Compensare 2D (X,Y)


Descriere Exemplu Program


     Exemplu numeric:

      În acest exemplu este prezentată compensarea unei reţele de triangulaţie-trilateraţie constrânsă pe puncte de coordonate cunoscute prin metoda observaţiilor indirecte. Datele vor fi preluate dintr-un fişier text (vezi figura 2), ce conţine coordonatele punctelor vechi şi noi, direcţiile unghiulare orizontale şi distanţele măsurate. Preciziile de afişare sunt cele corespunzătoare figurii 1.

Exemplu numeric - Compensarea unei reţele geodezice Figura 1. Exemplu numeric - Compensarea unei reţele geodezice.

,unde fişierul de date are următoarea formă:

Fişierul de date Figura 2. Fişierul de date.


      Rezultatul prelucrării este următorul:

1. Date de intrare.

1.1. Coordonatele punctelor.


Denumire X [m] Y [m] Tipul punctului
Capul Dealului415209.082623780.667F
Dambul Mare421454.562628434.384F
Dl. Tirului415361.131629711.313F
Ocna Mare412348.144625869.981F
Ocna Mica411580.323627999.432F
PG01409380.880629556.610P
PG02412134.240629546.680P
PG03410105.430627276.330P
PG04412605.300626982.220P
PG05411539.230624166.100P
PG06413609.880624486.320P
PG07416689.600623026.270P
PG08419185.250625220.290P
PG09416755.770626191.750P
PG10414696.720626558.720P
PG11414845.390628400.580P
PG12417457.150629303.180P

1.2. Precizii de măsurare ale aparatului.


Precizia de măsurare a direcţiilor unghiulare orizontale: ± 10cc

Precizia de măsurare a distanţelor: ± (2mm+1.5ppm)

1.3. Direcţii unghiulare orizontale măsurate.


P.S. P.V. Direcţie [G]
Dambul Mare PG08147.0007
PG09114.4872
PG1272.5178
Dl. Tirului PG1244.5029
PG11332.8806
Ocna Mica283.8141
PG02259.9907
Ocna Mica PG01399.2362
PG02316.5749
Dl. Tirului265.5251
PG11246.2440
PG04188.7025
PG0367.4772
Ocna Mare PG03203.1065
PG04124.2959
PG1056.9216
PG06385.8298
PG05310.5421
Capul Dealului PG0598.3735
PG0678.5818
PG09368.7274
PG08327.1528
PG07275.0363
PG01PG0287.2510
Ocna Mica48.2616
PG037.0663
PG02Dl. Tirului59.9989
PG1131.2883
Ocna Mica334.8619
PG01256.5216
PG03PG0169.7703
Ocna Mica379.2089
PG04342.7308
Ocna Mare314.5348
PG05277.6921
PG04 Ocna Mica258.1634
PG02219.4878
PG11143.8526
PG1095.2006
Ocna Mare393.4552
PG03300.4614
PG05PG03362.7321
Ocna Mare307.0129
PG06245.0017
Capul Dealului228.5725
PG07221.3683
PG06PG05263.3442
Ocna Mare200.6508
PG10122.8304
PG0985.2074
Capul Dealului27.1219
PG07PG05240.3128
Capul Dealului224.1759
PG09152.8425
PG08100.0896
PG08PG0721.1098
Capul Dealului397.3153
PG09350.9804
Dambul Mare236.0584
PG10Ocna Mare185.0658
PG04154.1892
PG1161.7780
PG1216.7215
PG09355.6787
PG06236.1560
PG09 Dambul Mare371.1475
PG08318.5810
PG07241.4697
Capul Dealului206.4855
PG06174.4280
PG10131.5680
PG1188.1948
PG1228.6872
PG11 PG1240.2279
PG09364.4429
PG10313.9227
PG04254.9822
Ocna Mica226.8322
PG02193.5853
PG12 Dambul Mare296.9257
PG08236.0365
PG09196.4378
PG10160.3628
PG11131.7316
Dl. Tirului98.3043

1.4. Distanţe măsurate.


P.S. P.V. Distanţă [m]
Dambul Mare PG083934.498
Dambul Mare PG095206.601
Dambul Mare PG124090.850
Dl. Tirului PG122135.317
Dl. Tirului PG111408.499
Dl. Tirului PG023230.973
Ocna Mica PG012694.788
Ocna Mica PG021643.361
Ocna Mica PG113289.509
Ocna Mica PG041444.005
Ocna Mica PG031642.550
Ocna Mare PG032647.093
Ocna Mare PG04 1141.541
Ocna Mare PG102447.407
Ocna Mare PG061872.502
Ocna Mare PG051886.079
Capul Dealului PG053689.901
Capul Dealului PG061747.910
Capul Dealului PG092864.434
Capul Dealului PG084228.609
Capul Dealului PG071661.583
PG01 PG022753.280
PG01 Ocna Mica2694.783
PG01 PG032392.545
PG02 Dl. Tirului3230.975
PG02 PG112943.337
PG02 Ocna Mica1643.359
PG02 PG012753.283
PG03 PG012392.540
PG03 Ocna Mica1642.560
PG03 PG042517.024
PG03 Ocna Mare2647.089
PG03 PG053424.697
PG04 Ocna Mica1444.007
PG04 PG022607.281
PG04 PG112651.272
PG04 PG102133.792
PG04 Ocna Mare1141.540
PG04 PG032517.025
PG05 PG033424.683
PG05 Ocna Mare1886.084
PG05 PG062095.192
PG05 Capul Dealului3689.908
PG05 PG075274.803
PG06 PG052095.192
PG06 Ocna Mare1872.501
PG06 PG102340.025
PG06 PG093578.295
PG06 Capul Dealului1747.903
PG07 Capul Dealului1661.587
PG07 PG055274.801
PG07 PG093166.060
PG07 PG083322.835
PG08 PG073322.835
PG08 Capul Dealului4228.617
PG08 PG092616.411
PG08 Dambul Mare3934.493
PG09 Dambul Mare5206.591
PG09 PG082616.417
PG09 PG073166.068
PG09 Capul Dealului2864.430
PG09 PG063578.300
PG09 PG102091.426
PG09 PG112920.263
PG09 PG123189.385
PG10 Ocna Mare2447.408
PG10 PG042133.796
PG10 PG111847.791
PG10 PG123892.429
PG10 PG092091.427
PG10 PG062340.019
PG11 Dl. Tirului1408.494
PG11 PG122763.230
PG11 PG092920.258
PG11 PG101847.792
PG11 PG042651.277
PG11 Ocna Mica3289.512
PG11 PG022943.352
PG12 Dambul Mare4090.850
PG12 PG084433.384
PG12 PG093189.393
PG12 PG103892.420
PG12 PG112763.238
PG12 Dl. Tirului2135.306

2.1. Direcţiile unghiulare orizontale compensate şi preciziile acestora.


P.S. P.V. Direcţie
măsurată [G] 		Corecţie [cc] Direcţie
compensată [G] 		Abaterea
standard [cc]
Dambul Mare PG08 147.0007 -14.43 146.9992 ± 47.49
PG09 114.4872 14.02 114.4886 ± 47.49
PG12 72.5178 0.41 72.5179 ± 47.49
Dl. Tirului PG12 44.5029 -16.88 44.5013 ± 47.51
PG11 332.8806 -13.62 332.8793 ± 47.54
Ocna Mica 283.8141 0.15 283.8141 ± 47.49
PG02 259.9907 30.36 259.9937 ± 47.50
Ocna Mica PG01 399.2362 30.33 399.2393 ± 47.50
PG02 316.5749 -42.28 316.5707 ± 47.52
Dl. Tirului 265.5251 7.45 265.5259 ± 47.49
PG11 246.2440 -17.55 246.2422 ± 47.50
PG04 188.7025 -18.53 188.7006 ± 47.53
PG03 67.4772 40.59 67.4813 ± 47.52
Ocna Mare PG03 203.1065 -35.59 203.1029 ± 47.50
PG04 124.2959 -1.45 124.2957 ± 47.56
PG10 56.9216 4.95 56.9221 ± 47.50
PG06 385.8298 5.76 385.8304 ± 47.51
PG05 310.5421 26.34 310.5448 ± 47.51
Capul Dealului PG05 98.3735 -0.98 98.3734 ± 47.49
PG06 78.5818 -39.41 78.5778 ± 47.52
PG09 368.7274 8.66 368.7282 ± 47.50
PG08 327.1528 9.18 327.1537 ± 47.49
PG07 275.0363 22.55 275.0385 ± 47.52
PG01 PG02 87.2510 6.19 87.2517 ± 47.50
Ocna Mica 48.2616 -7.43 48.2609 ± 47.50
PG03 7.0663 1.24 7.0664 ± 47.50
PG02 Dl. Tirului 59.9989 -18.43 59.9971 ± 47.50
PG11 31.2883 14.87 31.2898 ± 47.50
Ocna Mica 334.8619 3.61 334.8622 ± 47.52
PG01 256.5216 -0.05 256.5216 ± 47.50
PG03 PG01 69.7703 34.03 69.7737 ± 47.50
Ocna Mica 379.2089 12.72 379.2102 ± 47.52
PG04 342.7308 22.90 342.7331 ± 47.50
Ocna Mare 314.5348 -34.76 314.5313 ± 47.50
PG05 277.6921 -34.89 277.6886 ± 47.50
PG04 Ocna Mica 258.1634 -24.49 258.1610 ± 47.53
PG02 219.4878 -45.14 219.4833 ± 47.50
PG11 143.8526 21.47 143.8547 ± 47.50
PG10 95.2006 12.28 95.2019 ± 47.51
Ocna Mare 393.4552 3.98 393.4555 ± 47.56
PG03 300.4614 31.90 300.4646 ± 47.50
PG05 PG03 362.7321 7.08 362.7328 ± 47.50
Ocna Mare 307.0129 44.13 307.0173 ± 47.51
PG06 245.0017 -6.29 245.0011 ± 47.51
Capul Dealului 228.5725 -31.74 228.5693 ± 47.49
PG07 221.3683 -13.17 221.3670 ± 47.49
PG06 PG05 263.3442 34.46 263.3476 ± 47.51
Ocna Mare 200.6508 -13.99 200.6494 ± 47.51
PG10 122.8304 21.70 122.8325 ± 47.50
PG09 85.2074 -26.16 85.2048 ± 47.49
Capul Dealului 27.1219 -16.02 27.1203 ± 47.52
PG07 PG05 240.3128 -33.04 240.3095 ± 47.49
Capul Dealului 224.1759 10.91 224.1770 ± 47.52
PG09 152.8425 39.54 152.8464 ± 47.50
PG08 100.0896 -17.41 100.0878 ± 47.50
PG08 PG07 21.1098 8.00 21.1106 ± 47.50
Capul Dealului 397.3153 -3.56 397.3149 ± 47.49
PG09 350.9804 20.56 350.9824 ± 47.50
Dambul Mare 236.0584 -25.00 236.0559 ± 47.49
PG10 Ocna Mare 185.0658 23.85 185.0682 ± 47.50
PG04 154.1892 -11.05 154.1881 ± 47.51
PG11 61.7780 -4.57 61.7776 ± 47.52
PG12 16.7215 -18.32 16.7197 ± 47.49
PG09 355.6787 -25.56 355.6762 ± 47.51
PG06 236.1560 35.65 236.1596 ± 47.50
PG09 Dambul Mare 371.1475 -8.47 371.1466 ± 47.49
PG08 318.5810 28.05 318.5838 ± 47.50
PG07 241.4697 7.92 241.4705 ± 47.50
Capul Dealului 206.4855 53.00 206.4908 ± 47.50
PG06 174.4280 -31.80 174.4248 ± 47.49
PG10 131.5680 11.34 131.5691 ± 47.51
PG11 88.1948 -17.21 88.1931 ± 47.50
PG12 28.6872 -42.83 28.6829 ± 47.50
PG11 PG12 40.2279 11.71 40.2290 ± 47.50
PG09 364.4429 -4.55 364.4424 ± 47.50
PG10 313.9227 -28.11 313.9199 ± 47.52
PG04 254.9822 11.69 254.9833 ± 47.50
Ocna Mica 226.8322 -9.88 226.8312 ± 47.50
PG02 193.5853 19.14 193.5872 ± 47.50
PG12 Dambul Mare 296.9257 12.82 296.9270 ± 47.49
PG08 236.0365 29.63 236.0395 ± 47.49
PG09 196.4378 -37.93 196.4340 ± 47.50
PG10 160.3628 8.99 160.3637 ± 47.49
PG11 131.7316 -8.35 131.7308 ± 47.50
Dl. Tirului 98.3043 -5.16 98.3038 ± 47.51

2.2. Distanţele compensate şi preciziile acestora.


P.S. P.V. Distanţă
măsurată [m] 		Corecţie [mm] Distanţă
compensată [m] 		Abaterea
standard [mm]
Dambul Mare PG08 3934.498 4.63 3934.503 ± 37.52
Dambul Mare PG09 5206.601 49.83 5206.651 ± 46.58
Dambul Mare PG12 4090.850 -21.26 4090.829 ± 38.64
Dl. Tirului PG12 2135.317 -28.64 2135.288 ± 24.71
Dl. Tirului PG11 1408.499 49.21 1408.548 ± 19.53
Dl. Tirului PG02 3230.973 76.59 3231.050 ± 32.51
Ocna Mica PG01 2694.788 -51.94 2694.736 ± 28.69
Ocna Mica PG02 1643.361 4.79 1643.366 ± 21.20
Ocna Mica PG11 3289.509 48.70 3289.558 ± 32.93
Ocna Mica PG04 1444.005 37.69 1444.043 ± 19.78
Ocna Mica PG03 1642.550 11.11 1642.561 ± 21.20
Ocna Mare PG03 2647.093 2.32 2647.095 ± 28.35
Ocna Mare PG04 1141.541 36.51 1141.578 ± 17.63
Ocna Mare PG10 2447.407 20.07 2447.427 ± 26.93
Ocna Mare PG06 1872.502 37.39 1872.539 ± 22.84
Ocna Mare PG05 1886.079 -22.62 1886.056 ± 22.93
Capul Dealului PG05 3689.901 24.68 3689.926 ± 35.78
Capul Dealului PG06 1747.910 46.51 1747.957 ± 21.95
Capul Dealului PG09 2864.434 54.56 2864.489 ± 29.90
Capul Dealului PG08 4228.609 10.61 4228.620 ± 39.62
Capul Dealului PG07 1661.583 -13.41 1661.570 ± 21.33
PG01 PG02 2753.280 30.94 2753.311 ± 29.11
PG01 Ocna Mica 2694.783 -46.94 2694.736 ± 28.69
PG01 PG03 2392.545 24.47 2392.569 ± 26.54
PG02 Dl. Tirului 3230.975 74.59 3231.050 ± 32.51
PG02 PG11 2943.337 -21.26 2943.316 ± 30.46
PG02 Ocna Mica 1643.359 6.79 1643.366 ± 21.20
PG02 PG01 2753.283 27.94 2753.311 ± 29.11
PG03 PG01 2392.540 29.47 2392.569 ± 26.54
PG03 Ocna Mica 1642.560 1.11 1642.561 ± 21.20
PG03 PG04 2517.024 -13.98 2517.010 ± 27.43
PG03 Ocna Mare 2647.089 6.32 2647.095 ± 28.35
PG03 PG05 3424.697 49.61 3424.747 ± 33.89
PG04 Ocna Mica 1444.007 35.69 1444.043 ± 19.78
PG04 PG02 2607.281 9.78 2607.291 ± 28.07
PG04 PG11 2651.272 69.41 2651.341 ± 28.38
PG04 PG10 2133.792 2.51 2133.795 ± 24.70
PG04 Ocna Mare 1141.540 37.51 1141.578 ± 17.63
PG04 PG03 2517.025 -14.98 2517.010 ± 27.43
PG05 PG03 3424.683 63.61 3424.747 ± 33.89
PG05 Ocna Mare 1886.084 -27.62 1886.056 ± 22.93
PG05 PG06 2095.192 7.06 2095.199 ± 24.42
PG05 Capul Dealului 3689.908 17.68 3689.926 ± 35.78
PG05 PG07 5274.803 38.42 5274.841 ± 47.07
PG06 PG05 2095.192 7.06 2095.199 ± 24.42
PG06 Ocna Mare 1872.501 38.39 1872.539 ± 22.84
PG06 PG10 2340.025 10.97 2340.036 ± 26.17
PG06 PG09 3578.295 -54.26 3578.241 ± 34.99
PG06 Capul Dealului 1747.903 53.51 1747.957 ± 21.95
PG07 Capul Dealului 1661.587 -17.41 1661.570 ± 21.33
PG07 PG05 5274.801 40.42 5274.841 ± 47.07
PG07 PG09 3166.060 26.84 3166.087 ± 32.05
PG07 PG08 3322.835 -15.21 3322.820 ± 33.17
PG08 PG07 3322.835 -15.21 3322.820 ± 33.17
PG08 Capul Dealului 4228.617 2.61 4228.620 ± 39.62
PG08 PG09 2616.411 15.30 2616.426 ± 28.14
PG08 Dambul Mare 3934.493 9.63 3934.503 ± 37.52
PG09 Dambul Mare 5206.591 59.83 5206.651 ± 46.58
PG09 PG08 2616.417 9.30 2616.426 ± 28.14
PG09 PG07 3166.068 18.84 3166.087 ± 32.05
PG09 Capul Dealului 2864.430 58.56 2864.489 ± 29.90
PG09 PG06 3578.300 -59.26 3578.241 ± 34.99
PG09 PG10 2091.426 15.67 2091.442 ± 24.40
PG09 PG11 2920.263 37.85 2920.301 ± 30.30
PG09 PG12 3189.385 11.24 3189.396 ± 32.22
PG10 Ocna Mare 2447.408 19.07 2447.427 ± 26.93
PG10 PG04 2133.796 -1.49 2133.795 ± 24.70
PG10 PG11 1847.791 17.10 1847.808 ± 22.66
PG10 PG12 3892.429 0.23 3892.429 ± 37.22
PG10 PG09 2091.427 14.67 2091.442 ± 24.40
PG10 PG06 2340.019 16.97 2340.036 ± 26.17
PG11 Dl. Tirului 1408.494 54.21 1408.548 ± 19.53
PG11 PG12 2763.230 13.86 2763.244 ± 29.18
PG11 PG09 2920.258 42.85 2920.301 ± 30.30
PG11 PG10 1847.792 16.10 1847.808 ± 22.66
PG11 PG04 2651.277 64.41 2651.341 ± 28.38
PG11 Ocna Mica 3289.512 45.70 3289.558 ± 32.93
PG11 PG02 2943.352 -36.26 2943.316 ± 30.46
PG12 Dambul Mare 4090.850 -21.26 4090.829 ± 38.64
PG12 PG08 4433.384 -51.68 4433.332 ± 41.08
PG12 PG09 3189.393 3.24 3189.396 ± 32.22
PG12 PG10 3892.420 9.23 3892.429 ± 37.22
PG12 PG11 2763.238 5.86 2763.244 ± 29.18
PG12 Dl. Tirului 2135.306 -17.64 2135.288 ± 24.71

2.3. Coordonatele compensate ale punctelor noi şi preciziile acestora.


Denumire
punct 		Coordonate
provizorii [m] 		Corecţii [mm] Coordonate
compensate [m] 		Abaterea
standard [mm] 		Abaterea
standard totală [mm]
PG01 X 409380.880 108.54 409380.989 ± 22.06 ± 35.09
Y 629556.610 -87.65 629556.522 ± 27.29
PG02 X 412134.240 41.66 412134.282 ± 15.67 ± 20.92
Y 629546.680 -63.16 629546.617 ± 13.85
PG03 X 410105.430 80.01 410105.510 ± 11.51 ± 21.70
Y 627276.330 -39.51 627276.290 ± 18.39
PG04 X 412605.300 -17.43 412605.283 ± 11.25 ± 14.95
Y 626982.220 1.52 626982.222 ± 9.84
PG05 X 411539.230 116.60 411539.347 ± 14.42 ± 21.57
Y 624166.100 45.49 624166.145 ± 16.04
PG06 X 413609.880 46.05 413609.926 ± 11.69 ± 19.50
Y 624486.320 75.14 624486.395 ± 15.61
PG07 X 416689.600 -20.47 416689.580 ± 15.59 ± 25.90
Y 623026.270 115.49 623026.385 ± 20.68
PG08 X 419185.250 -193.03 419185.057 ± 17.33 ± 29.69
Y 625220.290 115.48 625220.405 ± 24.11
PG09 X 416755.770 -139.24 416755.631 ± 13.90 ± 21.05
Y 626191.750 33.27 626191.783 ± 15.81
PG10 X 414696.720 -78.06 414696.642 ± 12.39 ± 20.33
Y 626558.72069.15 626558.789 ± 16.12
PG11 X 414845.390 -63.22 414845.327 ± 12.85 ± 18.06
Y 628400.580 25.53 628400.606 ± 12.68
PG12 X 417457.150 -114.21 417457.036 ± 12.35 ± 23.81
Y 629303.180 -82.00 629303.098 ± 20.36


Abaterea standard a unităţii de pondere: ± 4.75

Abaterea standard totală a reţelei: ± 22.71 mm

2.4. Elementele elipselor erorilor.


Denumire
punct 		a - semiaxa
mare [mm] 		b - semiaxa
mică [mm] 		Orientarea
semiaxei mari [G]
PG01 31.61 15.23 60.92
PG02 16.24 13.19 170.44
PG03 18.40 11.50 98.35
PG04 11.41 9.66 20.03
PG05 17.10 13.15 136.40
PG06 16.44 10.50 73.36
PG07 22.12 13.48 70.47
PG08 25.10 15.87 123.30
PG09 16.48 13.10 130.81
PG10 16.60 11.73 121.97
PG11 14.79 10.36 151.21
PG12 20.41 12.26 105.99

2.5. Coordonatele finale ale punctelor.


Denumire
punct 		X(Nord) [m] Y(Est) [m] Sx [mm] Sy [mm] Sp [mm]
Capul Dealului 415209.082 623780.667 --- --- ---
Dambul Mare 421454.562 628434.384 --- --- ---
Dl. Tirului 415361.131 629711.313 --- --- ---
Ocna Mare 412348.144 625869.981 --- --- ---
Ocna Mica 411580.323 627999.432 --- --- ---
PG01 409380.989 629556.522 ± 22.06 ± 27.29 ± 35.09
PG02 412134.282 629546.617 ± 15.67 ± 13.85 ± 20.92
PG03 410105.510 627276.290 ± 11.51 ± 18.39 ± 21.70
PG04 412605.283 626982.222 ± 11.25 ± 9.84 ± 14.95
PG05 411539.347 624166.145 ± 14.42 ± 16.04 ± 21.57
PG06 413609.926 624486.395 ± 11.69 ± 15.61 ± 19.50
PG07 416689.580 623026.385 ± 15.59 ± 20.68 ± 25.90
PG08 419185.057 625220.405 ± 17.33 ± 24.11 ± 29.69
PG09 416755.631 626191.783 ± 13.90 ± 15.81 ± 21.05
PG10 414696.642 626558.789 ± 12.39 ± 16.12 ± 20.33
PG11 414845.327 628400.606 ± 12.85 ± 12.68 ± 18.06
PG12 417457.036 629303.098 ± 12.35 ± 20.36 ± 23.81