Conceptual models of space, data models and representation data structures

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2. Learning objectives. In this section you will learn: how the conceptual perception is already based on a model of space and how this conceptual perception determines the selection of an appropriate data model, and how the selection of a particular data model influences the appropriate data type

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Conceptual models of space, data models and representation data structures

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1. 1 Conceptual models of space, data models and representation (data structures) Josef Fürst

2. 2 Learning objectives In this section you will learn: how the conceptual perception is already based on a model of space and how this conceptual perception determines the selection of an appropriate data model, and how the selection of a particular data model influences the appropriate data types to represent the phenomena of interest and the possible spatial analyses Understanding of important geographical data structures and their relevance, Importance of topology and its utility for spatial analysis, Relevance and implementation of thematic information (attributes) Recognition of thematic hierarchies and their robust and efficient representation Advantages and disadvantages of vector and raster data structures

3. 3 Outline Introduction Conceptual models of real world geographical phenomena Coding the basic data models for input to the computer Data organisation in vector data structures Object oriented data structures Data organisation in raster data structures Images Attributes Attributes and topological consistency Vector versus raster data structures Summary

4. 4 Introduction ‘Models‘ are created from key features What we regard as the respective key characteristics and how we build the model, depends on our cultural background and the purpose of the view. ‘A fisherman’s view of a river is different from an engineer’s view’ Should the Danube be seen as a polyline, a waterbody, a trench in the earths’s surface or a place to live for animals and plants? Is it an exactly defined and bounded object or rather given by the continuously varying field of the river bed’s elevation? Conceptual models of space: entities continuous fields

5. 5 Conceptual models of space 2 questions What is present? ? house, river, ... Where is it? ? coordinates Entities: Collection of objects (entities): Definition and recognition (house, utility line, forest, river, etc.); Properties to describe boundaries and position continuous fields Continuous function of cartesian coordinates in 2, 3 or 4 (if time is included) dimensions The variable is a „smooth“ function, continuously varying in space

6. 6 Levels of creating a model A view of reality; the conceptual model. Human conceptualization leading to an analogue abstraction (analogue model). A formalization of the analogue abstraction without any conventions or restrictions of implementation (spatial data model) A representation of the data model that reflects how the data are recorded in the computer (database model) A file structure (physical computational model) Accepted axioms and rules for handling the data Accepted rules and procedures for displaying and presenting spatial data (graphical model)

7. 7 From observation to standardized data models

8. 8 Entities or continuous field? Pragmatic decision, determined by the application, In administration rather entities, in science more often continuous fields Examples:

9. 9 Entities or continuous fields? Representation of reality in a data model requires 3 steps: Conceptual model of the „world“ (Entities ? ? continuous variation) Data model: collection of discrete objects ? ? smooth continuous field Representation Entities: primitives, combinations of them or Fields: a) discrete; b) differentiable, mathematical functions; c) non differentiable functions administration: entity model preferred sciences, dynamic processes: continuous fields (mostly raster)

10. 10 Geographical data models and geographical data primitives geographical data primitives : points, lines, polygons (vector model) Pixels (raster model)

11. 11 Data models of entities Vector models simple points, lines and polygons complex points, lines, polygons and objects More complex definitions of points, lines and polygons can be used to capture the internal structure of an entity; functional or descriptive. E.g.: ‘city’ contains streets, houses and parks, each having different functionality and may respond differntly to queries or operations. Object-oriented systems support a hierarchical construction of objects from simple building blocks and a framework for description of properties as well as behaviour. Raster models Mainly integer grids with lookup table of categories Loss of spatial resolution

12. 12 Data models of continuous fields Vector Triangulation (TIN) Raster (grid) Floating point grids

13. 13 Raster or vector model? Raster model can also represent points, lines and polygons Loss of spatial resolution, because location is only expressed by multiples of pixel size Contour maps: Entities or fields? e.g: soil map

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18. 18 Data modelling and spatial analysis There are links between the selected data model, the data types and the possible analyses If location and shape of an entity are time-invariant and exactly known ? Vector model. If attributes are fixed, but the entity may change shape but not position (e.g. drying up of a lake) ? Raster model If attributes can vary, object changes position, but not shape ? behaviour can be represented by object-oriented models If no clear entities can be discerned, then often a discretized, continuous field is preferable

19. 19 Examples for the use of data models Water bodies Changing water levels in lakes, reservoirs or rivers can change their size, shape and position During flood events, rivers can change their path (breakthrough of meanders, new reaches) ? change of geometry and topology! Continuous fields in hydrological models Continuous fields in GIS only spatially discretized (TIN, raster) Dimension of time not represented

20. 20 Representation (data structures) Data models are independent of a specific implementation in a GIS. Also analogue maps are based on models of the area. digital coding of the information, in several stages from the data model, data structures, data types up to their binary representation We need efficient data structures, that represent the selected data models completely and unambiguously, are robust, efficiently support the desired analyses and use storage space economically.

21. 21 Coding the basic data models for input to the computer discrete primitives of geographical data to create entities as well as continuous fields Representation of position, relationships and attributes of different types Points, lines and polygons are the spatial primitives in a vector model, pixels in raster models. Spatial relationships between entities are defined by topology

22. 22 Data organisation in vector data structures Vector-based geographical databases are composing a complex theme of several layers, each of which combines a certain class of phenomena. E.g. hydrological map: rivers, lakes, observation sites, land use, etc., each in a separate layer Layer (Coverage) consists of entities of one type, with relationships, different attributes Layers are handled independently from each other E.g. data structure does not force a gauge to be on the river bank Vector-GIS use implicit relations (tables) for storage Software packages use different structures.

23. 23 Points Position of points is defined by a single pair of coordinates (X, Y) Additional info: type of point, attributes Layer of point entities created from simple table E.g. event theme in ArcView

24. 24 Lines Sequence of (X, Y) coordinate pairs and connecting straight lines or curves

25. 25 Networks Information about connectivity with other line entities to represent street networks, utilities, rivers topological information in the data structures ? connectivity tables Topological terms: „node“ and „arc“ arc-node topology

26. 26 Polygons Shape, neighbours, hierarchy simple polygons: sequence of x,y coordinate pairs Border lines between polygons are digitized and stored twice. Error: gaps, overlaps No information on neighbourhood. islands only graphically represented. Difficult to validate

27. 27 Polygons Polygons by arc-node-topology Underlying principle: free of redundancy

28. The shape file format (1) ESRI file based format for vector datasets Proprietary, but open documentation ? „industry standard“ A shapefile consists of several files with different extensions, e.g. myshapes.shp, myshapes.dbf, … A shape files holds only one type of entities: points OR lines OR polygons myshapes.shp: the geometry in binary format myshapes.dbf: the attributes, in dBase IV format myshapes.shx: a spatial index Optional: myshapes.sbx: index for joins myshapes.prj: the projection Myshapes.shp.xml Metadata for shapefile … 28

29. The shape file format (2) Open source libraries to read and write No arc-node-topology! 3D lines possible (but not widely supported!) For details, see: 29

30. 30 Triangulation of continuous fields Node list and triangle list Optimal TIN by Delaunay criteria

31. 31 Object oriented data structures Object oriented systems encapsulate data objects together with methods applicable to them. Access to objects is only done by the methods defined for them Data structures get a defined behaviour „Hydrant“ should delete itself, when the last pipe connecting it to the network is removed. inheritance Structural object orientation: capability, to create composed objects (Arc Hydro) Behavioural object orientation: behaviour of data types with specifically defined functions and procedures CASE-Tools (Computer Aided Software Engineering) for design and implementation

32. 32 Object oriented data structures UML (unified modeling language) diagram of a part of a geodatabase

33. 33 Object oriented data structures Arc Hydro Framework

34. 34 Data organisation in raster data structures Raster resembles photo 3 ways to interprete a pixel classification: a range of values is allocated to certain objects (gray pixels are roads, blue pixels are water surfaces,...). measure the value: intensity of a colour, concentration, etc. relative height over reference height.

35. 35 Raster data structure Position is represented by discrete cells Types of raster maps Nominal data like land use (forest, grassland, farmland, ...) Continuous values, concentration, light intensity relative measures like elevation.

36. 36 Raster data structure Entities also in raster model Cell size determines resolution: cell size max. 50% of smallest recognized object

37. 37 Raster data structure Topology described implicitly by raster Cell raster – point raster

38. 38 Images Pictures can be used as map displays (e.g. satellite image, orthophoto) or also as attribute information (e.g. pictures of the measuring instruments linked to the measuring points on a measuring point map, photo of the houses in the information system of a real estate agent).

39. 39 Storage of images Similar to raster maps, with some specific properties Pixel (from picture element) Economical storage 1, 8, 24 or 32 bit for coding of a colour value Number of bits per pixel: colour depth monochrome, grayscale, RGB, CMY, CMYK Use of a lookup table

40. 40 Georeferencing of images Depending on the orientation of the coordinate system, objects equal in nature are represented differently in the raster model If distortions of image are small (flat terrain) ?georeferencing by affine projection with >= 4 ground control points (polynomial transformation). Pixel are re-computed by interpolation or areal averaging, according to the type of variable ? loss of information

41. 41 Storing vector and raster data in DBMS Efficient access to large volumes of data with complex relationships B-Trees R-Trees Use of DBMS Geo-relational model Hybrid concept: geometry data in vendor-specific binary format, attributes in RDBMS (INFO, ORACLE, INGRES, INFORMIX, MS ACCESS) Storage of attribute data independently from spatial data extension, updating, deletion of attribute data do not influence spatial data Commercial RDBMS ensure use of latest developments and standardisation Use of standard query language like SQL

42. 42 Attribute information Geoinformation is based on two main elements Geometry and topology (Question: Where?) and Thematic information (attributes) (Question: What?). Approach via thematic maps Analogy of transparencies

43. 43 Attribute information in a raster model Geometry and topology determined by definition of the raster (origin, resolution) Attribute information is additional dimension Spatial query, thematic query, and combined query

44. 44 Thematic information in vector models A theme is assigned to each topological object (node, edge, polygon) by one or more attributes (often tied to a label point) M:N relationship between different thematic layers ? resolve into n units with 1:M relationship

45. 45 Thematic attributes thematic attributes quantitatively classify objects, e.g., a land parcel is attributed by ID, area, prize, owner, address, etc. Logically organized in tables A key-field uniquely relates attributes and topological objects required and optional attributes computed attributes (area, length) Hierarchical inheritance of attributes in object-oriented systems

46. 46 Thematic information and topological consistency Consistency of data is one of the most important criteria of an information system. It must be warranted when new data are added as well as after updates

47. 47 Thematic information and topological consistency Topology- rules in ArcGIS 8.3 Polygons:

48. 48 Thematic information and topological consistency Topology- rules in ArcGIS 8.3 Lines:

49. 49 Thematic information and topological consistency Topology- rules in ArcGIS 8.3 Points:

50. 50 Vector versus raster data structures Decision depends on classes of represented objects Linear phenomena are better handled in vector models Raster model has advantages with areal data If high positional accuracy is important, rasters need too much storage Applications define the criteria Coordinate transformation is easy in vector models Coordinate transformation is more difficult for raster models, because input pixel generally do not have only a single output pixel ? irreversible process

51. 51 Data exchange, standardization De-facto-standards for exchange of geometry and attribute information Topology is not so common Meta data national, European and international standards Open­GIS Consortium (OGC): Interoperability of GIS

52. 52 Summary Data structures should represent spatial phenomena completely and clearly and support efficient analysis Discrete primitives for entities and continuous fields Topology: Relationship between entities. Arc-node topology supports connectivity, definition of areas and connectivity Vector-GIS generally implement a layer concept with basic elements of points, lines, networks or polygons TIN is a vector data structure for continuous fields Object oriented data structures encapsulate data objects together with methods for their behavour.

53. 53 Summary Raster data structures: generally grid of square cells, aligned with coordinate axes Images are special raster data sets with high resolution Thematic attributes describe „what“ an object is (semantics) DBMS for robust storage of geo-data Adherence to national and international standards for exchange of geo-data between different systems and institutions

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