Outdated version of the documentation. Find the latest one here.

Topologia

gentlelogo

Obiective:

Să înțelegem topologia datelor vectoriale

Cuvinte cheie:

Vector, topologie, normele de topologie, erorile de topologie, raza de căutare, distanța de acroșare, entitate simplă

Vedere generală

Topologia exprimă relațiile spațiale dintre entitățile vectoriale conectate sau adiacente (puncte, polilinii și poligoane) dintr-un GIS. Datele topologice, sau pe bază de topologie, sunt utile pentru detectarea și corectarea erorilor de digitizare (de exemplu, două linii dintr-un strat de drumuri vectoriale care nu se întâlnesc perfect la o intersecție). Topologia este necesară pentru realizarea unor genuri de analize spațiale, cum ar fi analiza de rețea.

Imaginați-vă că vă deplasați spre Londra. Cu ajutorul unei hărți turistice vă planificați mai întâi o vizită la Catedrala Sf Paul, urmată de alta la Covent Garden Market, pentru unele suveniruri. Privind pe harta metroului londonez (a se vedea figure_topology_london) va trebui să identificați trenurile de legătură dintre Covent Garden și Sf. Paul. Acest lucru necesită informații topologice (date) cu privire la posibilitatea de schimbare a trenurilor. Privind la o hartă a metroului, relațiile topologice sunt ilustrate prin cercuri care arată conexiunile.

Figure London Underground Network 1:

../../_images/london_underground.png

Topologia rețelei de metrou din Londra

Erori de topologie

Există diferite tipuri de erori topologice, ele putând fi grupate în funcție de caracterul de poligon sau polilinie al entităților vectoriale. Printre erorile topologice, în cazul entităților de tip poligon, se pot include poligoanele nefinalizate, breșele sau suprapunerile limitelor poligoanelor. O eroare topologică obișnuită, în cazul entităților de tip polilinie, o reprezintă faptul că acestea nu sunt tangente la un punct (nod). Acest tip de eroare poartă numele neîncadrare dacă există o breșă între linii, sau depășire dacă o linie se termină dincolo de linia la care ar trebui să se conecteze (a se vedea figure_topology_errors).

Figure Topology Errors 1:

../../_images/topology_errors.png

Erorile de neîncadrare (1) apar atunci când liniile vectoriale digitizate, care ar trebuie să fie conectate între ele, nu se ating. Depășirile (2) apar atunci când o linie se termină dincolo de linia la care ar trebui să se conecteze. Așchiile (3) apar atunci când vârfurile a două poligoane nu aderă perfect la laturile lor.

Rezultatul erorilor de neîncadrare și de depășire sunt așa-numitele ‘noduri incerte’ de la capătul liniilor. Nodurile incerte sunt acceptabile în cazuri speciale, cum ar fi cazul în care sunt atașate unor străzi care se înfundă.

Topological errors break the relationship between features. These errors need to be fixed in order to be able to analyse vector data with procedures like network analysis (e.g. finding the best route across a road network) or measurement (e.g. finding out the length of a river). In addition to topology being useful for network analysis and measurement, there are other reasons why it is important and useful to create or have vector data with correct topology. Just imagine you digitise a municipal boundaries map for your province and the polygons overlap or show slivers. If such errors were present, you would be able to use the measurement tools, but the results you get will be incorrect. You will not know the correct area for any municipality and you will not be able to define exactly, where the borders between the municipalities are.

It is not only important for your own analysis to create and have topologically correct data, but also for people who you pass data on to. They will be expecting your data and analysis results to be correct!

Reguli topologice

Din fericire, multe din erorile care pot apărea la digitizarea entităților vectoriale pot fi prevenite prin regulile de topologie care sunt implementate în multe aplicații GIS.

Except for some special GIS data formats, topology is usually not enforced by default. Many common GIS, like QGIS, define topology as relationship rules and let the user choose the rules, if any, to be implemented in a vector layer.

The following list shows some examples of where topology rules can be defined for real world features in a vector map:

  • Marginile hărții unei municipalități nu trebuie să se suprapună.

  • Marginile unei hărți pentru o municipalitate nu trebuie să aibă lacune (șuvițe).

  • Poligoanele care indică limitele de proprietate trebuie să fie închise. Depășirile liniilor de frontieră, inclusiv cele negative, nu sunt permise.

  • Curbele de nivel dintr-un strat vectorial de tip linie nu trebuie să se intersecteze (nu au voie să se încrucișeze).

Instrumente topologice

Many GIS applications provide tools for topological editing. For example in QGIS you can enable topological editing to improve editing and maintaining common boundaries in polygon layers. A GIS such as QGIS ‘detects’ a shared boundary in a polygon map so you only have to move the edge vertex of one polygon boundary and QGIS will ensure the updating of the other polygon boundaries as shown in figure_topological_tools (1).

Another topological option allows you to prevent** polygon overlaps** during digitising (see figure_topological_tools (2)). If you already have one polygon, it is possible with this option to digitise a second adjacent polygon so that both polygons overlap and QGIS then clips the second polygon to the common boundary.

Figure Topological Tools 1:

../../_images/topological_tools.png

(1) Topological editing to detect shared boundaries, when moving vertices. When moving a vertex, all features that share that vertex are updated. (2) To avoid polygon overlaps, when a new polygon is digitised (shown in red) it is clipped to avoid overlapping neighbouring areas.

Distanța de acroșare

Snapping distance is the distance a GIS uses to search for the closest vertex and / or segment you are trying to connect when you digitise. A segment is a straight line formed between two vertices in a polygon or polyline geometry. If you aren’t within the snapping distance, a GIS such as QGIS will leave the vertex where you release the mouse button, instead of snapping it to an existing vertex and / or segment (see figure_snapping_distance).

Figure Snapping Distance 1:

../../_images/snapping_distance.png

The snapping distance (black circle) is defined in map units (e.g. decimal degrees) for snapping to either vertices or segments.

Raza de căutare

Search radius is the distance a GIS uses to search for the closest vertex you are trying to move when you click on the map. If you aren’t within the search radius, the GIS won’t find and select any vertex of a feature for editing. In principle, it is quite similar to the snapping distance functionality.

Snapping distance and search radius are both set in map units so you may need to experiment to get the distance value set right. If you specify a value that is too big, the GIS may snap to a wrong vertex, especially if you are dealing with a large number of vertices close together. If you specify the search radius too small the GIS application won’t find any feature or vertex to move or edit.

Probleme comune / lucruri de care trebuie să fiți conștienți

Mainly designed for simplicity and for fast rendering but not for data analysis that require topology (such as finding routes across a network). Many GIS applications are able to show topological and simple feature data together and some can also create, edit and analyse both.

Ce am învățat?

Să recapitulăm subiectele abordate în acest capitol:

  • Topology shows the spatial relation of neighbouring vector features.
  • Topologia în GIS poate fi accesată de către instrumentele topologice.

  • Topology can be used to detect and correct digitizing errors.
  • For some tools, such as network analysis, topological data is essential.
  • Snapping distance and search radius help us to digitise topologically correct vector data.
  • Simple feature data is not a true topological data format but it is commonly used by GIS applications.

Încercați acum!

Aici sunt câteva idei care pot fi testate împreună cu elevii dumneavoastră:

  • Mark your local bus stops on a toposheet map and then task your learners to find the shortest route between two stops.
  • Think of how you would create vector features in a GIS to represent a topological road network of your town. What topological rules are important and what tools can your learners use in QGIS to make sure that the new road layer is topologically correct?

De reținut

If you don’t have a computer available, you can use a map of a bus or railway network and discuss the spatial relationships and topology with your learners.

Lecturi suplimentare

Cărți:

  • Chang, Kang-Tsung (2006). Introduction to Geographic Information Systems. 3rd Edition. McGraw Hill. ISBN: 0070658986
  • DeMers, Michael N. (2005). Fundamentals of Geographic Information Systems. 3rd Edition. Wiley. ISBN: 9814126195

Site-uri web:

The QGIS User Guide also has more detailed information on topological editing provided in QGIS.

Ce urmează?

In the section that follows we will take a closer look at Coordinate Reference Systems to understand how we relate data from our spherical earth onto flat maps!