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SISTEME DE MASURARE IN INDUSTRIE - Determinarea coordonatelor punctelor de detaliu, intersecia spatiala inainte (in domeniul apropiat)

Geologie



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UNIVERSITATEA TEHNICA DE CONSTRUCTII BUCURESTI

FACULTATEA DE GEODEZIE






SISTEME DE MASURARE IN INDUSTRIE



Determinarea coordonatelor punctelor de detaliu

Metoda: intersecia spatiala inainte (in domeniul apropiat)


Specializarea:Geomatica




2010-2011

VARIANTA 1 (sistem local, cu originea în punctul S3)

Pct.

Coordonate

X

Y

Z

S2

0

78.7155

91.1138

S3

0

0

93.5175


b

78.7156

ZS3S2

-2.3757


Pct.

[g c cc]

[g c cc]

wS3 [g c cc]

wS2 [g c cc]

x [m]

y [m]

z [m]

89

101.062

74.6211

99.3149

98.6675

194.58995

-3.24642

2.06244

98

56.5378

123.3754

96.4225

94.947

183.69230

149.36777

13.29157

96

56.0868

124.0136

96.7397

95.3225

183.57062

151.44172

12.17106

94

55.3495

125.0551

97.2792

95.965

183.31431

154.83282

10.23457

92

54.6324

126.0741

97.8372

96.6348

183.06153

158.18650

8.19598

47

75.3563

99.4196

99.2932

98.4542

188.86207

76.99372

2.23084

48

75.5535

99.1956

99.2868

98.4525

188.90235

76.32860

2.24300

51

77.262

97.2884

99.2922

98.4625

189.31478

70.64710

2.21709

59

82.3275

91.8789

99.2891

98.491

190.49366

54.28242

2.18772

60

82.54

91.6576

99.2846

98.496

190.52622

53.60474

2.18773

61

82.7591

91.4359

99.2877

98.4983

190.60275

52.91905

2.18078

63

84.3472

89.8181

99.2849

98.5083

190.93409

47.91512

2.17708

65

85.9799

88.1951

99.2852

98.5192

191.31550

42.82751

2.17008

66

86.1727

88.0058

99.2861

98.5213

191.36119

42.22957

2.16682

67

86.398

87.7856

99.2857

98.5224

191.41771

41.53217

2.16740

71

89.6283

84.6814

99.2869

98.5518

192.10484

31.57726

2.14578

72

89.8648

84.4586

99.284

98.5508

192.15142

30.85225

2.15387

73

90.0977

84.2431

99.2833

98.552

192.22292

30.14279

2.15560

75

91.7247

82.7361

99.2853

98.5668

192.57407

25.17429

2.14564

77

93.3504

81.2606

99.2938

98.5845

192.93131

20.22561

2.12280

78

93.5946

81.0411

99.2953

98.5915

192.98228

19.48285

2.11222

79

93.838

80.8244

99.2996

98.5953

193.04490

18.74386

2.10265

81

95.466

79.3819

99.3022

98.6115

193.39080

13.79661

2.09275

83

97.0801

77.9804

99.3072

98.6298

193.75297

8.89285

2.07724

84

97.3382

77.7574

99.3083

98.634

193.80030

8.10780

2.07218

85

97.5918

77.5416

99.3095

98.637

193.86969

7.33719

2.06924

87

99.2034

76.1719

99.3117

98.6515

194.20535

2.43021

2.06530

89

101.0651

74.6211

99.3142

98.6675

194.61338

-3.25629

2.06391

53

78.7879

95.6204

99.2898

98.473

189.67326

65.64648

2.20534

54

78.9958

95.3964

99.2908

98.4758

189.72656

64.97190

2.19984

55

79.2046

95.1726

99.2904

98.4763

189.78399

64.29690

2.20010

57

80.7569

93.5176

99.2875

98.484

190.13255

59.28811

2.19576


RELATII DE CALCUL UTILIZATE



Pct.

X [m]

Y [m]

Z [m]

89

194.5899

-3.2464

95.5869

98

183.6923

149.3678

106.8161

96

183.5706

151.4417

105.6956

94

183.3143

154.8328

103.7591

92

183.0615

158.1865

101.7205

47

188.8621

76.9937

95.7553

48

188.9024

76.3286

95.7675

51

189.3148

70.6471

95.7416

59

190.4937

54.2824

95.7122

60

190.5262

53.6047

95.7122

61

190.6027

52.9190

95.7053

63

190.9341

47.9151

95.7016

65

191.3155

42.8275

95.6946

66

191.3612

42.2296

95.6913

67

191.4177

41.5322

95.6919

71

192.1048

31.5773

95.6703

72

192.1514

30.8522

95.6784

73

192.2229

30.1428

95.6801

75

192.5741

25.1743

95.6701

77

192.9313

20.2256

95.6473

78

192.9823

19.4829

95.6367

79

193.0449

18.7439

95.6271

81

193.3908

13.7966

95.6172

83

193.7530

8.8928

95.6017

84

193.8003

8.1078

95.5967

85

193.8697

7.3372

95.5937

87

194.2054

2.4302

95.5898

89

194.6134

-3.2563

95.5884

53

189.6733

65.6465

95.7298

54

189.7266

64.9719

95.7243

55

189.7840

64.2969

95.7246

57

190.1326

59.2881

95.7203




VARIANTA 2 (sistem local, cu o origine oarecare a retelei de sprijin)


b [m]

78.7156

ZS3S2 [m]

-2.389700

S3S2 [g c cc]

193.5221471

Pct.

Coordonate

X [m]

Y [m]

Z [m]

S2

1087.5823

999.9871

91.1138

S3

1165.8907

991.9913

93.5175


Metoda a) –utilizand relatiile de la intersectia inainte

Relatii utilizate:

-calculul orientarilor:

P.S.  S2

P.S.  S3

- calculul coordonatelor punctelor noi prin intersectie inainte







-calculul cotelor

Se va face media valorilor



P.S.

P.V.

Diri oriz [g c cc]

[g c cc]

[g c cc]

[g c cc]

S2

S3

325.3824



393.5221471

89

0.0035

74.6211


68.1432471

87

1.5543

76.1719


69.6940471

85

2.924

77.5416


71.0637471

84

3.1398

77.7574


71.2795471

83

3.3628

77.9804


71.5025471

81

4.7643

79.3819


72.9040471

79

6.2068

80.8244


74.3465471

78

6.4235

81.0411


74.5632471

77

6.643

81.2606


74.7827471

75

8.1185

82.7361


76.2582471

73

9.6255

84.2431


77.7652471

72

9.841

84.4586


77.9807471

71

10.0638

84.6814


78.2035471

63

15.2005

89.8181


83.3402471

61

16.8183

91.4359


84.9580471

60

17.04

91.6576


85.1797471

59

17.2613

91.8789


85.4010471

57

18.9

93.5176


87.0397471

55

20.555

95.1726


88.6947471

54

20.7788

95.3964


88.9185471

53

21.0028

95.6204


89.1425471

51

22.6708

97.2884


90.8105471

49

24.3545

98.9721


92.4942471

48

24.578

99.1956


92.7177471

47

24.802

99.4196


92.9417471

92

51.4565

126.0741


119.5962471

94

50.4375

125.0551


118.5772471

96

49.396

124.0136


117.5357471

98

48.7578

123.3754


116.8975471

S2

S3

222.6768



393.5221471

65

310.8719

88.1951


81.7172471

66

310.6826

88.0058


81.5279471

67

310.4624

87.7856


81.3077471

71

307.3608

84.684


78.2061471

72

307.1384

84.4616


77.9837471

73

306.9209

84.2441


77.7662471

S3

S2

19.0732



193.5221471

89

318.0112


101.062

92.4601471

98

362.5354


56.5378

136.9843471

96

362.9864


56.0868

137.4353471

94

363.7237


55.3495

138.1726471

92

364.4408


54.6324

138.8897471

47

343.7169


75.3563

118.1658471

48

343.5197


75.5535

117.9686471

51

341.8112


77.262

116.2601471

59

336.7457


82.3275

111.1946471

60

336.5332


82.54

110.9821471

61

336.3141


82.7591

110.7630471

63

334.726


84.3472

109.1749471

65

333.0933


85.9799

107.5422471

66

332.9005


86.1727

107.3494471

67

332.6752


86.398

107.1241471

69

331.0615


88.0117

105.5104471

71

329.4449


89.6283

103.8938471

72

329.2084


89.8648

103.6573471

73

328.9755


90.0977

103.4244471

75

327.3485


91.7247

101.7974471

77

325.7228


93.3504

100.1717471

78

325.4786


93.5946

99.9275471

79

325.2352


93.838

99.6841471

81

323.6072


95.466

98.0561471

83

321.9931


97.0801

96.4420471

84

321.735


97.3382

96.1839471

85

321.4814


97.5918

95.9303471

87

319.8698


99.2034

94.3187471

89

318.0081


101.0651

92.4570471

53

340.2853


78.7879

114.7342471

54

340.0774


78.9958

114.5263471

55

339.8686


79.2046

114.3175471

57

338.3163


80.7569

112.7652471



Pct.

X [m]

Y [m]

Y [m]

S3-P [g c cc]

S2-P [g c cc]

89

1188.8864

1185.2449

1185.2449

92.4601471

68.1432471

98

1035.9548

1189.9059

1189.9059

136.9843471

116.8975471

96

1033.8792

1189.9955

1189.9955

137.4353471

117.5357471

94

1030.4796

1190.0850

1190.0850

138.1726471

118.5772471

92

1027.1176

1190.1742

1190.1742

138.8897471

119.5962471

47

1108.4796

1187.6973

1187.6973

118.1658471

92.9417471

48

1109.1453

1187.6698

1187.6698

117.9686471

92.7177471

51

1114.8393

1187.5030

1187.5030

116.2601471

90.8105471

59

1131.2391

1187.0134

1187.0134

111.1946471

85.4010471

60

1131.9166

1186.9770

1186.9770

110.9821471

85.1797471

61

1132.6065

1186.9835

1186.9835

110.7630471

84.9580471

63

1137.6182

1186.8048

1186.8048

109.1749471

83.3402471

65

1142.7182

1186.6675

1186.6675

107.5422471

81.7172471

66

1143.3177

1186.6522

1186.6522

107.3494471

81.5279471

67

1144.0173

1186.6376

1186.6376

107.1241471

81.3077471

71

1153.9898

1186.3202

1186.3202

103.8938471

78.2048471

72

1154.7158

1186.2945

1186.2945

103.6573471

77.9822471

73

1155.4293

1186.2857

1186.2857

103.4244471

77.7657471

75

1160.4080

1186.1263

1186.1263

101.7974471

76.2582471

77

1165.3721

1184.2036

1184.2036

100.1717471

74.5632471

78

1166.1094

1184.1974

1184.1974

99.9275471

74.3465471

79

1166.7973

1174.7262

1174.7262

99.6841471

72.9040471

81

1171.8098

1185.7831

1185.7831

98.0561471

72.9040471

83

1176.7250

1185.6453

1185.6453

96.4420471

71.5025471

84

1177.5108

1185.6126

1185.6126

96.1839471

71.2795471

85

1178.2844

1185.6034

1185.6034

95.9303471

71.0637471

87

1183.2001

1185.4389

1185.4389

94.3187471

69.6940471

89

1188.8986

1185.2672

1185.2672

92.4570471

68.1432471

53

1119.8505

1187.3516

1187.3516

114.7342471

89.1425471

54

1120.5270

1187.3361

1187.3361

114.5263471

88.9185471

55

1121.2044

1187.3247

1187.3247

114.3175471

88.6947471

57

1126.2226

1187.1627

1187.1627

112.7652471

87.0397471


Pct.

wS3 [g c cc]

wS2 [g c cc]

D S3-P [m]

D S2-P [m]

Z [m]

Z[m]

Zmed [m]

89

99.3149

98.6675

194.616915

211.1468

95.61196

95.53393

95.57294

98

96.4225

94.947

236.75625

196.8109

106.8361

106.768

106.8021

96

96.7397

95.3225

237.976257

197.4518

105.7156

105.6475

105.6816

94

97.2792

95.965

239.952636

198.4891

103.7789

103.7112

103.7451

92

97.8372

96.6348

241.93888

199.5673

101.7401

101.6729

101.7065

47

99.2932

98.4542

203.953096

188.8698

95.78196

95.70072

95.74134

48

99.2868

98.4525

203.740288

188.9173

95.80008

95.70692

95.7535

51

99.2922

98.4625

202.066941

189.4865

95.76419

95.69098

95.72758

59

99.2891

98.491

198.076676

192.0541

95.72947

95.66697

95.69822

60

99.2846

98.496

197.923377

192.1738

95.74175

95.65471

95.69823

61

99.2877

98.4983

197.812506

192.3404

95.73087

95.65169

95.69128

63

99.2849

98.5083

196.854363

193.4023

95.72881

95.64635

95.68758

65

99.2852

98.5192

196.050433

194.6523

95.71886

95.6423

95.68058

66

99.2861

98.5213

195.965297

194.8083

95.71513

95.6395

95.67731

67

99.2857

98.5224

195.871429

194.9956

95.71531

95.64048

95.67789

71

99.2869

98.5518

194.692973

197.813

95.69842

95.61448

95.65645

72

99.284

98.5508

194.624288

198.0337

95.70651

95.62261

95.66456

73

99.2833

98.552

194.575791

198.2684

95.70811

95.62422

95.66616

75

99.2853

98.5668

194.212447

199.8785

95.69791

95.61435

95.65613

77

99.2938

98.5845

192.212951

199.9674

95.6498

95.56073

95.60527

78

99.2953

98.5915

192.206185

200.2497

95.64519

95.54498

95.59509

79

99.2996

98.5953

182.737194

191.8562

95.52803

95.34779

95.43791

81

99.3022

98.6115

193.882186

203.9961

95.64273

95.56376

95.60325

83

99.3072

98.6298

193.956827

205.9499

95.62831

95.54716

95.58773

84

99.3083

98.634

193.969713

206.2619

95.6251

95.54026

95.58268

85

99.3095

98.637

194.008369

206.5921

95.62186

95.5376

95.57973

87

99.3117

98.6515

194.220444

208.6507

95.61745

95.53414

95.5758

89

99.3142

98.6675

194.64051

211.1722

95.61435

95.53446

95.57441

53

99.2898

98.473

200.712124

190.1229

95.7567

95.67497

95.71583

54

99.2908

98.4758

200.542933

190.2236

95.75166

95.66902

95.71034

55

99.2904

98.4763

200.379656

190.3308

95.7511

95.67009

95.71059

57

99.2875

98.484

199.161794

191.1224

95.7466

95.66591

95.70625



Metoda b) –utilizand o transformare conforma


Transformarea conforma (Transformarea Helmert cu 4 parametri)


Consideram un camp de puncte pentru care se avem puncte cu coordonate in sistem local

si puncte cu coordonate atat in sistem local cat si in sistem general (sistem “national”, “istoric”) – puncte comune .

Fie un sistem national (istoric) XOY si un sitem local xOy. Pentru un punct P legatura dintre cele doua siteme este data prin relatiile:


(1)- cand se cunosc coordonatele in sistem local


(2) – cand se cunosc coordonatele in sistem istoric


Transformarea conforma este o transformare cu 4 parametri, acestia fiind:

doua translatii: Tx, Ty

un factor de scara: m (m=1 in cazul de fata)

unghiul de rotatie: φ (φ=S3-S2-100 in cazul de fata)


Relatia (1) mai poate fi scrisa sub forma:


(3)



Daca in aceasta relatie se aplica transaltiile si factorul de scara, avem:


(4)


In relatia (4) se considera urmatoarele relatii:

(5) (c=XS3; d=YS3)


punct

sistem local

sist global

x [m]

Y [m]

X [m]

Y [m]

S2

0.0000

78.7155

1087.5823

999.9871

S3

0.0000

0.0000

1165.8907

991.9913

89

194.5899

-3.2464



98

183.6923

149.3678



96

183.5706

151.4417



94

183.3143

154.8328



92

183.0615

158.1865



47

188.8621

76.9937



48

188.9024

76.3286



51

189.3148

70.6471



59

190.4937

54.2824



60

190.5262

53.6047



61

190.6027

52.9190



63

190.9341

47.9151



65

191.3155

42.8275



66

191.3612

42.2296



67

191.4177

41.5322



71

192.1048

31.5773



72

192.1514

30.8522



73

192.2229

30.1428



75

192.5741

25.1743



77

192.9313

20.2256



78

192.9823

19.4829



79

193.0449

18.7439



81

193.3908

13.7966



83

193.7530

8.8928



84

193.8003

8.1078



85

193.8697

7.3372



87

194.2054

2.4302



89

194.6134

-3.2563



53

189.6733

65.6465



54

189.7266

64.9719



55

189.7840

64.2969



57

190.1326

59.2881



Utilizand transformarea conforma:

punct

sist global

X [m]

Y [m]

89

1188.8865

1185.2450

98

1035.9547

1189.9060

96

1033.8791

1189.9956

94

1030.4795

1190.0851

92

1027.1175

1190.1743

47

1108.4795

1187.6974

48

1109.1453

1187.6699

51

1114.8393

1187.5031

59

1131.2391

1187.0136

60

1131.9166

1186.9771

61

1132.6065

1186.9836

63

1137.6182

1186.8049

65

1142.7182

1186.6676

66

1143.3177

1186.6523

67

1144.0173

1186.6377

71

1153.9905

1186.3101

72

1154.7165

1186.2827

73

1155.4295

1186.2818

75

1160.4080

1186.1265

77

1165.3674

1185.9792

78

1166.1114

1185.9544

79

1166.8530

1185.9417

81

1171.8098

1185.7832

83

1176.7250

1185.6454

84

1177.5108

1185.6128

85

1178.2844

1185.6035

87

1183.2001

1185.4390

89

1188.8987

1185.2673

53

1119.8505

1187.3517

54

1120.5270

1187.3362

55

1121.2043

1187.3248

57

1126.2226

1187.1628

(x,y se preiau de la varianta 1)




Cotele Z sunt aceleasi calculate la metoda a).



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