152ZFG Základy fyzikální geodézie - úloha3
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
číslo zadání | bod | x [m] | y [m] | z [m] | číslo zadání | bod | x [m] | y [m] | z [m] | číslo zadání | bod | x [m] | y [m] | z [m] |
1 | 50 | 15 | 48.170 | 16 | 6 | 48.457 | 97 | 33 | 4.142 | 626011.79 | ||||
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 | ||||
45 | 50 | 2 | 55.470 | 17 | 20 | 19.369 | 152 | 0 | 24.562 | 502851.98 | ||||
46 | 48 | 40 | 29.685 | 17 | 45 | 43.826 | 10 | 22 | 51.331 | 610361.35 | ||||
47 | 49 | 9 | 57.177 | 12 | 27 | 43.765 | 272 | 4 | 1.093 | 694141.67 | ||||
48 | 51 | 30 | 29.602 | 13 | 49 | 49.335 | 137 | 45 | 30.444 | 448601.42 | ||||
49 | 48 | 40 | 9.507 | 12 | 3 | 27.772 | 7 | 36 | 32.571 | 430671.04 | ||||
50 | 48 | 7 | 57.240 | 14 | 57 | 5.203 | 182 | 18 | 6.562 | 461701.12 | ||||
51 | 51 | 14 | 40.465 | 16 | 25 | 52.947 | 95 | 40 | 5.798 | 583001.99 | ||||
52 | 49 | 45 | 6.890 | 17 | 28 | 36.212 | 238 | 32 | 10.263 | 512951.13 | ||||
53 | 51 | 21 | 8.136 | 13 | 15 | 1.294 | 171 | 55 | 25.830 | 627161.54 | ||||
54 | 50 | 17 | 54.683 | 12 | 48 | 43.606 | 219 | 57 | 27.016 | 482661.80 | ||||
55 | 48 | 12 | 45.955 | 14 | 4 | 38.842 | 259 | 49 | 31.187 | 509811.05 | ||||
56 | 49 | 1 | 3.703 | 14 | 3 | 12.192 | 283 | 44 | 28.156 | 569561.76 | ||||
57 | 50 | 45 | 34.540 | 13 | 20 | 57.175 | 228 | 3 | 37.062 | 714511.39 | ||||
58 | 49 | 51 | 17.466 | 15 | 8 | 39.213 | 52 | 10 | 25.410 | 668641.43 | ||||
59 | 48 | 19 | 43.377 | 14 | 33 | 48.899 | 53 | 1 | 57.830 | 518591.62 | ||||
60 | 51 | 20 | 23.111 | 12 | 2 | 40.622 | 203 | 13 | 48.283 | 535651.28 | ||||
61 | 49 | 35 | 18.752 | 16 | 31 | 35.372 | 169 | 4 | 29.970 | 492681.94 | ||||
62 | 51 | 0 | 50.739 | 12 | 44 | 21.109 | 142 | 34 | 43.365 | 645921.62 | ||||
63 | 49 | 57 | 39.301 | 15 | 49 | 32.647 | 278 | 58 | 26.074 | 712771.44 | ||||
64 | 48 | 35 | 1.347 | 14 | 36 | 13.765 | 278 | 46 | 6.729 | 542441.93 | ||||
65 | 51 | 5 | 52.555 | 14 | 9 | 48.587 | 172 | 14 | 19.107 | 409201.72 | ||||
66 | 51 | 5 | 11.379 | 16 | 57 | 6.480 | 92 | 5 | 31.936 | 479401.44 | ||||
67 | 48 | 58 | 9.482 | 14 | 21 | 3.676 | 85 | 40 | 60.650 | 680461.93 | ||||
68 | 48 | 17 | 6.712 | 12 | 34 | 4.049 | 126 | 59 | 60.633 | 534431.43 | ||||
69 | 51 | 6 | 44.632 | 14 | 26 | 54.965 | 29 | 17 | 21.400 | 595321.86 | ||||
70 | 50 | 4 | 40.552 | 16 | 18 | 55.611 | 154 | 32 | 1.709 | 702021.96 | ||||
71 | 50 | 47 | 39.658 | 16 | 33 | 32.709 | 190 | 30 | 6.783 | 435251.56 | ||||
72 | 48 | 12 | 60.825 | 16 | 16 | 10.105 | 83 | 0 | 59.015 | 401311.48 | ||||
73 | 49 | 58 | 58.884 | 13 | 28 | 7.373 | 50 | 58 | 60.907 | 434641.79 | ||||
74 | 48 | 34 | 55.399 | 13 | 7 | 9.503 | 168 | 46 | 35.926 | 582931.31 | ||||
75 | 50 | 1 | 19.623 | 14 | 35 | 60.304 | 299 | 24 | 25.997 | 578771.25 | ||||
76 | 48 | 49 | 27.105 | 17 | 41 | 40.976 | 177 | 22 | 15.869 | 642241.19 | ||||
77 | 49 | 10 | 41.851 | 12 | 44 | 28.156 | 214 | 46 | 12.300 | 630341.82 | ||||
78 | 49 | 11 | 39.949 | 13 | 3 | 5.138 | 230 | 29 | 21.677 | 532581.60 | ||||
79 | 51 | 21 | 56.685 | 16 | 15 | 44.584 | 154 | 33 | 55.180 | 701961.60 | ||||
80 | 51 | 6 | 33.667 | 16 | 58 | 31.814 | 270 | 13 | 37.112 | 613531.53 | ||||
81 | 48 | 18 | 50.914 | 12 | 6 | 44.143 | 35 | 13 | 37.811 | 561951.21 | ||||
82 | 51 | 7 | 44.912 | 14 | 16 | 11.212 | 52 | 52 | 1.377 | 452821.14 | ||||
83 | 49 | 44 | 54.156 | 17 | 44 | 4.595 | 84 | 8 | 3.282 | 612621.83 | ||||
84 | 48 | 41 | 45.316 | 14 | 53 | 3.047 | 1 | 8 | 43.938 | 585621.98 | ||||
85 | 48 | 13 | 24.372 | 17 | 3 | 17.429 | 138 | 57 | 18.216 | 434471.67 | ||||
86 | 49 | 37 | 39.637 | 12 | 3 | 1.597 | 254 | 52 | 6.085 | 585561.58 | ||||
87 | 51 | 11 | 1.312 | 14 | 11 | 41.068 | 102 | 0 | 53.565 | 456971.02 | ||||
88 | 49 | 33 | 41.701 | 13 | 4 | 22.801 | 130 | 30 | 16.887 | 400361.26 | ||||
89 | 51 | 21 | 56.375 | 17 | 21 | 47.972 | 44 | 46 | 20.901 | 683201.15 | ||||
90 | 48 | 38 | 12.634 | 15 | 51 | 7.260 | 55 | 37 | 27.778 | 600101.47 | ||||
91 | 48 | 14 | 49.003 | 13 | 25 | 49.896 | 21 | 51 | 53.803 | 718401.96 | ||||
92 | 49 | 6 | 34.044 | 15 | 58 | 20.425 | 193 | 53 | 38.930 | 626811.22 | ||||
93 | 48 | 10 | 56.494 | 17 | 11 | 42.562 | 209 | 23 | 13.497 | 600251.48 | ||||
94 | 48 | 13 | 14.492 | 17 | 14 | 27.223 | 215 | 48 | 27.091 | 523691.96 | ||||
95 | 49 | 46 | 45.336 | 15 | 56 | 49.323 | 73 | 24 | 46.652 | 454901.57 | ||||
96 | 49 | 39 | 37.338 | 16 | 18 | 42.636 | 234 | 55 | 6.496 | 645151.15 | ||||
97 | 48 | 34 | 21.703 | 16 | 16 | 35.918 | 68 | 51 | 43.749 | 442771.03 | ||||
98 | 49 | 30 | 32.591 | 14 | 4 | 40.304 | 163 | 6 | 21.478 | 566201.91 | ||||
99 | 51 | 49 | 5.712 | 12 | 26 | 44.146 | 15 | 47 | 33.573 | 656501.33 | ||||
100 | 48 | 25 | 22.412 | 12 | 57 | 13.240 | 41 | 4 | 49.674 | 539721.92 | ||||
101 | 49 | 52 | 31.213 | 12 | 47 | 48.079 | 226 | 43 | 44.736 | 469041.50 | ||||
102 | 48 | 41 | 56.147 | 15 | 1 | 45.868 | 154 | 34 | 59.383 | 494161.82 |