Multidimensional (spatial) Data and Modelling (3)

Transcription

1 Multidimensional (spatial) Data and Modelling (3) 1

2 GIS-centric approach l Focus on management of spatial data l Goal: Creation of a solely spatial data representation like maps (spatial partition, map layers, layers) l Offering operations on these spatial data structures like overlay, fusion, projection, superimposition, windowing and so on. 2

3 GIS-centric approach l GIS-centric approaches are dedicated solely to the management of spatial data. Specialized data structures also are used to associate spatial with conventional data, but the handling of these structures takes place outside the GIS. l In an informal approach, map layers (termed simply maps) and operations on them are described at a conceptual level. l A map m can be seen as a set of pairs (p, v), where p is a location (a 2-d point in the plane) and v is a number assigned to p, which indicates a property of p. 3

4 GIS-centric approach l Distinct maps are used to record distinct properties of locations, such as height, degree of pollution, and so forth. l The approach enables recording properties of areas that change gradually from one location to another, termed continuous changes. l Spatial data types are not defined. A zone of m is a set of pairs Z = {(p1, v), (p2, v),..., (pk, v)} (adjacent or not) with identical values on the second coordinate. l An open-ended set of operations is proposed. They all apply to maps and produce a new map. 4

5 GIS-centric approach The approach classifies operations into four categories: l (i) Local: The value of each location p depends on value of the same location p in input maps. l (ii) Zonal: The result value of each location p depends on values of the locations contained in zone of p in one or more input maps. l (iii) Focal: The result value of each location p depends on values of the locations contained in neighbourhood of p in one or more input maps. l (iv) Incremental: They extend set of Focal operations by taking into account type of zone at each location. One of the local operations resembles Full Overlay. 5

6 Example: Mapping SD to ORDMBS l Three maps with simple spatial data: 6

7 Creation of OR-Types l create suitable object-relational data types //type declaration CREATE TYPE POINT AS OBJECT (x NUMBER,y NUMBER) CREATE TYPE POINT_TABLE AS TABLE OF POINT; CREATE TYPE POLYGON AS OBJECT( points POINT_TABLE, MEMBER FUNCTION intersects (p POLYGON) RETURN BOOLEAN ); CREATE TYPE LINE AS OBJECT (start_x NUMBER, start_y NUMBER, end_x NUMBER, end_y NUMBER); //functional predicate binding CREATE OPERATOR INTERSECTS(a POLYGON, b POLYGON) RETURN BOOLEAN BEGIN RETURN a.intersects(b); END; 7

8 Creation of OR-Tables l create object-relational types of tables //table declaration CREATE TABLE_TYPE CITIES( id NUMBER PRIMARY KEY, geom POINT ); CREATE TABLE_TYPE HIGHWAYS( id NUMBER PRIMARY KEY, geom LINE ); CREATE TABLE_TYPE COUNTIES( id NUMBER PRIMARY KEY, geom POLYGON ); 8

9 Actual mapping of data to ORDMBS l create specific objects from spatial data and store them into tables //create tables from table_types CREATE TABLE city_table AS TABLE_TYPE CITIES; CREATE TABLE highway_table AS TABLE_TYPE HIGHWAYS; CREATE TABLE counties_table AS TABLE_TYPE COUNTIES; //fill tables with objects from maps INSERT INTO city_table ((1,new POINT(5,7);2,new POINT(6,6);3,new POINT(8,6.5)); INSERT INTO highway_table ((1,new LINE(0,7.2,5,7);2,new LINE(5,7,8,6.5);3,new LINE (8,6.5,6,6);4,new LINE(6,6,2.5,0)); INSERT INTO counties_table (1,new POLYGON(points(new POINT(0,2.1),new POINT(8,6), new POINT(0,6)));2, new POLYGON(points(new POINT(0,6),new POINT(7,9)));3,new POLYGON(points(new POINT(11,8.5),new POINT(7,6)))); 9

10 Result in ORDBMS - tables TABLE city_table TABLE highway_table id geom id geom 1 POINT(5,7) 1 LINE(0,7.2,5,7) 2 POINT(6,6) 2 LINE(5,7,8,6.5) 3 POINT(8,6.5) 3 LINE(8,6.5,6,6) 4 LINE(6,6,2.5,0) TABLE county_table id geom 1 POLYGON(points(POINT(0,2.1),POINT(8,6), POINT(0,6))) 2 POLYGON(points(POINT(0,6), POINT(7,9))) 3 POLYGON(points(POINT(11,8.5), POINT(7,6))) all variables in italics in the above displayed tables are references (addresses) of the actual geom-objects saved in different meta-tables in the db. In fact, POLYGON( ) with id 1 consists of references to three lower objects: First the POLYGON-object itself, the underlying POINTS-table and within these table there are POINTS objects saved. 10

11 Ex: Operations on raster grids Possible implementation: l A map is modelled as a 2-d raster grid data structure, which represents a partition of a given rectangular area into a matrix of a finite set of squares, called cells or pixels. l Each cell represents one of locations. l All these approaches consider only surfaces. Examples of operations on grids are shown below. Note that the functionality of operation Combine (Figure 3(f)) resembles that of Full Overlay on surfaces. 11

12 Ex: Operations on raster grids 12

13 Ex: Operations on raster grids 13

14 Ex: Operations on raster grids of the spatio-temporal model (d Onofrio & Pourabbas, 2001). It considers 14 maps of surfaces or lines, but it does not achieve the functionality of all the operations

15 Ex: Functionality for maps l A map (called spatial partition) of a given area is defined as a set of non-overlapping, adjacent surfaces. l Each such surface is associated with a tuple of conventional data. l Surfaces associated with the same conventional data merge automatically into a single surface. l Point and Line types are not defined. l Three primitive operations are defined and, based on them, a representative functionality for map management is achieved (below). 15

16 Ex: Functionality for maps 16

17 Ex: Functionality for maps 17

18 Ex: Functionality for maps 18

19 Ex: relations and operations l Point, simple polyline and polygon data types (Figure 5(a-c)) are proposed as usually. l A map (called layer) M is defined as a mapping from a set of spatial values G to the Cartesian product of a set of conventional attributes (M: G C1,C2,...,Cn). Hence, a map can be seen as a relation with just one spatial attribute G. l Operations on maps also are defined. Operation Attribute derivation (Spatial computation) enables the application of conventional (spatial) functions and predicates. 19

20 Ex: relations and operations l Operation Reclassification merges into one all those tuples of a layer that have identical values in a given attribute and also are associated to adjacent spatial objects. l It can apply only to layers of type simple polyline or polygon. l Operation Overlay or Full Overlay applies to two maps L1 and L2 of any data type. l Its result is the union of three sets. 20

21 Ex: relations and operations l (i) I, consisting of the pieces of spatial objects l both in L1 and L2, l (ii) L, consisting of the pieces of spatial objects in L1 that are not inside the spatial objects in L2, l (iii) R, consisting of the pieces of spatial objects in L2 that are not inside the spatial objects in L1. 21

22 Representation of spatial objects in various approaches 22

23 Other approaches l ESRI (2003) approach considers data types of the form point, set of points, set of lines and set of surfaces and a large set of operations. l To illustrate operation Overlay, consider layer L1, with objects of any type; layer L2, consisting of only surfaces; and the sets I, L and R. l Then each of the Overlay operations is associated with one of the result sets I, I L, I R, I L R. l Operation Erase yields a new map with the pieces of the spatial objects in L1 that are outside all the surfaces in L2. 23

24 Other approaches l Update yields the Superimposition of two compatible maps. l Other functionalities are Buffer, Clipping, Cover, one that yields the Voronoi diagram of a set of points; and operation Reclassification. l In place of the ESRI (2003) point data type, the commercial GIS in Intergraph Corp. supports a type of the form set of spatial objects. l Set of spatial objects is the only one supported in MapInfo Corp. (2002) and Bentley Systems (2001). 24