UNIVERSITATEA TEHNICA DE CONSTRUCTII BUCURESTI

UNIVERSITATEA DE TIINE AGRONOMICE I MEDICIN VETERINAR BUCURETIFACULTATEA DE MBUNTIRI FUNCIARE I INGINERIA MEDIULUIDOMENIUL INGINERIE GEODEZICLUCRARE PRACTICFOTOGRAMMETRIE

ANALITIC

Student: ______________________________________ Grupa ____________2014-2015PRELUCRAREA PRELIMINARA A COORDONATELOR

IMAGINE MASURATE LA STECOMETRU Tema nr. 16/2

Se dau coordonatele imagine masurate pentru cei 4 indici de referinta si pentru un numar de 12 puncte de reper de pe stereograma 6472 / 6473:

Nr. pct.x' (mm)y'' (mm)(x'' (mm)(y' (mm)

1400.205400.033299.742299.851

2611.315399.352299.738299.486

3610.274188.229299.383299.489

4399.171188.911299.398299.857

3172507.202212.727363.443297.889

5022486.756236.635363.182298.204

22485.794233.742363.028298.226

5213529.420257.487362.571297.648

217539.536238.215360.931297.462

3173570.917206.977361.067296.767

14592.906304.941366.277297.208

229556.557282.441364.990297.347

5211509.466280.762362.591297.823

13484.658342.584366.420297.565

5234565.606331.508370.178297.347

1172492.113398.928373.010296.875

Se cere sa se corecteze aceste coordonate imagine pentru ambele fotograme cunoscand urmatoarele date:

1. constanta camerei: ck = 151.840 mm;

2. coordonatele punctului principal P al camerei (8) cu care s-a realizat aerofotografierea:

xP = 3.9 (m

yP = 8.7 (m

3. curba de distorsiune radiala a obiectivului:

ri (mm)20406080100120140148

(ri ((m)3620-4-829

4. coordonatele calibrate ale indicilor de referinta:

Nr. indicex (mm)y (mm)

1-106.008106.008

2106.008106.008

3106.008-106.008

4-106.008-106.008

5. inaltimea de zbor la care s-a facut aerofotografierea: Hzbor = 2.80 km.

Stecometrul este un aparat care reprezinta o versiune imbunatatita a stereocomparatorului. Acest aparat este utilizat pentru masurarea coordonatelor imagine pe o stereograma, cuplat cu un coordimetru electronic, interfata, masina de scris sau cuplat cu coordimetru electronic , microcalculator si imprimanta.

Stecometrul este folosit in fotogrammetria analitica, cu aplicatii in aerotriangulatie si restitutie analitica acoperind, de asemenea, domenii ale fotogrammetriei precum: fotogrammetria terestra si la scurta distanta.

Formatul maxim ce poate fi masurat este de 240mm / 240mm.; aparatul dispune de 6 marci de masurare, de diferite forme, marimi si culori; luminozitatea imaginii si a marcii de masurare sunt reglabile.

Masurarea la stecometru se poate efectua cu fotogramele orientate sau cu fotogramele orientate aproximativ. In acest caz masuratorile au fost efectuate cu fotogramele orientate aproximativ in portcliseele aparatului, caz cel mai folosit in practica.

Eroarea medie de masurare a coordonatelor si a paralaxelor este de ( 0.002mm.

1). Reducerea valorilor masurate:

Observatii la stecometru:

Nr. pct.x' (mm)y'' (mm)(x'' (mm)(y' (mm)

1400.205400.033299.742299.851

2611.315399.352299.738299.486

3610.274188.229299.383299.489

4399.171188.911299.398299.857

3172507.202212.727363.443297.889

5022486.756236.635363.182298.204

22485.794233.742363.028298.226

5213529.420257.487362.571297.648

217539.536238.215360.931297.462

3173570.917206.977361.067296.767

14592.906304.941366.277297.208

229556.557282.441364.990297.347

5211509.466280.762362.591297.823

13484.658342.584366.420297.565

5234565.606331.508370.178297.347

1172492.113398.928373.010296.875

Coordonatele si paralaxele punctului mijlociu M, care va deveni originea sistemului de coordonate pentru valorile masurate, se calculeaza pe baza coordonatelor si paralaxelor indicilor de referinta:

unde:

Coordonatele punctelor stereogramei se reduc la origine cu relatiile:

Calculul coordonatelor reduse:

Numarx' (mm)y'' (mm)x'' (mm)y' (mm)

punctx'x' y''y'' x''x'' y'y'

1400.205-105.036400.033105.902299.7420.177299.8510.180

2611.315106.074399.352105.221299.7380.173299.486-0.185

3610.274105.033188.229-105.902299.383-0.182299.489-0.182

4399.171-106.070188.911-105.220299.398-0.167299.8570.186

M505.241294.131299.565299.671

3172507.2021.961212.727-81.404363.44363.878297.889-1.782

5022486.756-18.485236.635-57.496363.18263.617298.204-1.467

22485.794-19.447233.742-60.389363.02863.463298.226-1.445

5213529.4224.179257.487-36.644362.57163.006297.648-2.023

217539.53634.295238.215-55.916360.93161.366297.462-2.209

3173570.91765.676206.977-87.154361.06761.502296.767-2.904

14592.90687.665304.94110.810366.27766.712297.208-2.463

229556.55751.316282.441-11.690364.9965.425297.347-2.324

5211509.4664.225280.762-13.369362.59163.026297.823-1.848

13484.658-20.583342.58448.453366.4266.855297.565-2.106

5234565.60660.365331.50837.377370.17870.613297.347-2.324

1172492.113-13.128398.928104.797373.0173.445296.875-2.796

2). Calculul coordonatelor in sistemul fiecarei fotograme:

Coordonatele stereogramei se calculeaza cu relatiile:

Coordonate pe stereograma:

NumarFotogrma F'Fotograma F''

punctx' (mm)y' (mm)x'' (mm)y'' (mm)

1-105.036106.082-105.213105.902

2106.074105.036105.901105.221

3105.033-106.084105.215-105.902

4-106.070-105.034-105.903-105.220

31721.961-83.186-61.917-81.404

5022-18.485-58.963-82.102-57.496

22-19.447-61.834-82.910-60.389

521324.179-38.667-38.827-36.644

21734.295-58.125-27.071-55.916

317365.676-90.0584.174-87.154

1487.6658.34720.95310.810

22951.316-14.014-14.109-11.690

52114.225-15.217-58.801-13.369

13-20.58346.347-87.43848.453

523460.36535.053-10.24837.377

1172-13.128102.001-86.573104.797

3). Orientarea fotogramelor si aplicarea corectiei datorata influentei contractiei suportului emulsiei:

Relatiile utilizate pentru orientarea, corectarea si reducerea coordonatelor masurate la punctul principal sunt de forma:

xi , yi = coordonatele corectate;

xi , yi = coordonatele masurate;

xP , yP = coordonatele punctului principal;

a0 , a1 , a2 , a3 , b0 , b1 , b2 , b3 = parametrii transformarii;

Translatiile a0 si b0 se neglijeaza.

FOTOGRAMA F':Ecuatiile de corectii pentru x:

a1*10-2a2*10-2a3*10-4l*10-2Suma

-1.050361.06082-1.11424551.06008-0.0437080

1.060741.050361.1141562-1.060082.1651737

1.05033-1.06084-1.1142294-1.06008-2.1848219

-1.06070-1.050341.11409831.060080.0631358

Ecuatiile normale:

a1a2a3lSuma Control

4.4567031-0.00022050.0001564-4.4757956-0.0191565-0.0191565

4.45719080.00008840.02221934.47927804.4792780

4.9656094-0.00007864.96577574.9657757

Rezolvarea ecuatiilor normale pentru x:

a1a2a3lSuma Control

4.4567031-0.00022050.0001564-4.4757956-0.0191565-0.0191565

-1.00000000.0000495-0.00003511.00428400.00429840.0042984

4.45719080.00008840.02221934.47927804.4792780

4.45719080.00008840.02199794.47927704.4792770

-1.0000000-0.0000198-0.0049354-1.0049552-1.0049552

4.9656094-0.00007864.96577574.9657757

4.96560940.00007814.96568754.9656875

-1.0000000-0.0000157-1.0000157-1.0000157

a1= 1.0042838

a2=-0.0049354

a3=-0.0000157

Ecuatiile de corectii pentru y:

b1*10-2b2*10-2b3*10-4l*10-2Suma

-1.050361.06082-1.1142455-1.06008-2.1638680

1.060741.050361.1141562-1.060082.1651737

1.05033-1.06084-1.11422941.06008-0.0646619

-1.06070-1.050341.11409831.060080.0631358

Ecuatiile normale:

b1b2b3lSuma Control

4.4567031-0.00022050.0001564-0.02199674.43464244.4346424

4.45719080.0000884-4.4760394-0.0189807-0.0189807

4.9656094-0.00004444.96580984.9658098

Rezolvarea ecuatiilor normale pentru y:

b1b2b3lSuma Control

4.4567031-0.00022050.0001564-0.02199674.43464244.4346424

-1.00000000.0000495-0.00003510.0049356-0.9950500-0.9950500

4.45719080.0000884-4.4760394-0.0189807-0.0189807

4.45719080.0000884-4.4760405-0.0187613-0.0187613

-1.0000000-0.00001981.00422900.00420920.0042092

4.9656094-0.00004444.96580984.9658098

4.96560940.00004514.96565464.9656546

-1.0000000-0.0000091-1.0000091-1.0000091

b1= 0.0049853

b2= 1.0042290

b3=-0.0000091

Calculul coordonatelor transformate pentru fotograma F:

NumarCoordonate masurateCoordonate corectate

punctx' (mm)y' (mm)x (mm)y (mm)Coeficientii

31721.961-83.1862.378-83.535a1=1.0042838

5022-18.485-58.963-18.294-59.323a2=-0.0049354

22-19.447-61.834-19.248-62.212a3=-0.0000157

521324.179-38.66724.484-38.710b1=0.0049853

21734.295-58.12534.756-58.190b2=1.0042290

317365.676-90.05866.491-90.066b3=-0.0000091

1487.6658.34787.9848.804xP=0.0039mm

22951.316-14.01451.612-13.820yP=0.0087mm

52114.225-15.2174.315-15.268

13-20.58346.347-20.88946.440

523460.36535.05360.41335.474

1172-13.128102.001-13.671102.370

FOTOGRAMA F'':

Ecuatiile de corectii pentru x:

a1*10-2a2*10-2a3*10-4l*10-2Suma

-1.052131.05902-1.11422411.06008-0.0472566

1.059011.052211.1142983-1.060082.1654358

1.05215-1.05902-1.1142505-1.06008-2.1812030

-1.05903-1.052201.11431401.060080.0631615

Ecuatiile normale:

a1a2a3lSuma Control

4.45704390.0001377-0.0000891-4.4759970-0.0189045-0.0189045

4.45731740.00002260.01444894.47192664.4719266

4.96640590.00004474.96638414.9663841

Rezolvarea ecuatiilor normale pentru x:

a1a2a3lSuma Control

4.45704390.0001377-0.0000891-4.4759970-0.0189045-0.0189045

-1.0000000-0.00003090.00002001.00425240.00424150.0042415

4.45731740.00002260.01444894.47192664.4719266

4.45731740.00002260.01458714.47192724.4719272

-1.0000000-0.0000051-0.0032726-1.0032777-1.0032777

4.96640590.00004474.96638414.9663841

4.9664059-0.00004484.96636114.9663611

-1.00000000.0000090-0.9999910-0.9999910

a1= 1.0042525

a2=-0.0032726

a3= 0.0000090

Ecuatiile de corectii pentru y:

b1*10-2b2*10-2b3*10-4l*10-2Suma

-1.052131.05902-1.1142241-1.06008-2.1674166

1.059011.052211.1142983-1.060082.1654358

1.05215-1.05902-1.11425051.06008-0.0610430

-1.05903-1.052201.11431401.060080.0631615

Ecuatiile normale:

b1b2b3lSuma Control

4.45704390.0001377-0.0000891-0.01458674.44250584.4425058

4.45731740.0000226-4.4761348-0.0186571-0.0186571

4.9664059-0.00001134.96632804.9663280

Rezolvarea ecuatiilor normale pentru y:

b1b2b3lSuma Control

4.45704390.0001377-0.0000891-0.01458674.44250584.4425058

-1.0000000-0.00003090.00002000.0032727-0.9967382-0.9967382

4.45731740.0000226-4.4761348-0.0186571-0.0186571

4.45731740.0000226-4.4761343-0.0187943-0.0187943

-1.0000000-0.00000511.00422160.00421650.0042165

4.9664059-0.00001134.96632804.9663280

4.96640590.00001104.96641694.9664169

-1.0000000-0.0000022-1.0000022-1.0000022

b1= 0.0032417

b2= 1.0042216

b3=-0.0000022

Calculul coordonatelor transformate pentru fotograma F:

NumarCoordonate masurateCoordonate corectate

punctx'' (mm)y'' (mm)x (mm)y (mm)Coeficientii

3172-61.917-81.404-61.872-81.969a1=1.0042525

5022-82.102-57.496-82.224-58.024a2=-0.0032726

22-82.910-60.389-83.024-60.933a3=0.0000090

5213-38.827-36.644-38.863-36.937b1=0.0032417

217-27.071-55.916-26.993-56.252b2=1.0042216

31734.174-87.1544.470-87.517b3=-0.0000022

1420.95310.81021.00510.914xP=0.0039mm

229-14.109-11.690-14.133-11.794yP=0.0087mm

5211-58.801-13.369-59.004-13.627

13-87.43848.453-88.01148.375

5234-10.24837.377-10.42137.493

1172-86.573104.797-87.370104.970

4). Corectarea influentei distorsiunii obiectivului camerei de preluare:

Distorsiunea obiectivului, corespunzator constantei camerei aerofotogrammetrice rezulta in urma etalonarii, este un element al orientarii interioare. Influenta sa asupra pozitiei punctelor pe fotograma poate fi corectata pe cale analitica.

ri = deplasarea in planul imagine intre pozitia reala si cea corectata a punctului P

din spatiul obiect;

ri (mm)20406080100120140148

(ri ((m)3620-4-829

Coeficientii ai se determina prin metoda patratelor minime.

cx , cy = corectii;

xi , yi = coordonate corectate;

Ecuatiile de corectii:

a1*10-2a2*10-5a3*10-9a4*10-13lSuma

0.200.080.00320.000128-0.0030.280328

0.400.640.10240.016384-0.0061.152784

0.602.160.77760.279936-0.0023.815536

0.805.123.27682.0971520.00011.293952

1.0010.0010.000010.0000000.00431.004000

1.2017.2824.883235.8318080.00879.203008

1.4027.4453.7824105.413504-0.002188.033904

1.4832.4179271.008212155.536387-0.009260.433519

Ecuatiile normale:

a1a2a3a4lSumaControl

7.7904122.794522223.376954432.623191-0.00672786.5783786.5783

2233.7695374326.2319118665.238935-0.1768015347.858115347.8581

8665.23893517712.453358-0.5097530926.791430926.7914

36691.969804-1.28465963501.000663501.0006

Rezolvarea ecuatiilor normale:

a1a2a3a4lSumaControl

7.7904122.7945223.3770432.6232-0.006720786.578346786.578346

-1.0000-15.762287-28.673361-55.5328600.0008626-100.9676456-100.967646

2233.7695374326.2319118665.238935-0.17680115347.85810315347.858103

298.2470306805.3002301846.107981-0.0708792949.5843632949.584363

-1.000000-2.700111-6.1898620.000238-9.889736-9.889736

8665.23893517712.453358-0.50975230926.79140630926.791406

85.870447322.994957-0.125687408.739717408.739717

-1.000000-3.7614220.001464-4.759958-4.759958

36691.969804-1.28465963501.00063063501.000630

25.0928030.00001325.09281625.092816

-1.000000-0.000001-1.000001-1.000001

a1= 1.744750*10-4

a2=-3.716519*10-8

a3= 1.465643*10-12

a4=-5.217658*10-20

Calculul coordonatelor corectate:

FOTOGRAMA F':

Numar Coordonate initialeCorectiiCoordonate corectate

punctx' (mm)y' (mm)r (mm)dr (()cx (()cy (()x (mm)y (mm)

31722.378-83.53583.569-1.140.0-1.12.378-83.536

5022-18.294-59.32362.0803.291.03.1-18.294-59.320

22-19.248-62.21265.1222.810.82.7-19.247-62.209

521324.484-38.71045.8034.72-2.54.024.481-38.706

21734.756-58.19067.7802.35-1.22.034.755-58.188

317366.491-90.066111.951-6.854.1-5.566.495-90.072

1487.9848.80488.423-2.352.30.287.9868.804

22951.612-13.82053.4304.29-4.11.151.608-13.818

52114.315-15.26815.8662.62-0.72.54.314-15.266

13-20.88946.44050.9224.481.8-4.1-20.88746.436

523460.41335.47470.0581.92-1.7-1.060.41235.473

1172-13.671102.370103.279-5.71-0.85.7-13.671102.376

FOTOGRAMA F'':

Numar Coordonate initialeCorectiiCoordonate corectate

punctx'' (mm)y'' (mm)r (mm)dr (()cx (()cy (()x (mm)y (mm)

3172-61.872-81.969102.699-5.60-3.4-4.5-61.876-81.973

5022-82.224-58.024100.636-5.20-4.2-3.0-82.229-58.027

22-83.024-60.933102.984-5.65-4.6-3.3-83.028-60.936

5213-38.863-36.93753.6164.283.12.9-38.860-36.934

217-26.993-56.25262.3933.241.42.9-26.992-56.249

31734.470-87.51787.631-2.150.1-2.14.470-87.519

1421.00510.91423.6713.65-3.2-1.721.00210.912

229-14.133-11.79418.4082.982.31.9-14.131-11.792

5211-59.004-13.62760.5573.513.40.8-59.001-13.626

13-88.01148.375100.429-5.16-4.52.5-88.01548.377

5234-10.42137.49338.9154.731.3-4.6-10.42037.489

1172-87.370104.970136.573-1.25-0.81.0-87.371104.971

6). Prelucrarea preliminara a coordonatelor imagine:

Corectarea influentei refractiei atmosferice:

Directiile fascicolului fotogrametric, in timpul formarii imaginii strabat atmosfera considerata a fi formata din straturi de aer de temperatura, presiune, compozitie diferite, deci si de indici de refractie diferiti. Acest lucru induce o deplasare radiala a pozitiei punctelor din planul imagine fata de punctul principal.

ck = 151.840 mm

(=206264.806

( = unghi nadiral

Corectia datorata curburii Pamantului:

Aceasta corectie se aplica atunci cand utilizam sistemele de coordonate in planul de proiectie; deplasarea punctelor este radiala fata de punctul principal si are sens negativ pe directia radiala fata de acesta.

R = 6370000m

Hzbor = 2.80 km

Valorile unghiului (( functie de ( si de H:

(0800750700650600550500450400350300200100

H (km)((((((((((((((((((((((((((

2.028181411976544321

3.04026191512108765431

FOTOGRAMA F':

Calculul corectiilor de refractie si de curbura a Pamantului:

Numar Coordonate initialeCorectia de refractie atmosfericaCorectia de curburaCoord.corectate

punctx' (mm)y' (mm)r (mm)(0(((ri (()cx (()cy (()(ri (()cx (()cy (()x (mm)y (mm)

31722.378-83.53683.570290093.73.60.1-3.65.60.2-5.62.378-83.538

5022-18.294-59.32062.077210092.92.5-0.7-2.42.3-0.7-2.2-18.293-59.320

22-19.247-62.20965.119220183.02.6-0.8-2.52.6-0.8-2.5-19.247-62.209

521324.481-38.70645.799150081.91.50.8-1.30.90.5-0.824.481-38.706

21734.755-58.18867.777230183.12.81.4-2.43.01.5-2.534.755-58.189

317366.495-90.072111.958380025.36.03.6-4.813.47.9-10.866.499-90.078

1487.9868.80488.425300523.93.83.80.46.66.60.787.9898.804

22951.608-13.81853.426170552.42.01.9-0.51.51.4-0.451.608-13.818

52114.314-15.26615.86440590.00.00.00.00.00.00.04.314-15.266

13-20.88746.43650.918170002.31.9-0.81.71.3-0.51.1-20.88746.436

523460.41235.47370.056240103.22.92.51.53.32.81.760.41235.473

1172-13.671102.376103.285350404.95.2-0.75.210.5-1.410.4-13.672102.381

FOTOGRAMA F:

Calculul corectiilor de refractie si de curbura a Pamantului:

Numar Coordonate initialeCorectia de refractie atmosfericaCorectia de curburaCoord.corectate

punctx' (mm)y' (mm)r (mm)(0(((ri (()cx (()cy (()(ri (()cx (()cy (()x (mm)y (mm)

3172-61.876-81.973102.704370045.15.5-3.3-4.410.3-6.2-8.2-61.879-81.977

5022-82.229-58.027100.641330324.54.7-3.9-2.79.7-7.9-5.6-82.233-58.030

22-83.028-60.936102.990340084.65.0-4.0-2.910.4-8.4-6.2-83.033-60.939

5213-38.860-36.93453.612190262.72.2-1.6-1.51.5-1.1-1.0-38.860-36.933

217-26.992-56.24962.390220203.02.6-1.1-2.32.3-1.0-2.1-26.992-56.249

31734.470-87.51987.633290593.83.70.2-3.76.40.3-6.44.470-87.521

1421.00210.91223.66780510.00.00.00.00.10.10.121.00210.912

229-14.131-11.79218.40560540.00.00.00.00.10.00.0-14.131-11.793

5211-59.001-13.62660.554210440.00.00.00.02.1-2.1-0.5-59.003-13.626

13-88.01548.377100.434330284.54.7-4.12.39.7-8.54.7-88.01948.379

5234-10.42037.48938.910140221.71.3-0.41.30.6-0.20.5-10.42037.488

1172-87.371104.971136.574410585.97.9-5.06.124.3-15.518.7-87.381104.984

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