« HANDLING STANDARD GIS FEATURES »

1. «  HANDLING STANDARD GIS FEATURES  » « Performing spatial analysis in vector mode»

2. Contents • Definitions • Spatial analysis operators • Spatial attribute request • Spatial metric operators • Topological model • 2D topological relationships • Spatial topological operators for one layer • Spatial topological operators for two layers • Spatial topological operators for network topology • Statistic operators • Stochastic operators

3. Definitions • Vector mode (reminder) • vector data : points, lines, polygons • Geographic data : • vector object  alphanumerical attributes (=semantic) • At least one attribute, to join external databases : identifier • Spatial Analysis • Phenomenon Analysis (feature proximity, intersecting features,…) whose location (x,y,z) and extent (xb,yb,zb) boundaryare known

4. attribute operators spatial operators Spatial analysis operators

5. IDENTIFIANT DONNEES U 1 A 2 B 3 B 4 A 5 C Automatic selection on map 1 2 3 automatic selection in attribute table 4 5 Spatial attribute request ATTRIBUTE SELECTION SPATIAL SELECTION conversely from attribute table From map 1 2 3 4 5

6. d d perimeter area 1 2 3 4 5 Spatial metric operators • Definition: based on metric information from geometry of geographic entities • Stored metric information • Position • Arc length • Polygon perimeter • Polygon area • Calculated metric information • Orientation of a segment • Euclidean distance • Lenght along an arc • Selection in perimeter of

7. Node Face Topological model • Definition (remind) • Manage connectivity and contiguity rules between features • Features creation in topological mode is longer and more complex than for non- or pseudo-topological data • Geoprocessing (layer crossing) is faster and more reliable than for non- or pseudo-topological data Planar topology Network Topology

8. 2D topological relationships • A set of boolean operators • disjoining • neighborhood • inclusion • intersection • equality • use in the requests • Features selection in layer • No feature to be created contrary to using spatial topological operators

9. orge blé céréale + seigle + friche chêne pacage forêt + pré pin Spatial topological operators for one layer • Agregation: Merging polygons Detail • Generalization: geometry change Detail • Buffer: processing of inclusions and euclidean distance Detail

10. 1 2 20 3 4 5 10 30 Specified attribute orge blé céréale seigle friche chêne pacage forêt pré pin Spatial topological operators for one layer • Agregation

11. + + According to option «merge limits » + Spatial topological operators for one layer • Generalization • Buffer or •  Ex : Define different zones to protect harnessing water resource

12. Spatial topological operators for two layers • Crossing two layers • Be careful with: • Reference frame (same) • relative precision • micro-polygons can be created by the crossing

13. 1 1 1 2 2 2 1 5 3 3 3 2 6 1 1 1 4 4 4 5 5 5 3 3 3 3 4 7 2 2 2 1 14 5 10 13 15 2 6 12 11 3 7 4 8 9 Spatial topological operators for two layers • Intersection : processing of inclusions Detail 3 slides • Union : processing of inclusions and supplementaries • Difference Detail • « sectioning - insertion » functions Detail

14. 1 2 3 4 5 1 5 2 6 3 7 4 1 3 2 Spatial topological operators for two layers • Intersection (1)

15. Spatial topological operators for two layers • Intersection (2) 1 1 + + 1 3 2 + + 3 2 3 3 + + 2 2 1 3 4 2 1 + 2 + 3 +

16. Spatial topological operators for two layers • Intersection (3) • Difference Crossing two layer (one in black, the other in blue) : point+pointpoint line+line line • Symmetric difference

17. Spatial topological operators for two layers • « sectioning - insertion » functions In-layer operator Parameter-layer Out-layer Example with polygon in-layer, but it’s the same with line or point in-layer Split Clip Erase operator ‘’Update’’ only between two polygon layers Update Operator ‘’Cut’’ only with line or polygon in-layer Cut

18. Spatial topological operators for network topology • Path calculating • Connection of lines and nodes • Rules of flow traffic on each feature network (edge or node called junction too) • Assign weight to different feature network • Take into account the temporary closing of network’s part • Examples of applications • Optimisation of routes for farm machinery to cover several sites • Study of irrigation network when a valve was broken

19. Statistic operators • Calculating based on semantic information linked to geographic features (only numeric attributes  average, minimum value …) • Histogram • Statistic recapitulation (all types of attributes) • Thematic mapping. According to distribution of values, different methods • Natural breaks • Quantile • Equal interval • Standard deviation

20. Stochastic operators • Spatial relationships between features (points, polygons) to explain and model the spatial distribution of variables in a probabilistic mode • When discrete spatial unit (segment, polygon) : spatial autocorrelation index(Moran, Geary) = degree of similitude between values of a variable according to the neighborhood of spatial unit (lattices) Application: spatial structures modeling • When whole space and point-by-point observations : degree of dissimilitude between values of a variable according to distance between data points (semi-variogram). Application: estimate or complete lacked data (kriging), simulate probable dataset, cartographybased on spatial sampling plane •  the geostatistic