1. GIS Analysis

2. Questions to answer Position – what is here? Condition – where are …? Trends – what has changed? Pattern – what spatial patterns exist? Modeling – what happens if...?

3. Tools to answer the questions I. Selection Based on database tables (Where are …?) Spatial conditions (What is here?) SQL queries Clicking at a point Inside a circle Inside a box Inside a polygon Contains entire, contains partly, contains the centroid Spatial join of two layers

4. Buffers Near of far from spatial objects Constant buffer distance Buffer distance from an attribute Multiple buffers Tools to answer the questions II.

5. Tools to answer the questions III. Overlay analysis (two layers, one of them contains polygons Union Intersection Other operations Cut Paste dissolve Sliver polygons

6. Analysis sample 10 km buffer WatersSoilsSunshine Soil = 8 and sunshine > 1800 All conditions are fulfilled intersection

7. Results of analysis

8. Analysis on raster I. Grids with the same resolution and extent Operations among cell at the same position Grid algebra „No data” value, involving any operation the result is „No data” Arithmetic operators +, -, *, / Functions

9. Raster analysis II. Resampling Nearest neighborhood Bilinear interpolation (2x2) Bicubic interpolation (4x4)

10. Fuzzy mathematics (Zadeh 1965) Handling spatial uncertainty Instead of 0/1 (yes/no) values many categories or continuous value, It fits better to the human logic Subjective information can be considered Membership function:  (l)  [0,1] Set operations: Complement  l  L :  3 (l) = 1 -  1 (l) Union  l  L :  3 (l) = max{  1 (l),  2 (l)} Intersection  l  L :  3 (l) = min{  1 (l),  2 (l)} It can be solved for raster data simply Fuzzy module available in Idrisi

11. Finding routes Utility network models (road network, sewers, etc.) Directed weighted graph Edges Nodes Impedances Topology

12. Optimal route (shortest path) Optimal route between two nodes (minimal weight sum) Dijkstra algorithm 1959 Other restrictions, one-way edges, turning impedances

13. Finding addresses 2 1 24 17 Apple str. Road network, street name, house numbers from and to Apple str 5th Linear interpolation Difficulties: house number like 2-4, 8/a, squares For example criminal statistics Finding road intersections Address nodes x, y coordinates for each address Joining databases to the map

14. Nodes are the midpoint of pixels 4/8 directions Impedance function Application: Watershed boundary Flow directions Flow accumulation Optimal route on raster