QGIS sta facendo passi da gigante nello sviluppo del codice e sta sempre più avvicinandosi al mondo 3D con nuove funzionalità come per esempio la definizione di shapefile 3D, info 3D ecc… ma ancora molte funzioni (come calcolo area $area, $perimetro, $lunghezza ecc…) sono sempre in 2D anche se lo shapefile è 3D.
In questo articolo utilizzerò Python per calcolare superfici e lunghezze di shapefile 3D partendo dai vertici (punti x,y,z) delle features (per esempio un file CSV di punti (x,y,z)).
unisco questi punti per formare tanti triangoli utilizzando lo SNAP di QGIS che si aggancia anche alla Z, cosi da realizzare triangoli nello spazio 3D:
esporto lo shapefile ‘tring_3D’ utilizzando il plugin ‘wkt export‘ ottenendo un file cosi strutturato:
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| PolygonZ ((967569.83999999996740371 4165799.08000000007450581 829, 954254.42000000004190952 4152822.06000000005587935 755, 957341.85999999998603016 4173449.14999999990686774 458, 967569.83999999996740371 4165799.08000000007450581 829)) | |
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| PolygonZ ((986701.2099999999627471 4155965.89000000013038516 900, 1003161.91000000003259629 4173698.75999999977648258 382, 1008400.43999999994412065 4177627.31000000005587935 874, 986701.2099999999627471 4155965.89000000013038516 900)) |
questo formato va modificato per utilizzarlo in seguito: elimino il testo (PoligonZ), le parentesi e aggiungo una virgola per separare le coordinate, ottenendo un file CSV:
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| 967569.83999999996740371 | 4165799.08000000007450581 | 829 | 954254.42000000004190952 | 4152822.06000000005587935 | 755 | 957341.85999999998603016 | 4173449.14999999990686774 | 458 | 967569.83999999996740371 | 4165799.08000000007450581 | 829 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 967569.83999999996740371 | 4165799.08000000007450581 | 829 | 959935.60999999998603016 | 4147696.77000000001862645 | 669 | 954254.42000000004190952 | 4152822.06000000005587935 | 755 | 967569.83999999996740371 | 4165799.08000000007450581 | 829 | |
| 967569.83999999996740371 | 4165799.08000000007450581 | 829 | 973804.56999999994877726 | 4151234.29999999981373549 | 883 | 959935.60999999998603016 | 4147696.77000000001862645 | 669 | 967569.83999999996740371 | 4165799.08000000007450581 | 829 | |
| 967569.83999999996740371 | 4165799.08000000007450581 | 829 | 976720.17000000004190952 | 4165318.29999999981373549 | 657 | 973804.56999999994877726 | 4151234.29999999981373549 | 883 | 967569.83999999996740371 | 4165799.08000000007450581 | 829 | |
| 967569.83999999996740371 | 4165799.08000000007450581 | 829 | 981652.81999999994877726 | 4173070.77000000001862645 | 466 | 976720.17000000004190952 | 4165318.29999999981373549 | 657 | 967569.83999999996740371 | 4165799.08000000007450581 | 829 | |
| 967569.83999999996740371 | 4165799.08000000007450581 | 829 | 973609.97999999998137355 | 4180161.54999999981373549 | 739 | 981652.81999999994877726 | 4173070.77000000001862645 | 466 | 967569.83999999996740371 | 4165799.08000000007450581 | 829 | |
| 967569.83999999996740371 | 4165799.08000000007450581 | 829 | 963006.18000000005122274 | 4178101.87999999988824129 | 333 | 973609.97999999998137355 | 4180161.54999999981373549 | 739 | 967569.83999999996740371 | 4165799.08000000007450581 | 829 | |
| 967569.83999999996740371 | 4165799.08000000007450581 | 829 | 957341.85999999998603016 | 4173449.14999999990686774 | 458 | 963006.18000000005122274 | 4178101.87999999988824129 | 333 | 967569.83999999996740371 | 4165799.08000000007450581 | 829 | |
| 976720.17000000004190952 | 4165318.29999999981373549 | 657 | 986701.2099999999627471 | 4155965.89000000013038516 | 900 | 973804.56999999994877726 | 4151234.29999999981373549 | 883 | 976720.17000000004190952 | 4165318.29999999981373549 | 657 | |
| 976720.17000000004190952 | 4165318.29999999981373549 | 657 | 981652.81999999994877726 | 4173070.77000000001862645 | 466 | 986701.2099999999627471 | 4155965.89000000013038516 | 900 | 976720.17000000004190952 | 4165318.29999999981373549 | 657 | |
| 986701.2099999999627471 | 4155965.89000000013038516 | 900 | 989900.02000000001862645 | 4176380.87999999988824129 | 459 | 1003161.91000000003259629 | 4173698.75999999977648258 | 382 | 986701.2099999999627471 | 4155965.89000000013038516 | 900 | |
| 986701.2099999999627471 | 4155965.89000000013038516 | 0 | 981652.81999999994877726 | 4173070.77000000001862645 | 466 | 989900.02000000001862645 | 4176380.87999999988824129 | 459 | 986701.2099999999627471 | 4155965.89000000013038516 | 0 | |
| 1003161.91000000003259629 | 4173698.75999999977648258 | 382 | 997619.93000000005122274 | 4182769.43999999994412065 | 377 | 1008400.43999999994412065 | 4177627.31000000005587935 | 874 | 1003161.91000000003259629 | 4173698.75999999977648258 | 382 | |
| 997619.93000000005122274 | 4182769.43999999994412065 | 377 | 1003161.91000000003259629 | 4173698.75999999977648258 | 382 | 989900.02000000001862645 | 4176380.87999999988824129 | 459 | 997619.93000000005122274 | 4182769.43999999994412065 | 377 | |
| 980723.56000000005587935 | 4186202.18999999994412065 | 629 | 989900.02000000001862645 | 4176380.87999999988824129 | 459 | 981652.81999999994877726 | 4173070.77000000001862645 | 466 | 980723.56000000005587935 | 4186202.18999999994412065 | 629 | |
| 980723.56000000005587935 | 4186202.18999999994412065 | 629 | 988030.52000000001862645 | 4189083.22000000020489097 | 837 | 989900.02000000001862645 | 4176380.87999999988824129 | 459 | 980723.56000000005587935 | 4186202.18999999994412065 | 629 | |
| 988030.52000000001862645 | 4189083.22000000020489097 | 837 | 997619.93000000005122274 | 4182769.43999999994412065 | 377 | 989900.02000000001862645 | 4176380.87999999988824129 | 459 | 988030.52000000001862645 | 4189083.22000000020489097 | 837 | |
| 988030.52000000001862645 | 4189083.22000000020489097 | 837 | 997075.91000000003259629 | 4194992.03000000026077032 | 640 | 997619.93000000005122274 | 4182769.43999999994412065 | 377 | 988030.52000000001862645 | 4189083.22000000020489097 | 837 | |
| 997075.91000000003259629 | 4194992.03000000026077032 | 640 | 1008400.43999999994412065 | 4177627.31000000005587935 | 874 | 997619.93000000005122274 | 4182769.43999999994412065 | 377 | 997075.91000000003259629 | 4194992.03000000026077032 | 640 | |
| 973609.97999999998137355 | 4180161.54999999981373549 | 739 | 980723.56000000005587935 | 4186202.18999999994412065 | 629 | 981652.81999999994877726 | 4173070.77000000001862645 | 466 | 973609.97999999998137355 | 4180161.54999999981373549 | 739 | |
| 963006.18000000005122274 | 4178101.87999999988824129 | 333 | 968416.25 | 4192046.33999999985098839 | 646 | 973609.97999999998137355 | 4180161.54999999981373549 | 739 | 963006.18000000005122274 | 4178101.87999999988824129 | 333 | |
| 968416.25 | 4192046.33999999985098839 | 646 | 973036.16000000003259629 | 4192947.14000000013038516 | 873 | 973609.97999999998137355 | 4180161.54999999981373549 | 739 | 968416.25 | 4192046.33999999985098839 | 646 | |
| 973036.16000000003259629 | 4192947.14000000013038516 | 873 | 980723.56000000005587935 | 4186202.18999999994412065 | 629 | 973609.97999999998137355 | 4180161.54999999981373549 | 739 | 973036.16000000003259629 | 4192947.14000000013038516 | 873 | |
| 973036.16000000003259629 | 4192947.14000000013038516 | 873 | 983555.25 | 4200077.79999999981373549 | 623 | 980723.56000000005587935 | 4186202.18999999994412065 | 629 | 973036.16000000003259629 | 4192947.14000000013038516 | 873 | |
| 980723.56000000005587935 | 4186202.18999999994412065 | 629 | 983555.25 | 4200077.79999999981373549 | 623 | 988030.52000000001862645 | 4189083.22000000020489097 | 837 | 980723.56000000005587935 | 4186202.18999999994412065 | 629 | |
| 983555.25 | 4200077.79999999981373549 | 623 | 997075.91000000003259629 | 4194992.03000000026077032 | 640 | 988030.52000000001862645 | 4189083.22000000020489097 | 837 | 983555.25 | 4200077.79999999981373549 | 623 | |
| 957341.85999999998603016 | 4173449.14999999990686774 | 458 | 968416.25 | 4192046.33999999985098839 | 646 | 963006.18000000005122274 | 4178101.87999999988824129 | 333 | 957341.85999999998603016 | 4173449.14999999990686774 | 458 | |
| 968416.25 | 4192046.33999999985098839 | 646 | 983555.25 | 4200077.79999999981373549 | 623 | 973036.16000000003259629 | 4192947.14000000013038516 | 873 | 968416.25 | 4192046.33999999985098839 | 646 | |
| 986701.2099999999627471 | 4155965.89000000013038516 | 900 | 1003161.91000000003259629 | 4173698.75999999977648258 | 382 | 1008400.43999999994412065 | 4177627.31000000005587935 | 874 | 986701.2099999999627471 | 4155965.89000000013038516 | 900 |
noterete che ogni riga ha quattro triplette di coordinate (x,y,z), questo perchè ogni poligono chiuso (i triangoli) il primo e l’ultimo vertice coincidono.
Questo file (tring_3D.csv) sarà utilizzato nello script Python per calcolare l’area dei triangoli (in 3D) con la formula di Erone:
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| """ | |
| /*************************************************************************** | |
| Name : Erone https://it.wikipedia.org/wiki/Formula_di_Erone | |
| Description : Calcolo superficie PoligonZ da file CSV (XYZ) | |
| Date : 25 – marzo – 2016 | |
| copyright : (C) 2016 by Salvatore Fiandaca | |
| email : pigrecoinfinito@gmail.com | |
| ***************************************************************************/ | |
| /*************************************************************************** | |
| * * | |
| * This program is free software; you can redistribute it and/or modify * | |
| * it under the terms of the GNU General Public License as published by * | |
| * the Free Software Foundation; either version 2 of the License, or * | |
| * (at your option) any later version. * | |
| * * | |
| ***************************************************************************/ | |
| """ | |
| def lungh (x1,y1,z1,x2,y2,z2): #funzione lunghezza | |
| dx,dy,dz= x1–x2, y1–y2, z1–z2 | |
| return (dx**2+dy**2+dz**2)**0.5,(dx**2+dy**2)**0.5 | |
| def Erone (a,b,c): #funzione formula di Erone | |
| p = (a+b+c)/2.0 | |
| return (p*(p–a)*(p–b)*(p–c))**0.5 | |
| # =============== importo il file CSV e creo lista coords =================== | |
| import csv | |
| with open ('triangoli3D.csv') as csvfile: | |
| readCSV = csv.reader(csvfile, delimiter=',') | |
| coords=[] #creo liste | |
| for row in readCSV: #popolo lista | |
| coords+=row | |
| # ========= calcolo lunghezze lati triangolo e creazione liste ============== | |
| lista_3D,lista_2D = [],[] #creo liste | |
| for i in range (0,len(coords)–3,3): | |
| x1,y1,z1=eval(coords [i]),eval(coords[i+1]),eval(coords[i+2]) | |
| x2,y2,z2=eval(coords [i+3]),eval(coords[i+4]),eval(coords[i+5]) | |
| lun3D,lun2D =lungh (x1,y1,z1,x2,y2,z2) #lunghezza lati 3D/2D | |
| lista_3D+=[lun3D] #popolo lista lunghezze lati 3D | |
| lista_2D+=[lun2D] #popolo lista lunghezze lati 2D | |
| # ================= calcolo elementi per formula di Erone =================== | |
| sup3D,sup2D = 0,0 | |
| for j in range (0, len(lista_3D)–2,4): | |
| a,b,c= lista_3D [j],lista_3D [j+1],lista_3D [j+2] | |
| a2,b2,c2 = lista_2D [j],lista_2D [j+1],lista_2D [j+2] | |
| Erone_3D,Erone_2D= Erone (a,b,c),Erone (a2,b2,c2) #formula di Erone | |
| sup3D+=Erone_3D | |
| sup2D+=Erone_2D | |
| # ========================== stampa risultati =============================== | |
| print "*==================*===================*" | |
| print sup3D,'mq Area 3D\n' | |
| print sup2D,'mq Area 2D\n' | |
| print sup3D–sup2D,'mq differenza Area 3D-2D\n' | |
| print round((sup3D–sup2D)/sup3D*100,3),'%' | |
| print "<+++++++++++++++pigreco++++++++++++++++>" |
Note finali: con questo articolo voglio dimostrare che con poche conoscenze di Python e con nozioni di matematica è possibile creare script per superare alcuni limiti di QGIS. Lo script di python è certamente migliorabile soprattutto nell’importazione del file csv.
Per chi volesse provare questo programma in python, mi raccomando, create il file csv per come spiegato sopra.
video.
pigrecoinfinito 
Buon giorno e complimenti per gli articoli, sempre chiari e puntuali
Volevo chiederti se è possibile disegnare un poligono rettangolare partendo da un shp punto e dalle informazioni della geometria contenute nei campi: lato maggiore, lato minore e orientamento.
"Mi piace"Piace a 1 persona
Ciao,
credo di sì.
Ma non ho mai provato.
"Mi piace""Mi piace"