152TG1 Teoretická geodézie 1 - úloha 4: Porovnání verzí

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Řádek 1: Řádek 1:
==Název úlohy==
==Název úlohy==
Transformace souřadnic, aplikace metody nejmenších čtverců
Helmertova prostorová transformace


==Zadání úlohy==
==Zadání úlohy==
Pomocí osmi identických bodů se zadanými prostorovými souřadnicemi v kartézských souřadnicových systémech S1 a S2 vypočítejte transformační klíč Helmertovy prostorové transformace a body transformujte ze systému S1 do systému S2. Vypočítejte aposteriorní charakteristiky přesnosti plynoucí ze zavedení podmínky MNČ.
Známy jsou zeměpisné elipsoidické souřadnice deseti identických bodů na elipsoidu WGS84 a na Besselově elipsoidu. Souřadnice identických bodů převeďte v obou souřadnicových soustavách příslušných elipsoidů na souřadnice kartézské. Vypočtěte transformační klíč Helmertovy prostorové transformace mezi oběma kartézskými souřadnicovými soustavami a uveďte též aposteriorní charakteristiky přesnosti vyrovnaných hodnot transformačního klíče plynoucí ze zavedení podmínky MNČ. Výsledné posuny počátků souřadnicových soustav uveďte v metrech, výsledné rotační úhly ve stupních, minutách, vteřinách. Rovněž vypočtěte vyrovnané hodnoty souřadnic identických bodů (zprostředkujících veličin) včetně jejich směrodatných odchylek.
 
Při výpočtu uvažujte transformaci ze souřadnicové soustavy elipsoidu WGS84 (vstupní soustava S1) do souřadnicové soustavy Besselova elipsoidu (výstupní soustava S2). Transformaci proveďte buď pomocí obecné Helmertovy sedmiprvkové transformace, nebo pomocí diferenciální (zjednodušené) Helmertovy transformace. Zvolený způsob řešení musí být jasně dokumentován v technické zprávě.


==Numerické zadání==
==Numerické zadání==
Souřadnice transformovaných bodů v systému S2 jsou pro všechna zadání stejné:
Numerické zadání s elipsoidickými souřadnicemi identických bodů v obou soustavách S1 a S2 naleznete v adresáři [ftp://athena.fsv.cvut.cz/TG1/helmert/zadani ftp://athena.fsv.cvut.cz/TG1/helmert/zadani] v souboru '''tg1_2014_u4_xx.m''', kde '''xx''' je číslo zadání. Číslo zadání studenta odpovídá číslování uvedenému na stránkách cvičení TG1.
{| class="border"
||    bod      ||        x [m] ||        y [m] ||        z [m]
|-
| A ||   0.000 ||   0.000 ||   0.000
|-
| B || 100.000 ||   0.000 ||   0.000
|-
| C || 100.000 || 100.000 ||   0.000
|-
| D ||   0.000 || 100.000 ||   0.000
|-
| E ||   0.000 ||   0.000 || 100.000
|-
| F || 100.000 ||   0.000 || 100.000
|-
| G || 100.000 || 100.000 || 100.000
|-
| H ||   0.000 || 100.000 || 100.000
|}
 
Individuální zadání včetně souřadnic identických bodů ve vstupní soustavě S1 naleznete v adresáři ... <!--[ftp://athena.fsv.cvut.cz/ZFG/web_data/helmert/zadani ftp://athena.fsv.cvut.cz/ZFG/web_data/helmert/zadani] v souboru '''zfg2012_1_xx.m''', kde '''xx''' je číslo zadání. Číslo zadání studenta odpovídá číslování uvedenému na stránkách cvičení ZFG.
-->
 
<!--
Souřadnice transformovaných bodů v systému S1:
{| class="border"
|číslo zadání |bod |x [m] |y [m] |z [m] |číslo zadání |bod |x [m] |y [m] |z [m]
|-
|rowspan="8"  | 1 || A || 93,170 || -295,133 || 48,646 ||rowspan="8"  | 51 || A || 30,977 || -52,407 || 155,159
|-
| B || -1,411 || -280,864 || 24,723 || B || 25,958 || 9,966 || 203,122
|-
| C || -22,338 || -261,377 || 119,082 || C || 31,794 || -37,672 || 265,678
|-
| D || 72,244 || -275,639 || 143,002 || D || 36,814 || -100,045 || 217,715
|-
| E || 111,543 || -199,539 || 32,973 || E || 109,452 || -44,876 || 153,571
|-
| F || 16,961 || -185,277 || 9,045 || F || 104,430 || 17,496 || 201,538
|-
| G || -3,961 || -165,780 || 103,413 || G || 110,259 || -30,144 || 264,102
|-
| H || 90,619 || -180,041 || 127,335 || H || 115,281 || -92,510 || 216,133
|-
|rowspan="8"  | 2 || A || -30,662 || -150,076 || -11,197 ||rowspan="8"  | 52 || A || -58,386 || 179,416 || -139,345
|-
| B || -65,948 || -64,049 || -107,415 || B || 6,015 || 194,213 || -161,630
|-
| C || -154,799 || -152,591 || -154,001 || C || -17,000 || 254,451 || -188,161
|-
| D || -119,508 || -238,628 || -57,778 || D || -81,406 || 239,658 || -165,875
|-
| E || -124,284 || -98,472 || 69,285 || E || -44,756 || 211,279 || -78,829
|-
| F || -159,575 || -12,443 || -26,942 || F || 19,643 || 226,073 || -101,114
|-
| G || -248,427 || -100,991 || -73,525 || G || -3,379 || 286,308 || -127,643
|-
| H || -213,138 || -187,020 || 22,695 || H || -67,779 || 271,515 || -105,356
|-
|rowspan="8"  | 3 || A || -58,640 || 90,084 || -100,064 ||rowspan="8"  | 53 || A || 15,080 || 334,609 || -140,155
|-
| B || 0,229 || 66,547 || -170,125 || B || -10,561 || 301,188 || -205,519
|-
| C || 8,938 || 157,707 || -193,421 || C || -82,489 || 298,753 || -176,064
|-
| D || -49,932 || 181,236 || -123,365 || D || -56,837 || 332,171 || -110,696
|-
| E || 14,759 || 98,137 || -41,104 || E || 0,375 || 404,779 || -170,263
|-
| F || 73,625 || 74,606 || -111,166 || F || -25,273 || 371,357 || -235,635
|-
| G || 82,330 || 165,765 || -134,457 || G || -97,197 || 368,929 || -206,162
|-
| H || 23,463 || 189,294 || -64,400 || H || -71,549 || 402,343 || -140,802
|-
|rowspan="8"  | 4 || A || -22,297 || 366,540 || 79,651 ||rowspan="8"  | 54 || A || -8,488 || -143,002 || -28,202
|-
| B || 58,657 || 324,191 || 109,487 || B || 23,660 || -248,992 || 37,987
|-
| C || 81,716 || 304,082 || 18,377 || C || 137,422 || -252,463 || -22,818
|-
| D || 0,769 || 346,426 || -11,462 || D || 105,272 || -146,469 || -89,012
|-
| E || 24,086 || 450,435 || 72,867 || E || 43,249 || -69,502 || 64,376
|-
| F || 105,043 || 408,096 || 102,706 || F || 75,397 || -175,489 || 130,568
|-
| G || 128,106 || 387,984 || 11,597 || G || 189,146 || -178,964 || 69,760
|-
| H || 47,145 || 430,327 || -18,239 || H || 156,998 || -72,964 || 3,571
|-
|rowspan="8"  | 5 || A || -1,349 || -53,984 || 107,577 ||rowspan="8"  | 55 || A || -14,581 || 174,102 || 53,660
|-
| B || 12,440 || -86,892 || 148,631 || B || 28,563 || 70,321 || 134,653
|-
| C || 2,987 || -130,181 || 117,101 || C || -26,818 || -21,311 || 46,746
|-
| D || -10,801 || -97,276 || 76,046 || D || -69,968 || 82,470 || -34,241
|-
| E || 50,412 || -53,127 || 90,890 || E || 104,835 || 169,093 || -16,376
|-
| F || 64,199 || -86,029 || 131,941 || F || 147,989 || 65,326 || 64,612
|-
| G || 54,745 || -129,331 || 100,408 || G || 92,597 || -26,310 || -23,282
|-
| H || 40,963 || -96,415 || 59,353 || H || 49,448 || 77,466 || -104,272
|-
|rowspan="8"  | 6 || A || 20,503 || 393,620 || -122,535 ||rowspan="8"  | 56 || A || 52,342 || -91,495 || -67,506
|-
| B || -70,711 || 328,401 || -189,274 || B || 140,410 || -21,181 || -38,826
|-
| C || -110,464 || 271,128 || -78,977 || C || 115,863 || 46,740 || -129,970
|-
| D || -19,252 || 336,338 || -12,231 || D || 27,786 || -23,572 || -158,655
|-
| E || -63,906 || 491,048 || -102,367 || E || -19,532 || -28,522 || -1,227
|-
| F || -155,123 || 425,836 || -169,100 || F || 68,544 || 41,791 || 27,459
|-
| G || -194,875 || 368,565 || -58,798 || G || 43,995 || 109,719 || -63,687
|-
| H || -103,669 || 433,771 || 7,940 || H || -44,074 || 39,398 || -92,368
|-
|rowspan="8"  | 7 || A || 23,910 || 233,940 || -36,316 ||rowspan="8"  | 57 || A || 9,814 || 296,466 || 45,020
|-
| B || 47,640 || 328,518 || 31,422 || B || 28,940 || 250,611 || 2,156
|-
| C || 113,328 || 374,688 || -56,040 || C || -28,290 || 256,288 || -29,442
|-
| D || 89,611 || 280,104 || -123,782 || D || -47,417 || 302,135 || 13,430
|-
| E || -72,106 || 288,901 || -79,422 || E || 35,604 || 343,065 || 6,690
|-
| F || -48,378 || 383,477 || -11,686 || F || 54,720 || 297,210 || -36,181
|-
| G || 17,322 || 429,648 || -99,147 || G || -2,511 || 302,888 || -67,783
|-
| H || -6,403 || 335,061 || -166,890 || H || -21,628 || 348,742 || -24,913
|-
|rowspan="8"  | 8 || A || -20,027 || -70,648 || 74,791 ||rowspan="8"  | 58 || A || -3,202 || 109,027 || -276,757
|-
| B || -69,042 || -104,138 || -14,136 || B || 30,042 || 109,602 || -155,182
|-
| C || -1,308 || -46,278 || -73,262 || C || 68,834 || -9,904 || -165,220
|-
| D || 47,710 || -12,786 || 15,660 || D || 35,584 || -10,481 || -286,802
|-
| E || 46,612 || -154,089 || 69,484 || E || 112,022 || 149,085 || -308,451
|-
| F || -2,402 || -187,578 || -19,445 || F || 145,268 || 149,662 || -186,879
|-
| G || 65,327 || -129,720 || -78,576 || G || 184,049 || 30,157 || -196,919
|-
| H || 114,347 || -96,232 || 10,353 || H || 150,803 || 29,582 || -318,496
|-
|rowspan="8"  | 9 || A || 7,668 || 475,089 || 117,180 ||rowspan="8"  | 59 || A || -26,543 || -449,172 || 53,068
|-
| B || 55,432 || 448,741 || 105,023 || B || -94,065 || -405,727 || -12,443
|-
| C || 58,815 || 477,063 || 56,954 || C || -76,285 || -481,408 || -80,962
|-
| D || 11,051 || 503,407 || 69,119 || D || -8,756 || -524,847 || -15,459
|-
| E || 36,482 || 515,435 || 142,970 || E || -103,099 || -505,062 || 94,924
|-
| F || 84,247 || 489,084 || 130,818 || F || -170,629 || -461,617 || 29,420
|-
| G || 87,627 || 517,405 || 82,748 || G || -152,853 || -537,301 || -39,100
|-
| H || 39,864 || 543,748 || 94,911 || H || -85,317 || -580,741 || 26,406
|-
|rowspan="8"  | 10 || A || -10,754 || 207,875 || -47,920 ||rowspan="8"  | 60 || A || -64,418 || -97,966 || -83,457
|-
| B || -10,878 || 308,067 || -145,458 || B || -51,266 || -199,514 || 7,477
|-
| C || -7,130 || 210,560 || -245,610 || C || 62,152 || -242,037 || -56,400
|-
| D || -7,003 || 110,378 || -148,066 || D || 49,001 || -140,488 || -147,334
|-
| E || -150,523 || 205,165 || -50,514 || E || 11,196 || -16,528 || -3,437
|-
| F || -150,652 || 305,357 || -148,061 || F || 24,337 || -118,066 || 87,504
|-
| G || -146,903 || 207,851 || -248,211 || G || 137,753 || -160,591 || 23,619
|-
| H || -146,771 || 107,671 || -150,669 || H || 124,610 || -59,047 || -67,308
|-
|rowspan="8"  | 11 || A || 31,664 || -50,081 || 155,170 ||rowspan="8"  | 61 || A || 59,875 || 450,368 || 138,025
|-
| B || -52,182 || -140,593 || 125,299 || B || 108,055 || 323,175 || 152,809
|-
| C || -75,069 || -160,097 || 248,634 || C || 176,116 || 361,985 || 264,955
|-
| D || 8,775 || -69,583 || 278,506 || D || 127,936 || 489,180 || 250,175
|-
| E || -60,856 || 36,761 || 151,733 || E || -48,583 || 418,229 || 214,972
|-
| F || -144,707 || -53,750 || 121,860 || F || -0,408 || 291,039 || 229,751
|-
| G || -167,596 || -73,250 || 245,195 || G || 67,656 || 329,852 || 341,905
|-
| H || -83,752 || 17,258 || 275,064 || H || 19,475 || 457,043 || 327,126
|-
|rowspan="8"  | 12 || A || -31,701 || -485,743 || 57,217 ||rowspan="8"  | 62 || A || -41,024 || 66,815 || -130,056
|-
| B || 5,844 || -600,552 || 76,992 || B || -18,336 || 104,006 || -232,024
|-
| C || -20,037 || -629,030 || -39,214 || C || -19,825 || 208,263 || -194,326
|-
| D || -57,585 || -514,217 || -58,985 || D || -42,504 || 171,080 || -92,366
|-
| E || 81,893 || -454,272 || 24,212 || E || 67,502 || 60,479 || -108,230
|-
| F || 119,439 || -569,094 || 43,982 || F || 90,180 || 97,664 || -210,194
|-
| G || 93,561 || -597,560 || -72,223 || G || 88,697 || 201,923 || -172,495
|-
| H || 56,011 || -482,750 || -91,989 || H || 66,008 || 164,740 || -70,536
|-
|rowspan="8"  | 13 || A || -4,189 || -333,380 || 49,056 ||rowspan="8"  | 63 || A || -67,013 || -193,237 || -73,333
|-
| B || -55,985 || -366,730 || 75,963 || B || -1,556 || -96,768 || -147,320
|-
| C || -26,682 || -363,468 || 136,377 || C || -122,706 || -52,028 || -196,167
|-
| D || 25,102 || -330,118 || 109,463 || D || -188,163 || -148,493 || -122,181
|-
| E || -35,473 || -275,111 || 61,071 || E || -77,163 || -105,157 || 32,521
|-
| F || -87,257 || -308,459 || 87,990 || F || -11,703 || -8,693 || -41,464
|-
| G || -57,964 || -305,192 || 148,400 || G || -132,855 || 36,052 || -90,314
|-
| H || -6,168 || -271,852 || 121,488 || H || -198,312 || -60,423 || -16,332
|-
|rowspan="8"  | 14 || A || 88,609 || 12,300 || -33,202 ||rowspan="8"  | 64 || A || -31,542 || 143,668 || -143,998
|-
| B || 91,936 || 10,873 || 26,841 || B || 43,403 || 230,953 || -84,738
|-
| C || 96,089 || -49,117 || 25,201 || C || 135,993 || 141,681 || -70,361
|-
| D || 92,771 || -47,702 || -34,849 || D || 61,041 || 54,400 || -129,617
|-
| E || 148,531 || 16,538 || -36,427 || E || 19,035 || 177,739 || -258,154
|-
| F || 151,860 || 15,117 || 23,627 || F || 93,978 || 265,024 || -198,892
|-
| G || 156,018 || -44,875 || 21,979 || G || 186,571 || 175,750 || -184,503
|-
| H || 152,690 || -43,453 || -38,075 || H || 111,620 || 88,469 || -243,773
|-
|rowspan="8"  | 15 || A || 62,366 || -70,046 || -71,843 ||rowspan="8"  | 65 || A || 47,520 || 175,522 || 2,294
|-
| B || 62,519 || -17,971 || 27,704 || B || 99,131 || 108,969 || 9,227
|-
| C || 62,970 || -117,513 || 79,774 || C || 107,478 || 124,061 || 91,954
|-
| D || 62,813 || -169,587 || -19,771 || D || 55,870 || 190,620 || 85,014
|-
| E || 174,707 || -69,713 || -72,181 || E || -18,864 || 125,683 || 18,085
|-
| F || 174,861 || -17,641 || 27,364 || F || 32,738 || 59,132 || 25,015
|-
| G || 175,311 || -117,185 || 79,437 || G || 41,089 || 74,228 || 107,739
|-
| H || 175,152 || -169,256 || -20,106 || H || -10,523 || 140,780 || 100,805
|-
|rowspan="8"  | 16 || A || -72,703 || -75,016 || 102,975 ||rowspan="8"  | 66 || A || -53,662 || -192,983 || 45,141
|-
| B || -51,746 || -91,605 || -16,242 || B || -17,421 || -81,679 || 21,396
|-
| C || -39,883 || 29,111 || -30,955 || C || -32,369 || -101,732 || -95,398
|-
| D || -60,836 || 45,694 || 88,266 || D || -68,602 || -213,034 || -71,653
|-
| E || 47,073 || -84,070 || 125,289 || E || -166,488 || -154,580 || 52,981
|-
| F || 68,034 || -100,656 || 6,074 || F || -130,242 || -43,279 || 29,233
|-
| G || 79,896 || 20,048 || -8,640 || G || -145,191 || -63,324 || -87,552
|-
| H || 58,947 || 36,635 || 110,584 || H || -181,430 || -174,625 || -63,812
|-
|rowspan="8"  | 17 || A || -49,473 || -187,835 || -225,023 ||rowspan="8"  | 67 || A || 28,574 || -185,482 || -3,599
|-
| B || 11,721 || -96,543 || -173,052 || B || 112,033 || -165,763 || -24,837
|-
| C || 116,730 || -148,165 || -206,000 || C || 126,158 || -249,973 || -47,490
|-
| D || 55,542 || -239,454 || -257,974 || D || 42,708 || -269,694 || -26,245
|-
| E || -52,145 || -126,349 || -329,865 || E || 3,266 || -167,481 || -86,301
|-
| F || 9,042 || -35,066 || -277,895 || F || 86,727 || -147,756 || -107,547
|-
| G || 114,056 || -86,692 || -310,841 || G || 100,858 || -231,974 || -130,204
|-
| H || 52,868 || -177,982 || -362,815 || H || 17,398 || -251,697 || -108,962
|-
|rowspan="8"  | 18 || A || -3,291 || 58,392 || -67,764 ||rowspan="8"  | 68 || A || 29,360 || 117,807 || 150,925
|-
| B || -13,778 || 102,437 || -43,675 || B || 71,436 || 90,590 || 291,160
|-
| C || -5,168 || 128,262 || -87,137 || C || 69,409 || 236,665 || 320,118
|-
| D || 5,312 || 84,214 || -111,235 || D || 27,328 || 263,878 || 179,875
|-
| E || -52,753 || 53,542 || -80,440 || E || -113,483 || 107,712 || 191,829
|-
| F || -63,235 || 97,591 || -56,343 || F || -71,399 || 80,495 || 332,066
|-
| G || -54,637 || 123,415 || -99,809 || G || -73,438 || 226,569 || 361,027
|-
| H || -44,151 || 79,368 || -123,899 || H || -115,522 || 253,776 || 220,780
|-
|rowspan="8"  | 19 || A || -26,093 || -7,702 || -58,331 ||rowspan="8"  | 69 || A || -29,898 || -316,569 || -27,757
|-
| B || -9,516 || 50,270 || -87,212 || B || -3,303 || -231,839 || -96,619
|-
| C || 1,414 || 77,141 || -26,977 || C || -34,166 || -158,019 || -17,718
|-
| D || -15,165 || 19,167 || 1,901 || D || -60,770 || -242,744 || 51,144
|-
| E || 37,754 || -27,356 || -61,147 || E || 74,829 || -316,334 || 12,989
|-
| F || 54,321 || 30,622 || -90,023 || F || 101,434 || -231,605 || -55,870
|-
| G || 65,251 || 57,496 || -29,791 || G || 70,567 || -157,781 || 23,033
|-
| H || 48,679 || -0,478 || -0,919 || H || 43,957 || -242,502 || 91,900
|-
|rowspan="8"  | 20 || A || -19,714 || 149,429 || 242,552 ||rowspan="8"  | 70 || A || -6,324 || 9,528 || -76,129
|-
| B || 1,831 || 90,967 || 295,510 || B || 41,615 || 60,008 || 18,026
|-
| C || -28,051 || 34,114 || 244,886 || C || 111,580 || 123,170 || -51,458
|-
| D || -49,595 || 92,582 || 191,928 || D || 63,629 || 72,686 || -145,608
|-
| E || 53,299 || 143,413 || 206,219 || E || -87,062 || 94,230 || -80,430
|-
| F || 74,838 || 84,941 || 259,177 || F || -39,121 || 144,713 || 13,730
|-
| G || 44,962 || 28,098 || 208,556 || G || 30,844 || 207,863 || -55,761
|-
| H || 23,420 || 86,563 || 155,596 || H || -17,099 || 157,393 || -149,912
|-
|rowspan="8"  | 21 || A || -1,496 || 50,358 || 30,936 ||rowspan="8"  | 71 || A || -17,985 || -78,194 || -28,835
|-
| B || 27,698 || -33,805 || 72,754 || B || -26,841 || -37,289 || -60,085
|-
| C || 21,239 || -79,295 || -14,278 || C || -31,192 || -69,479 || -100,980
|-
| D || -7,960 || 4,866 || -56,097 || D || -22,337 || -110,381 || -69,738
|-
| E || 92,257 || 73,432 || 11,916 || E || -69,271 || -82,530 || -19,975
|-
| F || 121,451 || -10,729 || 53,733 || F || -78,128 || -41,630 || -51,220
|-
| G || 114,997 || -56,216 || -33,290 || G || -82,480 || -73,809 || -92,122
|-
| H || 85,798 || 27,943 || -75,111 || H || -73,620 || -114,708 || -60,875
|-
|rowspan="8"  | 22 || A || 1,996 || 57,819 || 135,802 ||rowspan="8"  | 72 || A || 21,689 || -401,128 || 108,706
|-
| B || -21,399 || -15,302 || 170,653 || B || 5,663 || -475,434 || 192,354
|-
| C || -80,895 || -24,407 || 111,614 || C || 55,901 || -404,719 || 264,808
|-
| D || -57,495 || 48,707 || 76,761 || D || 71,928 || -330,405 || 181,171
|-
| E || 56,972 || 16,835 || 86,737 || E || -78,288 || -353,674 || 131,716
|-
| F || 33,570 || -56,290 || 121,594 || F || -94,312 || -427,992 || 215,354
|-
| G || -25,921 || -65,389 || 62,542 || G || -44,075 || -357,269 || 287,815
|-
| H || -2,525 || 7,732 || 27,688 || H || -28,043 || -282,955 || 204,169
|-
|rowspan="8"  | 23 || A || 1,756 || -73,171 || 74,601 ||rowspan="8"  | 73 || A || 16,964 || 375,085 || 247,244
|-
| B || 2,774 || -40,542 || 124,645 || B || -0,723 || 487,938 || 239,053
|-
| C || 5,957 || -90,542 || 157,181 || C || -103,043 || 468,448 || 191,430
|-
| D || 4,927 || -123,176 || 107,143 || D || -85,357 || 355,597 || 199,631
|-
| E || 61,402 || -71,074 || 72,013 || E || -31,354 || 375,058 || 351,084
|-
| F || 62,425 || -38,444 || 122,050 || F || -49,041 || 487,912 || 342,883
|-
| G || 65,603 || -88,446 || 154,593 || G || -151,362 || 468,421 || 295,263
|-
| H || 64,585 || -121,078 || 104,550 || H || -133,668 || 355,563 || 303,466
|-
|rowspan="8"  | 24 || A || -58,762 || -191,413 || -8,972 ||rowspan="8"  | 74 || A || 7,716 || 107,422 || -66,020
|-
| B || -48,805 || -172,763 || 51,033 || B || -1,935 || 147,772 || -22,712
|-
| C || -106,418 || -194,311 || 67,296 || C || -46,907 || 114,225 || -1,494
|-
| D || -116,380 || -212,962 || 7,278 || D || -37,248 || 73,877 || -44,805
|-
| E || -33,681 || -248,301 || 4,548 || E || 46,209 || 78,358 || -30,361
|-
| F || -23,723 || -229,650 || 64,556 || F || 36,550 || 118,711 || 12,944
|-
| G || -81,343 || -251,196 || 80,810 || G || -8,424 || 85,168 || 34,161
|-
| H || -91,300 || -269,851 || 20,797 || H || 1,234 || 44,823 || -9,156
|-
|rowspan="8"  | 25 || A || -14,816 || 312,924 || -88,682 ||rowspan="8"  | 75 || A || -30,726 || -336,403 || 19,400
|-
| B || -99,513 || 377,487 || -176,113 || B || -8,274 || -403,305 || 91,613
|-
| C || -66,758 || 286,964 || -274,700 || C || -106,287 || -425,369 || 101,646
|-
| D || 17,936 || 222,392 || -187,261 || D || -128,739 || -358,470 || 29,430
|-
| E || -118,459 || 231,536 || -48,393 || E || -21,595 || -408,737 || -50,451
|-
| F || -203,157 || 296,104 || -135,819 || F || 0,859 || -475,635 || 21,764
|-
| G || -170,389 || 205,581 || -234,405 || G || -97,154 || -497,698 || 31,789
|-
| H || -85,696 || 141,016 || -146,977 || H || -119,608 || -430,804 || -40,424
|-
|rowspan="8"  | 26 || A || 48,259 || -41,077 || -191,310 ||rowspan="8"  | 76 || A || -43,660 || 204,215 || -164,580
|-
| B || 15,108 || 18,228 || -225,919 || B || -137,467 || 266,163 || -67,163
|-
| C || 22,176 || -17,052 || -293,135 || C || -80,085 || 400,105 || -97,083
|-
| D || 55,328 || -76,361 || -258,529 || D || 13,731 || 338,149 || -194,495
|-
| E || -20,040 || -73,506 || -181,453 || E || -143,830 || 222,926 || -272,945
|-
| F || -53,188 || -14,207 || -216,064 || F || -237,633 || 284,876 || -175,536
|-
| G || -46,122 || -49,489 || -283,288 || G || -180,246 || 418,814 || -205,454
|-
| H || -12,970 || -108,788 || -248,679 || H || -86,438 || 356,866 || -302,868
|-
|rowspan="8"  | 27 || A || 72,657 || -16,129 || -62,558 ||rowspan="8"  | 77 || A || 64,212 || 120,027 || -257,009
|-
| B || 49,381 || -127,697 || -84,673 || B || 80,180 || 174,246 || -367,841
|-
| C || 62,283 || -152,717 || 27,952 || C || 18,757 || 80,811 || -422,392
|-
| D || 85,557 || -41,144 || 50,077 || D || 2,797 || 26,594 || -311,568
|-
| E || -40,354 || 3,996 || -45,133 || E || -42,800 || 181,741 || -242,230
|-
| F || -63,620 || -107,567 || -67,253 || F || -26,827 || 235,964 || -353,060
|-
| G || -50,715 || -132,594 || 45,378 || G || -88,243 || 142,527 || -407,615
|-
| H || -27,446 || -21,031 || 67,494 || H || -104,216 || 88,314 || -296,791
|-
|rowspan="8"  | 28 || A || 70,548 || -98,767 || -97,987 ||rowspan="8"  | 78 || A || 15,590 || 20,752 || 87,279
|-
| B || 20,523 || -114,915 || -70,311 || B || 10,979 || 72,163 || 141,186
|-
| C || 1,148 || -140,518 || -120,289 || C || -63,119 || 63,468 || 143,145
|-
| D || 51,172 || -124,376 || -147,964 || D || -58,513 || 12,056 || 89,234
|-
| E || 96,057 || -149,887 || -81,691 || E || 23,218 || -32,646 || 138,865
|-
| F || 46,030 || -166,024 || -54,022 || F || 18,607 || 18,766 || 192,767
|-
| G || 26,651 || -191,631 || -103,995 || G || -55,487 || 10,075 || 194,725
|-
| H || 76,676 || -175,485 || -131,667 || H || -50,881 || -41,335 || 140,821
|-
|rowspan="8"  | 29 || A || 19,154 || 157,384 || 153,406 ||rowspan="8"  | 79 || A || 7,879 || -100,695 || 129,989
|-
| B || 78,894 || 47,638 || 170,584 || B || -72,908 || -136,829 || 155,646
|-
| C || -30,186 || -13,998 || 156,108 || C || -32,830 || -173,666 || 229,988
|-
| D || -89,920 || 95,745 || 138,927 || D || 47,968 || -137,537 || 204,328
|-
| E || 40,151 || 149,384 || 29,293 || E || -11,004 || -24,351 || 178,007
|-
| F || 99,887 || 39,643 || 46,473 || F || -91,798 || -60,488 || 203,669
|-
| G || -9,189 || -22,001 || 31,991 || G || -51,717 || -97,333 || 278,004
|-
| H || -68,929 || 87,746 || 14,814 || H || 29,074 || -61,199 || 252,351
|-
|rowspan="8"  | 30 || A || -0,832 || 148,123 || -55,062 ||rowspan="8"  | 80 || A || -82,391 || 19,624 || 195,867
|-
| B || -3,177 || 83,383 || -82,664 || B || -126,755 || 13,600 || 235,381
|-
| C || 4,481 || 55,693 || -18,369 || C || -155,874 || -21,964 || 197,277
|-
| D || 6,819 || 120,437 || 9,226 || D || -111,512 || -15,951 || 157,758
|-
| E || -70,802 || 147,260 || -47,104 || E || -55,013 || -27,965 || 219,355
|-
| F || -73,142 || 82,515 || -74,709 || F || -99,374 || -33,982 || 258,868
|-
| G || -65,481 || 54,832 || -10,407 || G || -128,500 || -69,550 || 220,760
|-
| H || -63,142 || 119,582 || 17,182 || H || -84,143 || -63,530 || 181,251
|-
|rowspan="8"  | 31 || A || -62,187 || -290,838 || 74,947 ||rowspan="8"  | 81 || A || -10,413 || 205,562 || -99,978
|-
| B || -148,419 || -277,181 || 52,556 || B || -20,573 || 98,681 || -113,175
|-
| C || -122,249 || -237,171 || -23,850 || C || 75,377 || 83,682 || -65,540
|-
| D || -36,007 || -250,826 || -1,461 || D || 85,534 || 190,557 || -52,338
|-
| E || -63,819 || -370,443 || 32,697 || E || -59,316 || 198,329 || -3,776
|-
| F || -150,059 || -356,788 || 10,309 || F || -69,474 || 91,448 || -16,972
|-
| G || -123,886 || -316,776 || -66,108 || G || 26,476 || 76,444 || 30,672
|-
| H || -37,641 || -330,428 || -43,713 || H || 36,626 || 183,327 || 43,869
|-
|rowspan="8"  | 32 || A || 21,688 || 24,157 || 173,270 ||rowspan="8"  | 82 || A || -45,436 || 279,685 || -163,035
|-
| B || 35,864 || 10,746 || 240,885 || B || -84,684 || 320,165 || -149,056
|-
| C || 51,742 || 78,562 || 251,010 || C || -51,030 || 361,055 || -172,936
|-
| D || 37,573 || 91,973 || 183,389 || D || -11,771 || 320,577 || -186,922
|-
| E || -45,394 || 37,383 || 189,943 || E || -71,915 || 271,648 || -214,121
|-
| F || -31,224 || 23,972 || 257,570 || F || -111,174 || 312,136 || -200,137
|-
| G || -15,339 || 91,783 || 267,694 || G || -77,514 || 353,016 || -224,014
|-
| H || -29,509 || 105,189 || 200,071 || H || -38,255 || 312,536 || -237,997
|-
|rowspan="8"  | 33 || A || 44,183 || -183,082 || -7,037 ||rowspan="8"  | 83 || A || -25,582 || -156,980 || 151,171
|-
| B || 38,428 || -219,288 || 83,764 || B || 36,128 || -53,249 || 236,515
|-
| C || 29,366 || -128,530 || 119,376 || C || 35,072 || -146,795 || 350,972
|-
| D || 35,115 || -92,329 || 28,585 || D || -26,636 || -250,524 || 265,628
|-
| E || -53,143 || -189,398 || -15,719 || E || 108,740 || -205,366 || 112,860
|-
| F || -58,891 || -225,601 || 75,075 || F || 170,451 || -101,635 || 198,212
|-
| G || -67,959 || -134,848 || 110,694 || G || 169,393 || -195,183 || 312,666
|-
| H || -62,213 || -98,642 || 19,902 || H || 107,685 || -298,907 || 227,318
|-
|rowspan="8"  | 34 || A || 39,453 || 117,439 || -16,522 ||rowspan="8"  | 84 || A || -46,635 || 166,791 || 13,631
|-
| B || 33,907 || 39,298 || 86,838 || B || -71,644 || 60,654 || 67,095
|-
| C || 42,312 || -64,157 || 9,066 || C || 46,747 || 43,133 || 87,695
|-
| D || 47,865 || 13,995 || -94,293 || D || 71,758 || 149,260 || 34,235
|-
| E || 168,764 || 120,807 || -7,024 || E || -56,922 || 223,156 || 120,711
|-
| F || 163,206 || 42,664 || 96,330 || F || -81,942 || 117,013 || 174,178
|-
| G || 171,612 || -60,794 || 18,564 || G || 36,453 || 99,495 || 194,776
|-
| H || 177,166 || 17,359 || -84,797 || H || 61,469 || 205,633 || 141,314
|-
|rowspan="8"  | 35 || A || 41,180 || 17,938 || -167,878 ||rowspan="8"  | 85 || A || -51,182 || -51,542 || 18,228
|-
| B || 37,801 || 67,734 || -245,735 || B || -118,414 || -85,354 || 130,674
|-
| C || 106,456 || 121,247 || -214,492 || C || -103,162 || -216,350 || 100,410
|-
| D || 109,831 || 71,451 || -136,634 || D || -35,929 || -182,537 || -12,038
|-
| E || 103,051 || -38,713 || -206,801 || E || 65,247 || -53,904 || 87,134
|-
| F || 99,674 || 11,090 || -284,655 || F || -1,994 || -87,717 || 199,581
|-
| G || 168,327 || 64,599 || -253,411 || G || 13,265 || -218,713 || 169,308
|-
| H || 171,707 || 14,805 || -175,566 || H || 80,501 || -184,899 || 56,863
|-
|rowspan="8"  | 36 || A || 18,551 || -42,342 || 65,222 ||rowspan="8"  | 86 || A || -10,928 || 153,829 || -86,720
|-
| B || 22,249 || -14,504 || -47,899 || B || -17,656 || 30,629 || -10,708
|-
| C || 81,529 || -112,378 || -70,056 || C || 125,085 || 37,646 || 13,298
|-
| D || 77,831 || -140,224 || 43,063 || D || 131,820 || 160,845 || -62,715
|-
| E || -81,736 || -99,169 || 47,947 || E || -35,020 || 229,818 || 34,307
|-
| F || -78,037 || -71,326 || -65,177 || F || -41,751 || 106,619 || 110,312
|-
| G || -18,748 || -169,207 || -87,320 || G || 100,994 || 113,639 || 134,323
|-
| H || -22,459 || -197,050 || 25,792 || H || 107,727 || 236,836 || 58,305
|-
|rowspan="8"  | 37 || A || 21,819 || 222,345 || 35,209 ||rowspan="8"  | 87 || A || 29,723 || -86,649 || -35,592
|-
| B || 64,934 || 299,487 || 73,760 || B || 17,622 || -41,898 || 100,238
|-
| C || 62,447 || 257,521 || 160,516 || C || -74,921 || 59,585 || 58,562
|-
| D || 19,334 || 180,377 || 121,968 || D || -62,830 || 14,829 || -77,269
|-
| E || 108,020 || 182,552 || 18,432 || E || -79,309 || -177,746 || -15,287
|-
| F || 151,129 || 259,692 || 56,978 || F || -91,403 || -132,992 || 120,547
|-
| G || 148,641 || 217,725 || 143,745 || G || -183,957 || -31,512 || 78,877
|-
| H || 105,528 || 140,591 || 105,197 || H || -171,861 || -76,268 || -56,958
|-
|rowspan="8"  | 38 || A || -16,265 || -55,427 || -71,646 ||rowspan="8"  | 88 || A || 50,033 || 278,002 || -139,931
|-
| B || -25,671 || -131,166 || -43,586 || B || 50,039 || 216,948 || -236,550
|-
| C || -106,270 || -124,213 || -51,827 || C || 50,034 || 313,571 || -297,607
|-
| D || -96,861 || -48,463 || -79,890 || D || 50,022 || 374,625 || -200,989
|-
| E || -10,987 || -84,193 || -147,527 || E || 164,336 || 278,018 || -139,927
|-
| F || -20,397 || -159,943 || -119,457 || F || 164,339 || 216,961 || -236,546
|-
| G || -100,991 || -152,981 || -127,706 || G || 164,335 || 313,582 || -297,603
|-
| H || -91,590 || -77,240 || -155,770 || H || 164,319 || 374,643 || -200,984
|-
|rowspan="8"  | 39 || A || -53,192 || 129,839 || 73,707 ||rowspan="8"  | 89 || A || 3,685 || 475,694 || -68,483
|-
| B || -23,735 || 106,391 || 30,249 || B || 50,250 || 450,269 || -84,841
|-
| C || 20,100 || 142,101 || 40,698 || C || 80,158 || 484,614 || -53,084
|-
| D || -9,356 || 165,552 || 84,151 || D || 33,588 || 510,041 || -36,721
|-
| E || -30,466 || 91,359 || 109,873 || E || -0,736 || 440,246 || -25,970
|-
| F || -1,001 || 67,914 || 66,420 || F || 45,829 || 414,815 || -42,337
|-
| G || 42,831 || 103,618 || 76,868 || G || 75,737 || 449,169 || -10,583
|-
| H || 13,370 || 127,067 || 120,318 || H || 29,166 || 474,598 || 5,778
|-
|rowspan="8"  | 40 || A || -47,254 || -39,090 || -47,292 ||rowspan="8"  | 90 || A || 40,806 || -248,916 || 46,046
|-
| B || -44,379 || -81,587 || -14,591 || B || 64,657 || -294,153 || 16,219
|-
| C || -95,649 || -74,176 || -0,454 || C || 71,528 || -259,296 || -31,137
|-
| D || -98,528 || -31,681 || -33,159 || D || 47,679 || -214,070 || -1,306
|-
| E || -62,953 || -71,075 || -87,471 || E || 94,554 || -233,299 || 65,333
|-
| F || -60,073 || -113,573 || -54,767 || F || 118,401 || -278,535 || 35,513
|-
| G || -111,345 || -106,159 || -40,627 || G || 125,272 || -243,676 || -11,850
|-
| H || -114,228 || -63,675 || -73,338 || H || 101,419 || -198,451 || 17,980
|-
|rowspan="8"  | 41 || A || -74,761 || 30,164 || 183,471 ||rowspan="8"  | 91 || A || -38,767 || 105,181 || -70,416
|-
| B || -70,723 || 95,811 || 316,035 || B || -15,246 || 102,931 || -130,225
|-
| C || -70,850 || 228,428 || 250,361 || C || -30,973 || 40,700 || -134,058
|-
| D || -74,898 || 162,771 || 117,799 || D || -54,488 || 42,950 || -74,264
|-
| E || -222,685 || 31,843 || 187,150 || E || -96,502 || 121,202 || -93,723
|-
| F || -218,651 || 97,487 || 319,713 || F || -72,998 || 118,953 || -153,533
|-
| G || -218,781 || 230,096 || 254,042 || G || -88,711 || 56,727 || -157,367
|-
| H || -222,817 || 164,453 || 121,479 || H || -112,223 || 58,978 || -97,562
|-
|rowspan="8"  | 42 || A || -41,878 || -226,942 || -3,086 ||rowspan="8"  | 92 || A || -6,294 || 255,663 || -231,651
|-
| B || -38,826 || -304,573 || -25,689 || B || 38,261 || 154,536 || -249,454
|-
| C || -107,693 || -295,222 || -67,118 || C || 116,077 || 175,124 || -171,665
|-
| D || -110,749 || -217,588 || -44,521 || D || 71,528 || 276,260 || -153,860
|-
| E || 0,483 || -206,134 || -68,822 || E || -73,289 || 212,332 || -153,138
|-
| F || 3,540 || -283,767 || -91,425 || F || -28,737 || 111,199 || -170,950
|-
| G || -65,337 || -274,417 || -132,855 || G || 49,081 || 131,789 || -93,168
|-
| H || -68,390 || -196,782 || -110,245 || H || 4,523 || 232,920 || -75,365
|-
|rowspan="8"  | 43 || A || -7,819 || -55,712 || 12,582 ||rowspan="8"  | 93 || A || -75,723 || 244,498 || -135,815
|-
| B || -60,330 || -80,620 || 3,655 || B || -82,559 || 229,007 || -46,701
|-
| C || -74,640 || -37,204 || -33,324 || C || -85,390 || 139,720 || -62,434
|-
| D || -22,133 || -12,297 || -24,402 || D || -78,555 || 155,200 || -151,551
|-
| E || 14,446 || -86,572 || -32,251 || E || 14,681 || 240,532 || -129,582
|-
| F || -38,074 || -111,488 || -41,174 || F || 7,850 || 225,046 || -40,465
|-
| G || -52,388 || -68,062 || -78,169 || G || 5,021 || 135,755 || -56,195
|-
| H || 0,130 || -43,150 || -69,240 || H || 11,847 || 151,234 || -145,314
|-
|rowspan="8"  | 44 || A || 12,124 || 29,493 || -61,344 ||rowspan="8"  | 94 || A || 26,421 || -45,661 || 265,356
|-
| B || 6,872 || 5,332 || 8,602 || B || 2,414 || 39,092 || 221,112
|-
| C || 80,039 || 14,134 || 17,146 || C || 59,763 || 15,365 || 144,530
|-
| D || 85,293 || 38,298 || -52,807 || D || 83,771 || -69,402 || 188,771
|-
| E || 1,041 || 99,080 || -38,137 || E || -50,083 || -90,051 || 221,820
|-
| F || -4,216 || 74,920 || 31,812 || F || -74,083 || -5,292 || 177,589
|-
| G || 68,953 || 83,727 || 40,347 || G || -16,738 || -29,019 || 100,998
|-
| H || 74,216 || 107,887 || -29,595 || H || 7,266 || -113,787 || 145,242
|-
|rowspan="8"  | 45 || A || -14,290 || 305,473 || -38,546 ||rowspan="8"  | 95 || A || 59,456 || 169,514 || -55,338
|-
| B || -33,289 || 244,676 || -26,483 || B || 72,883 || 88,087 || -110,613
|-
| C || -88,751 || 266,977 || -1,417 || C || 27,474 || 132,458 || -187,016
|-
| D || -69,763 || 327,772 || -13,482 || D || 14,051 || 213,898 || -131,738
|-
| E || -41,951 || 302,495 || -97,100 || E || 146,782 || 205,112 || -86,567
|-
| F || -60,942 || 241,699 || -85,042 || F || 160,205 || 123,674 || -141,848
|-
| G || -116,416 || 264,001 || -59,971 || G || 114,796 || 168,052 || -218,246
|-
| H || -97,415 || 324,801 || -72,038 || H || 101,372 || 249,496 || -162,967
|-
|rowspan="8"  | 46 || A || 42,815 || 56,809 || 65,624 ||rowspan="8"  | 96 || A || 87,799 || 9,898 || 157,693
|-
| B || 59,197 || 180,782 || 131,551 || B || 168,746 || 47,893 || 60,760
|-
| C || 42,456 || 248,403 || 8,546 || C || 118,896 || 169,835 || 66,937
|-
| D || 26,080 || 124,431 || -57,384 || D || 37,963 || 131,834 || 163,874
|-
| E || -96,594 || 63,254 || 88,136 || E || 179,213 || 42,745 || 246,898
|-
| F || -80,215 || 187,223 || 154,067 || F || 260,161 || 80,738 || 149,963
|-
| G || -96,957 || 254,856 || 31,063 || G || 210,308 || 202,685 || 156,145
|-
| H || -113,336 || 130,881 || -34,871 || H || 129,369 || 164,682 || 253,079
|-
|rowspan="8"  | 47 || A || 16,659 || 216,633 || -245,483 ||rowspan="8"  | 97 || A || 15,320 || 50,805 || 120,047
|-
| B || 69,269 || 215,380 || -216,984 || B || 16,360 || 122,350 || 229,948
|-
| C || 78,347 || 272,789 || -231,217 || C || 13,706 || 12,471 || 301,494
|-
| D || 25,740 || 274,043 || -259,713 || D || 12,665 || -59,065 || 191,589
|-
| E || -10,379 || 233,470 || -194,822 || E || 146,436 || 48,013 || 120,621
|-
| F || 42,217 || 232,216 || -166,326 || F || 147,467 || 119,556 || 230,527
|-
| G || 51,294 || 289,627 || -180,557 || G || 144,812 || 9,675 || 302,069
|-
| H || -1,311 || 290,873 || -209,051 || H || 143,779 || -61,856 || 192,165
|-
|rowspan="8"  | 48 || A || -85,888 || 301,572 || -21,383 ||rowspan="8"  | 98 || A || 24,696 || 289,570 || -67,006
|-
| B || -104,608 || 351,179 || -120,655 || B || -33,685 || 352,622 || -151,554
|-
| C || -200,846 || 394,044 || -81,085 || C || 67,752 || 359,704 || -216,316
|-
| D || -182,129 || 344,439 || 18,178 || D || 126,129 || 296,647 || -131,759
|-
| E || -30,635 || 393,030 || 13,903 || E || -4,212 || 187,067 || -123,498
|-
| F || -49,346 || 442,638 || -85,362 || F || -62,592 || 250,121 || -208,043
|-
| G || -145,584 || 485,510 || -45,798 || G || 38,848 || 257,198 || -272,797
|-
| H || -126,869 || 435,905 || 53,478 || H || 97,217 || 194,146 || -188,253
|-
|rowspan="8"  | 49 || A || 29,200 || -214,223 || 271,379 ||rowspan="8"  | 99 || A || -21,738 || -63,055 || 1,821
|-
| B || -20,130 || -197,446 || 186,408 || B || 54,881 || 4,990 || -19,130
|-
| C || 22,774 || -107,751 || 179,213 || C || 24,411 || 8,511 || -119,116
|-
| D || 72,106 || -124,541 || 264,192 || D || -52,202 || -59,530 || -98,175
|-
| E || 104,453 || -254,365 || 219,770 || E || -86,078 || 16,289 || 24,217
|-
| F || 55,119 || -237,577 || 134,791 || F || -9,475 || 84,337 || 3,277
|-
| G || 98,023 || -147,884 || 127,604 || G || -39,942 || 87,862 || -96,718
|-
| H || 147,360 || -164,667 || 212,581 || H || -116,549 || 19,814 || -75,767
|-
 
 


==Dokumenty ke stažení==
Parametry užívaných elipsoidů naleznete [ftp://athena.fsv.cvut.cz/TG1/helmert/elipsoidy.png zde].


Stručné poznámky k obecné a diferenciální Helmertově transformaci: [ftp://athena.fsv.cvut.cz/TG1/helmert/helmert.pdf helmert.pdf].


Stručné poznámky k vyrovnání MNČ: [ftp://athena.fsv.cvut.cz/TG1/helmert/mnc.pdf mnc.pdf].


|rowspan="8"  | 50 || A || -46,150 || -37,165 || -63,817 ||rowspan="8" | 100 || A || -13,094 || -292,595 || -36,143
Užitečný text k různým typům transformací, včetně Helmertovy transformace: [ftp://athena.fsv.cvut.cz/TG1/helmert/transformace.pdf transformace.pdf].
|-
| B || -113,887 || -30,922 || -190,379 || B || 45,011 || -174,946 || -68,398
|-
| C || -8,846 || 52,106 || -242,495 || C || 152,991 || -207,928 || 5,840
|-
| D || 58,887 || 45,878 || -115,939 || D || 94,883 || -325,573 || 38,088
|-
| E || 24,724 || -154,257 || -107,523 || E || 43,665 || -350,296 || -144,34
|-
| F || -43,010 || -148,016 || -234,076 || F || 101,779 || -232,648 || -176,594
|-
| G || 62,026 || -64,979 || -286,205 || G || 209,752 || -265,623 || -102,354
|-
| H || 129,768 || -71,222 || -159,642 || H || 151,649 || -383,269 || -70,100
|-
|rowspan="8" | 101 || A || -23,015 || -35,636 || -89,787 ||rowspan="8" | 102 || A || 74,487 || 131,213 || -147,528
|-
| B || 67,309 || -11,943 || -172,643 || B || 43,481 || 203,541 || -267,277
|-
| C || 129,377 || -113,094 || -133,901 || C || 28,144 || 79,865 || -338,002
|-
| D || 39,057 || -136,789 || -51,048 || D || 59,158 || 7,545 || -218,252
|-
| E || -82,804 || -104,861 || -174,752 || E || -64,564 || 128,730 || -113,025
|-
| F || 7,520 || -81,177 || -257,608 || F || -95,576 || 201,049 || -232,773
|-
| G || 69,593 || -182,324 || -218,864 || G || -110,905 || 77,375 || -303,500
|-
| H || -20,727 || -206,010 || -136,009 || H || -79,891 || 5,0560 || -183,744
|}
-->


Pro testování správnosti vašich výpočtů můžete využít modelové náhodně vygenerované zadání s přehledem výsledků
* pro obecnou Helmertovu transformaci: [ftp://athena.fsv.cvut.cz/TG1/helmert/tg1ul4_helm3D_test.pdf tg1ul4_helm3D_test.pdf];
* pro diferenciální Helmertovu transformaci: [ftp://athena.fsv.cvut.cz/TG1/helmert/tg1ul4_helm3Ddif_test.pdf tg1ul4_helm3Ddif_test.pdf].
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[[152TG1|152TG1 Teoretická geodézie 1]]
[[152TG1|152TG1 Teoretická geodézie 1]]
{{Teoretická geodézie}}
{{Teoretická geodézie}}

Aktuální verze z 27. 11. 2014, 18:15

Název úlohy

Helmertova prostorová transformace

Zadání úlohy

Známy jsou zeměpisné elipsoidické souřadnice deseti identických bodů na elipsoidu WGS84 a na Besselově elipsoidu. Souřadnice identických bodů převeďte v obou souřadnicových soustavách příslušných elipsoidů na souřadnice kartézské. Vypočtěte transformační klíč Helmertovy prostorové transformace mezi oběma kartézskými souřadnicovými soustavami a uveďte též aposteriorní charakteristiky přesnosti vyrovnaných hodnot transformačního klíče plynoucí ze zavedení podmínky MNČ. Výsledné posuny počátků souřadnicových soustav uveďte v metrech, výsledné rotační úhly ve stupních, minutách, vteřinách. Rovněž vypočtěte vyrovnané hodnoty souřadnic identických bodů (zprostředkujících veličin) včetně jejich směrodatných odchylek.

Při výpočtu uvažujte transformaci ze souřadnicové soustavy elipsoidu WGS84 (vstupní soustava S1) do souřadnicové soustavy Besselova elipsoidu (výstupní soustava S2). Transformaci proveďte buď pomocí obecné Helmertovy sedmiprvkové transformace, nebo pomocí diferenciální (zjednodušené) Helmertovy transformace. Zvolený způsob řešení musí být jasně dokumentován v technické zprávě.

Numerické zadání

Numerické zadání s elipsoidickými souřadnicemi identických bodů v obou soustavách S1 a S2 naleznete v adresáři ftp://athena.fsv.cvut.cz/TG1/helmert/zadani v souboru tg1_2014_u4_xx.m, kde xx je číslo zadání. Číslo zadání studenta odpovídá číslování uvedenému na stránkách cvičení TG1.

Dokumenty ke stažení

Parametry užívaných elipsoidů naleznete zde.

Stručné poznámky k obecné a diferenciální Helmertově transformaci: helmert.pdf.

Stručné poznámky k vyrovnání MNČ: mnc.pdf.

Užitečný text k různým typům transformací, včetně Helmertovy transformace: transformace.pdf.

Pro testování správnosti vašich výpočtů můžete využít modelové náhodně vygenerované zadání s přehledem výsledků

152TG1 Teoretická geodézie 1

Citováno z „https://geo.fsv.cvut.cz/index.php?title=152TG1_Teoretická_geodézie_1_-_úloha_4&oldid=30065“