152ZFG Základy fyzikální geodézie - úloha1: Porovnání verzí

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==Zadání úlohy==
==Zadání úlohy==
;Příklad 1.1
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.
Je definována geodetická křivka na referenční kouli sférickými souřadnicemi bodu A <math>\left( \varphi_A, \lambda_A \right)</math> a azimutem v tomto bodu <math> \alpha_A </math>. Vypočítejte pomocí vzorců sférické trigonometrie souřadnice bodu B, který leží na této geodetické křivce v zadané vzdálenosti <math> l_A </math> od bodu A. Dále vypočítejte azimut této geodetické křivky v bodě B. Poloměr referenční koule, na které budou výpočty provedeny, volte roven střednímu poloměru křivosti v bodě A (uvažujte parametry Besselova elipsoidu).


;Příklad 1.2
==Numerické zadání úlohy==
Je zadána geodetická křivka na Besselově elipsoidu geodetickými souřadnicemi bodu A <math>\left( \varphi_A, \lambda_A \right)</math> a azimutem v tomto bodu <math> \alpha_A </math>, stejnými hodnotami jako v předchozí části. Vypočítejte polohu bodu B, který leží na této geodetické křivce ve vzdálenosti <math> l_A </math> od bodu A. Dále pro zadanou geodetickou křivku vypočítejte nejbližší průsečík s nultým poledníkem a nejbližší průsečík s rovníkem. Pro hledané průsečíky zjistěte i azimuty geodetické křivky v těchto bodech. Geodetickou úlohu řešte na Besselově elipsoidu.


==Numerické zadání úlohy==
Souřadnice transformovaných bodů v systému S2 jsou pro všechna zadání stejné:
{| class="border"
{| class="border"
|rowspan="2" valign="top"| číslo zadání
|bod
|colspan="3" | <math> \phi_A </math>
|x [m]
|colspan="3" | <math> \lambda_A </math>
|y [m]
|colspan="3" | <math> \alpha_A </math>
|z [m]
|| <math> l_A </math> 
|-
| 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
|-
|-
| [<math> \circ </math>]
| G || 100,000 || 100,000 || 100,000
|| [<math>\ '\ </math>]
|| [<math>\ ''\ </math>]
| [<math> \circ </math>]
|| [<math>\ '\ </math>]
|| [<math>\ ''\ </math>]
| [<math> \circ </math>]
|| [<math>\ '\ </math>]
|| [<math>\ ''\ </math>]
|| [m]
|-
|-
|   1|| 50||  15||  48.170||  16||  6||  48.457||  97||  33||  4.142||  626011.79
| H || 0,000 || 100,000 || 100,000
|-
|  2||  50||  19||  5.803||  13||  50||  33.605||  42||  55||  8.140||  543061.09
|-
|  3||  49||  57||  30.040||  14||  30||  16.079||  74||  49||  58.168||  491271.78
|-
|  4||  48||  20||  31.749||  15||  50||  53.515||  292||  52||  55.508||  696671.13
|-
|  5||  50||  50||  55.077||  12||  0|| 25.884||  102||  5||  47.791||  503751.05
|-
|  6||  48||  2||  43.092||  13||  13||  43.590||  115||  11||  13.571||  703251.93
|-
|  7||  48||  49||  49.444||  17||  8||  16.782||  79||  36||  17.654||  450491.06
|-
|  8||  51||  51||  11.037||  14||  32||  1.654||  128||  36||  34.240||  463451.84
|-
|  9||  49||  29||  10.746||  17||  29||  53.632||  88||  17||  58.785||  687051.11
|-
|  10||  51||  19||  6.991||  15||  20||  39.106||  297||  9||  13.774||  540311.35
|-
|  11||  49||  7||  19.135||  16||  34||  9.554||  295||  58||  1.912||  686301.78
|-
|  12||  50||  43||  47.608||  15||  47||  10.571||  91||  14|| 41.486||  608461.14
|-
|  13||  51||  23||  12.099||  16||  17||  33.924||  260||  6||  34.090||  437141.26
|-
|  14||  48||  0||  4.501||  14||  51||  56.790||  93||  53||  19.194||  481971.60
|-
|  15||  51||  30||  12.964||  15||  28||  37.709||  51||  5||  57.285||  422931.66
|-
|  16||  50||  18||  19.974||  12||  44||  3.888||  223||  27||  39.555||  515531.45
|-
|  17||  48||  55||  47.375||  15||  14||  1.550||  263||  32||  35.476||  661231.19
|-
|  18||  51||  10||  60.776||  14||  5||  17.013||  24||  19||  41.829||  631681.56
|-
|  19||  50||  14||  20.100||  14||  24||  42.260||  43||  52||  45.185||  432651.28
|-
|  20||  49||  56||  4.964||  17||  22||  43.362||  79||  27||  24.425||  666951.10
|-
|  21||  50||  35||  11.039||  13||  12||  36.662||  241||  1||  5.190||  491061.65
|-
|  22||  49||  45||  13.081||  17||  16||  3.243||  283||  49||  25.106||  634241.85
|-
|  23||  49||  39||  55.844||  13||  57||  10.843||    2||  6||  9.582||  535911.28
|-
|  24||  50||  33||  51.574||  17||  25||  40.071||  168||  27||  22.508||  645351.35
|-
|  25||  50||  3||  16.811||  16||  52||  42.352||  113||  44||  50.633||  619831.91
|-
|  26||  49||  16||  54.154||  15||  5||  12.602||  293||  10||  52.530||  401491.69
|-
|  27||  48||  46||  57.076||  14||  19||  15.032||    3||  32||  49.120||  583161.57
|-
|  28||  48||  17||  13.990||  16||  49||  29.635||  68||  43||  3.039||  617241.07
|-
|  29||  50||  34||  40.068||  17||  48||  8.484||  282||  42||  40.157||  618071.60
|-
|  30||  48||  7||  42.443||  15||  50||  36.424||  215||  22||  59.583||  715251.30
|-
|  31||  48||  14||  41.409||  12||  31||  38.685||  124||  20||  1.406||  658301.79
|-
|  32||  49||  31||  34.104||  17||  49||  53.206||    0||  56||  15.799||  727601.85
|-
|  33||  51||  30||  43.138||  17||  35||  24.391||  242||  50||  18.699||  714121.81
|-
|  34||  51||  26||  43.735||  13||  42||  29.460||  79||  15||  55.425||  430511.68
|-
|  35||  48||  53||  16.986||  13||  57||  22.528||  281||  42||  36.254||  504001.33
|-
|  36||  51||  37||  12.657||  12||  46||  36.338||  292||  40||  17.549||  699181.01
|-
|  37||  50||  6||  44.285||  12||  47||  32.129||  77||  58||  4.074||  502571.56
|-
|  38||  50||  30||  37.118||  12||  10||  14.030||  205||  32||  29.596||  437001.55
|-
|  39||  49||  33||  32.828||  12||  24||  4.085||  152||  49||  58.624||  462491.83
|-
|  40||  48||  36||  35.705||  12||  0||  31.175||  216||  59||  52.398||  619731.37
|-
|  41||  49||  21||  12.198||  17||  8||  42.367||  96||  36||  53.429||  479041.69
|-
|  42||  48||  53||  6.731||  16||  20||  25.862||  183||  54||  52.598||  616661.40
|-
|  43||  51||  52||  24.128||  17||  18||  55.520||  20||  13||  44.127||  655071.40
|-
|  44||  48||  10||  36.574||  16||  15||  14.513||  42||  47||  25.819||  623291.67
|}
|}


{{Teoretická geodézie}}
 
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
|-
 
 
 
 
 
 
|rowspan="8"  | 50 || A || -46,150 || -37,165 || -63,817 ||rowspan="8" | 100 || A || -13,094 || -292,595 || -36,143
|-
| 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
|}
[[Kategorie:Výuka]]

Verze z 4. 2. 2011, 10:36

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.

Numerické zadání úlohy

Souřadnice transformovaných bodů v systému S2 jsou pro všechna zadání stejné:

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


Souřadnice transformovaných bodů v systému S1:

číslo zadání bod x [m] y [m] z [m] číslo zadání bod x [m] y [m] z [m]
1 A 93,170 -295,133 48,646 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
2 A -30,662 -150,076 -11,197 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
3 A -58,640 90,084 -100,064 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
4 A -22,297 366,540 79,651 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
5 A -1,349 -53,984 107,577 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
6 A 20,503 393,620 -122,535 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
7 A 23,910 233,940 -36,316 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
8 A -20,027 -70,648 74,791 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
9 A 7,668 475,089 117,180 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
10 A -10,754 207,875 -47,920 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
11 A 31,664 -50,081 155,170 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
12 A -31,701 -485,743 57,217 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
13 A -4,189 -333,380 49,056 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
14 A 88,609 12,300 -33,202 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
15 A 62,366 -70,046 -71,843 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
16 A -72,703 -75,016 102,975 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
17 A -49,473 -187,835 -225,023 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
18 A -3,291 58,392 -67,764 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
19 A -26,093 -7,702 -58,331 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
20 A -19,714 149,429 242,552 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
21 A -1,496 50,358 30,936 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
22 A 1,996 57,819 135,802 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
23 A 1,756 -73,171 74,601 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
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