 |
y9 |
1674236,641 |
5129864,010 |
0 |
-3764896,244 |
0 |
1 |
0 |
z9 |
5129864,010 |
-1674236,641 |
3764896,244 |
0 |
0 |
0 |
1 |
x10 |
3698124,246 |
0 |
-5020305,009 |
1984562,305 |
1 |
0 |
0 |
y10 |
1984562,305 |
5020305,009 |
0 |
-3698124,246 |
0 |
1 |
0 |
z10 |
5020305,009 |
-1984562,305 |
3698124,246 |
0 |
0 |
0 |
1 |
x11 |
3876941,064 |
0 |
-4735687,123 |
1509647,238 |
1 |
0 |
0 |
y11 |
1509647,238 |
4735687,123 |
0 |
-3876941,064 |
0 |
1 |
0 |
z11 |
4735687,123 |
-1509647,238 |
3876941,064 |
0 |
0 |
0 |
1 |
Współczynniki transformacji:
|
0,0000008760924 |
μ |
|
-0,0000017536462 |
α |
|
-0,0000002299625 |
β |
X= |
0,0000041385574 |
γ |
|
- 33,9028321048609 |
xo |
|
146,4028265659510 |
yo |
|
75,6044218350507 |
zo |
Obliczone współrzędne wtórne:
Nr |
x |
y |
z |
1 |
3 904 609,611 |
1 360 314,861 |
4 840 712,152 |
2 |
3 814 227,444 |
1 410 483,416 |
4 911 586,414 |
3 |
3 628 917,874 |
1 029 479,424 |
5 123 770,086 |
4 |
3 479 629,310 |
1 938 390,636 |
4 747 645,149 |
5 |
3 794 869,438 |
1 568 866,462 |
5 049 045,125 |
6 |
3 548 953,938 |
1 789 664,999 |
4 848 774,304 |
7 |
3 528 719,649 |
1 866 546,157 |
4 947 340,706 |
8 |
3 856 464,367 |
1 568 465,263 |
4 926 066,149 |
9 |
3 764 873,748 |
1 674 359,933 |
5 129 946,179 |
10 |
3 698 102,951 |
1 984 686,338 |
5 020 387,641 |
11 |
3 876 917,895 |
1 509 770,614 |
4 735 768,632 |
Błąd: 0,047237
TRANSFORMACJA AFINICZNA:
Macierz A: Macierz L:
1 |
3904633,351 |
0 |
0 |
0 |
-4840630,819 |
1360191,915 |
1 |
0 |
0 |
|
|
0 |
1360191,915 |
0 |
4840630,819 |
0 |
-3904633,351 |
0 |
1 |
0 |
|
|
0 |
0 |
4840630,819 |
-1360191,915 |
3904633,351 |
0 |
0 |
0 |
1 |
|
2 |
3814251,039 |
0 |
0 |
0 |
-4911504,911 |
1410360,176 |
1 |
0 |
0 |
|
|
0 |
1410360,176 |
0 |
4911504,911 |
0 |
-3814251,039 |
0 |
1 |
0 |
|
|
0 |
0 |
4911504,911 |
-1410360,176 |
3814251,039 |
0 |
0 |
0 |
1 |
|
3 |
3628943,159 |
0 |
0 |
0 |
-5123689,022 |
1029356,123 |
1 |
0 |
0 |
|
|
0 |
1029356,123 |
0 |
5123689,022 |
0,000 |
-3628943,159 |
0 |
1 |
0 |
|
|
0 |
0 |
5123689,022 |
-1029356,123 |
3628943,159 |
0 |
0 |
0 |
1 |
|
8 |
3856487,268 |
0 |
0 |
0 |
-4925984,365 |
1568342,085 |
1 |
0 |
0 |
|
|
0 |
1568342,085 |
0 |
4925984,365 |
0 |
-3856487,268 |
0 |
1 |
0 |
|
|
0 |
0 |
4925984,365 |
-1568342,085 |
3856487,268 |
0 |
0 |
0 |
1 |
|
9 |
3764896,244 |
0 |
0 |
0 |
-5129864,010 |
1674236,641 |
1 |
0 |
0 |
|
|
0 |
1674236,641 |
0 |
5129864,010 |
0 |
-3764896,244 |
0 |
1 |
0 |
|
|
0 |
0 |
5129864,010 |
-1674236,641 |
3764896,244 |
0 |
0 |
0 |
1 |
|
10 |
3698124,246 |
0 |
0 |
0 |
-5020305,009 |
1984562,305 |
1 |
0 |
0 |
|
|
0 |
1984562,305 |
0 |
5020305,009 |
0 |
-3698124,246 |
0 |
1 |
0 |
|
|
0 |
0 |
5020305,009 |
-1984562,305 |
3698124,246 |
0 |
0 |
0 |
1 |
|
11 |
3876941,064 |
0 |
0 |
0 |
-4735687,123 |
1509647,238 |
1 |
0 |
0 |
|
|
0 |
1509647,238 |
0 |
4735687,123 |
0 |
-3876941,064 |
0 |
1 |
0 |
|
|
0 |
0 |
4735687,123 |
-1509647,238 |
3876941,064 |
0 |
0 |
0 |
1 |
|
23,662 |
||||||||||
-122,935 |
||||||||||
-81,365 |
||||||||||
23,606 |
||||||||||
-123,198 |
||||||||||
-81,465 |
||||||||||
25,275 |
||||||||||
-123,376 |
||||||||||
-81,065 |
||||||||||
22,914 |
||||||||||
-123,160 |
||||||||||
-81,751 |
||||||||||
22,524 |
||||||||||
-123,258 |
||||||||||
-82,154 |
||||||||||
21,301 |
||||||||||
-124,097 |
||||||||||
-82,691 |
||||||||||
23,199 |
||||||||||
-123,342 |
||||||||||
-81,503 |
||||||||||
Współczynniki transformacji:
|
0,0000010535216 |
μ x |
|
0,0000008635486 |
μ y |
|
0,0000008426026 |
μ z |
|
-0,0000017548940 |
α |
X= |
-0,0000003116570 |
β |
|
0,0000041343320 |
γ |
|
-34,9741175306262 |
xo |
|
146,4118680245440 |
yo |
|
76,0782868815585 |
zo |
Obliczone współrzędne wtórne:
Nr |
x |
y |
z |
1 |
3 904 609,623 |
1 360 314,864 |
4 840 712,146 |
2 |
3 814 227,445 |
1 410 483,417 |
4 911 586,414 |
3 |
3 628 917,861 |
1 029 479,429 |
5 123 770,093 |
4 |
3 479 629,236 |
1 938 390,629 |
4 747 645,182 |
5 |
3 794 869,446 |
1 568 866,461 |
5 049 045,122 |
6 |
3 548 953,884 |
1 789 664,995 |
4 848 774,328 |
7 |
3 528 719,600 |
1 866 546,152 |
4 947 340,728 |
8 |
3 856 464,376 |
1 568 465,263 |
4 926 066,144 |
9 |
3 764 873,757 |
1 674 359,931 |
5 129 946,175 |
10 |
3 698 102,937 |
1 984 686,331 |
5 020 387,648 |
11 |
3 876 917,892 |
1 509 770,614 |
4 735 768,633 |
Błąd: 0,051595
Zestawienie wyników:
dane: podobieństwo: różnice:
Nr |
X |
Y |
Z |
X |
Y |
Y |
X |
Y |
Z |
1 |
3 904 609,689 |
1 360 314,850 |
4 840 712,184 |
3 904 609,611 |
1 360 314,861 |
4 840 712,152 |
-0,078 |
0,011 |
-0,032 |
2 |
3 814 227,433 |
1 410 483,374 |
4 911 586,376 |
3 814 227,444 |
1 410 483,416 |
4 911 586,414 |
0,011 |
0,042 |
0,038 |
3 |
3 628 917,884 |
1 029 479,499 |
5 123 770,087 |
3 628 917,874 |
1 029 479,424 |
5 123 770,086 |
-0,010 |
-0,075 |
-0,001 |
4 |
3 479 629,265 |
1 938 390,556 |
4 747 645,149 |
3 479 629,310 |
1 938 390,636 |
4 747 645,149 |
0,045 |
0,080 |
0,000 |
5 |
3 794 869,429 |
1 568 866,437 |
5 049 045,188 |
3 794 869,438 |
1 568 866,462 |
5 049 045,125 |
0,009 |
0,025 |
-0,063 |
6 |
3 548 953,996 |
1 789 664,970 |
4 848 774,155 |
3 548 953,938 |
1 789 664,999 |
4 848 774,304 |
-0,058 |
0,029 |
0,149 |
7 |
3 528 719,620 |
1 866 546,186 |
4 947 340,685 |
3 528 719,649 |
1 866 546,157 |
4 947 340,706 |
0,029 |
-0,029 |
0,021 |
8 |
3 856 464,354 |
1 568 465,245 |
4 926 066,116 |
3 856 464,367 |
1 568 465,263 |
4 926 066,149 |
0,013 |
0,018 |
0,033 |
9 |
3 764 873,720 |
1 674 359,899 |
5 129 946,164 |
3 764 873,748 |
1 674 359,933 |
5 129 946,179 |
0,028 |
0,034 |
0,015 |
10 |
3 698 102,945 |
1 984 686,402 |
5 020 387,700 |
3 698 102,951 |
1 984 686,338 |
5 020 387,641 |
0,006 |
-0,064 |
-0,059 |
11 |
3 876 917,865 |
1 509 770,580 |
4 735 768,626 |
3 876 917,895 |
1 509 770,614 |
4 735 768,632 |
0,030 |
0,034 |
0,006 |
dane: afiniczna: różnice:
Nr |
X |
Y |
Z |
X |
Y |
Y |
X |
Y |
Z |
1 |
3 904 609,689 |
1 360 314,850 |
4 840 712,184 |
3 904 609,623 |
1 360 314,864 |
4 840 712,146 |
0,066 |
-0,014 |
0,038 |
2 |
3 814 227,433 |
1 410 483,374 |
4 911 586,376 |
3 814 227,445 |
1 410 483,417 |
4 911 586,414 |
-0,012 |
-0,043 |
-0,038 |
3 |
3 628 917,884 |
1 029 479,499 |
5 123 770,087 |
3 628 917,861 |
1 029 479,429 |
5 123 770,093 |
0,023 |
0,070 |
-0,006 |
4 |
3 479 629,265 |
1 938 390,556 |
4 747 645,149 |
3 479 629,236 |
1 938 390,629 |
4 747 645,182 |
0,029 |
-0,073 |
-0,033 |
5 |
3 794 869,429 |
1 568 866,437 |
5 049 045,188 |
3 794 869,446 |
1 568 866,461 |
5 049 045,122 |
-0,017 |
-0,024 |
0,066 |
6 |
3 548 953,996 |
1 789 664,970 |
4 848 774,155 |
3 548 953,884 |
1 789 664,995 |
4 848 774,328 |
0,112 |
-0,025 |
-0,173 |
7 |
3 528 719,620 |
1 866 546,186 |
4 947 340,685 |
3 528 719,600 |
1 866 546,152 |
4 947 340,728 |
0,020 |
0,034 |
-0,043 |
8 |
3 856 464,354 |
1 568 465,245 |
4 926 066,116 |
3 856 464,376 |
1 568 465,263 |
4 926 066,144 |
-0,022 |
-0,018 |
-0,028 |
9 |
3 764 873,720 |
1 674 359,899 |
5 129 946,164 |
3 764 873,757 |
1 674 359,931 |
5 129 946,175 |
-0,037 |
-0,032 |
-0,011 |
10 |
3 698 102,945 |
1 984 686,402 |
5 020 387,700 |
3 698 102,937 |
1 984 686,331 |
5 020 387,648 |
0,008 |
0,071 |
0,052 |
11 |
3 876 917,865 |
1 509 770,580 |
4 735 768,626 |
3 876 917,892 |
1 509 770,614 |
4 735 768,633 |
-0,027 |
-0,034 |
-0,007 |