1. Geographic Information Systems
Department of Survey and Geomatics
By Shoko M

2. Topology
Topology deals with spatial properties that do not change under certain transformations
Topology refers to the spatial relationships between geographical elements in a data set that do not change under a continous transformation

3. Topology contd

4. Topological relationships
For every point in a given space we can determine an X,Y,Z location of an object of interest
In that space we can define point, lines and polygons. Point (0-dimensional),Line(1 dim),Polygon(2 d) anda volume is 3d
The space is metric meaning we can compute distance,area,volume
We can define within that space features that can be used for geographic representation. These features are called simplices because they have the simplest geometric shapes of given dimension
Combined simplices give a simplical complex

5. Simplices

6. Two dimensional topology

7. Topological consistency
The rules guiding how simplices and simplical complexes can be embedded in space differ for a two d and a 3 d space
Such rules define the topological consistency of that space e.g cleaning of spagetti data is to let it conform to topological expectations
Once it is proved that all the rules are satisfied for all features in a space then that feature is called a topologically consistent feature

9. Three dimensional topology
Two and a half dimension a growing trend
Topological rules asme as 2d in the main
However every o simplex is associated with a Z value

10. GIS Analysis functions
GIS analysis functions can be defined under four major areas
1) Classification , retrival and measurement functions-these are performed on a single (vector or raster layer) often using attribute data)
Classification allows the assignment of features to a class on the basis of attribute values
Retrival allow the selective search of data
Generalisation is a function that joins classes of objects with common charectaristics to a higher level class e.g maize and potato as crops
Measurement functions allow the calculation of distance length,volume and areas

11. GIS analysis fxns contd
2) Overlay functions- these are most often used in GIS applications.They allow the combination of two or more spatial layers comparing them position by position and treating areas of overlap and non overlap in distinct ways.
3) Neighbourhood functions- thes scan he neighbourhood of given features and perform computations on them. E.g search fxn, buffer zone generation,interpolation fxn, topographic fxn like slope

12. GIS analysis fxns continued
4) Connectivity functions- these work on the basis of a network including road,rail,water etc
Examples include contiguity fxns,network analysis fxns,vissibility fxns

13. Measure function

14. Measure fxn contd

15. Measure fxn contd

16. Select a subset of objects
Selection is the picking out of attributes that match certain conditions of interest
Selection can be done by attribute
Selection can be done based on distances
Selection can be done based on adjacent features to an object etc
Selection conditions can also be combined or used as input for a fresh selection

17. Select a subset of objects

18. Select a subset of objects

19. Select a subset of objects

20. Select a subset of objects

21. SELECT A SUBSET OF OBJECTS

22. Classification
Classification is a technique of purposefully removing detail from input data with the hope of revealing patterns of distribution.
It involves the subprocesses of merging, aggregation or dissolving
Classification can be user controlled or automatic
Automatic classification makes use of equal interval or equal frequency techniques
Often a new layer is created with the new classes
Where input data was itself a result of classification we call that a Reclassification

23. An example of classification

24. Overlay Functions
Standard overlay functions take two or more data layers as input and assume they are georeferenced in the same system and overlap the study area.
The principle of spatial overlay is to compare the charectaristics of the same location in the data layers and produce a result for each location in the output data layer
In raster this involves comparing pairs of cells from the input raster
In vector the same principle of comparing locations applies but the underlying computation relies on determining spatial intersection of features from the layers

25. Vector Overlay Functions

26. Vector overlay
Two more vector overlay functions include polygon clipping and polygon overwrite
Vector overlays are useful but result in a lot of operators, whilst raster overlays are less complicated and are based on map algebra

28. Raster overlay operators

29. Neighbourhood functions
Neighbourhood functions compare charectaristics of the vicinity
E.g Select an all roads within 2km from the shopping centre
Neighbourhood functions include proximity functions( buffer and thiessen polygon) , calculation of spread (diffusion e.g spread of forest fires), resistance (cell resistance for selecting the best path for a river to flow) as well as cost and flow based analysis

30. Buffering in vector data

31. Thiessen polygon formation in vector data

32. A diffusion function in raster data

33. Flow computations in raster data

34. Network Analaysis Tools
A completely different set of GIS analysis tools deals with networks
A network is a set of lines representing some geographic phenomenontypically of the transportation type in most applications
The linear feature to be analysed is assigned typical charectaristics like cost per unit and capacity
A network is said to be directed if it associates a certain direction with transportation and undirected if goods can be transported in either directions
Network analysis can be performed on both vector and raster layers

35. Network analysis tools
Common network analysis tools include optimal path finding that tries to highligh the path to an object of interest that has the least cost. Optimal path can be ordered or undordered
Another tool is seervice area creation that assigns lines to taget locations based on cost e.g schools, water supply
Trace nalysis is another function that helps one determine the part of a newtwork that is upstream or downstream from a given location

36. Network analysis tools

37. Network analysis tools

38. Network analysis tools

39. Network analysis tools

40. GIS TWO: CASE STUDY Due Friday the 4th of February at 2pm
Imagine you are a GIS Specialist for the ministry of rural and urban planning. With growing health concerns such as HIV and AIDS you have been asked to identify the best 30 sites for new district hospitals in Zimbabwe. You are provided with the following data
Entire road network of all major roads in Zimbabwe prepared by South African engineers in the South African RD Datum Projection in vector format
Point format vector location map of existing medical centers in Zimbabwe captured using GPS in the world WGS84 system
A set of remote sensing image of Zimbabwe captured by a high resolution satellite showing all roads, rivers buildings and features in the country
A topographic map of scale 1:2500 showing all rivers and waterways in Zimbabwe
A digital vector polygon layer of all parcel boundaries in Zimbabwe that was digitized by a Wedley a student on attachment at the ministry from the Midlands University in Gweru.
A similar layer showing all buildings in Zimbabwe including district offices and resource centers
A table from the central statistics office showing populations per ward and area in the country
You may use all,some or non of the data in your solution. You are free to request additional information or material you may deem necessary through the ministry.
1) Construct a detailed conceptual model detailing the main GIS steps you would need to engage to solve this location allocation problem. Your model must be clear and indicate imprtant analysis functions and steps in arriving at a solution
2) Write a short essay of no more than two pages to explain the key components of your model highlighting major areas of interest and challenges that you are likely to face on the project and how you intend to address them.