1. Week 7. Feature relationship and topology Oct. 17 th, 2005

2. Outline  Relationships between GIS objects  Spatial relationships  Relationships as attributes  Object pairs  GIS topology  What is GIS topology  Importance of GIS topology  Topology and GIS analysis

3. Feature relationships  There are vast number of possible relationships in spatial data.  Relationships are important in GIS analysis.  "is contained in" relationship between a point and an area is important in relating objects to their surrounding environment.  "intersects" between two lines is important in analyzing routes through networks  Relationships can exist between entities of the same type or of different types.  for each shopping center, can find the nearest shopping center (same type)  for each customer, can find the nearest shopping center (different types)

4. Types of relationship  Relationships which are used to construct complex objects from simple primitives.  Relationship between a line and the ordered set of points which defines it.  Relationship between a polygon and the ordered set of lines which defines it.  Relationships which can be computed from the coordinates of the objects.  Areas can be examined to see which one encloses a given point - the "is contained in" relationship can be computed.  Areas can be examined to see if they overlap - the "overlaps" relationship.  Relationships which cannot be computed from coordinates  We can compute if two lines cross, but not if the highways they represent intersect (may be an overpass).  Objects representing "house", "lot", "cable", with associated attributes might be grouped together logically as "account“.

5. Spatial relationships  Point-point  "is within", e.g. find all of the customer points within 1 km of this retail store point  "is nearest to", e.g. find the hazardous waste site which is nearest to this groundwater well  Point-line  "ends at", e.g. find the intersection at the end of this street  "is nearest to", e.g. find the road nearest to this aircraft crash site  Point-area  "is contained in", e.g. find all of the customers located in this ZIP code boundary  "can be seen from", e.g. determine if any of this lake can be seen from this viewpoint

6. Spatial relationships  Line-line  "crosses", e.g. determine if this road crosses this river  "comes within", e.g. find all of the roads which come within 1 km of this railroad  "flows into", e.g. find out if this stream flows into this river  Line-area  "crosses", e.g. find all of the soil types crossed by this railroad  "borders", e.g. find out if this road forms part of the boundary of this airfield  Area-area.  "overlaps", e.g. identify all overlaps between types of soil on this map and types of land use on this other map  "is nearest to", e.g. find the nearest lake to this forest fire  "is adjacent to", e.g. find out if these two areas share a common boundary

7. Relationships as attributes  Example: “Flows-in” relationship Option AOption B Link IDDownstream 001004 002004 003005 004005 empty 001 003 004 002 005 Each stream link in a stream network could be given the ID of the downstream link which it flows into Flow could be traced from link to link by following pointers 0001 0002 Link IDPointer 0010001 0020001 0030002 0040002 005empty Point IDPointer 0001004 0002005 Each stream link in a stream network could be given the ID of the downstream point which it flows into Each stream point in a stream network could be given the ID of the downstream link which it flows into Flow could be traced from link to link by following pointers

8. Relationships as attributes  Example: “is contained in” relationship Well IDCounty 001A 002B 003A 004A County IDNo. of Wells A3 B1 County ACounty B 001 002 003 004 1.Find the containing county of each well (compute the “is contained in” relationship). 2.Store the result as a new attribute, County, of each well. 3.Using this revised attribute table, total flow by county and add results to the county table.

9. Object Pairs  Some attribute is between a pair of objects.  Distance is the attribute of a pair of objects.  Flow of commuters between two places.  Trade between two counties.  In some cases these attributes can be attached to an object linking the origin and destination objects.  For example, trade can be attached to an arrow pointing from county A to B.  In general, these kind of attributes shall be described using separate tables or matrix. ABCD A011.52.5 B1012 C1.5103 D2.52 0 A distance table between points A, B, C, and D A B C D

10. GIS topology  Topology is a mathematics approach that defines unchangeable spatial relationships.  When a map is stretched or distorted, some properties change,  Distance  Angles  Relative proximities  Some properties won’t change,  Adjacencies  Most other relationships, such as "is contained in", "crosses"  Types of spatial objects - areas remain areas, lines remain lines, points remain points  These unchanged properties are called topological properties.

11. Topological examples Network connectivityPolygon adjacency Topology well-denfined Topology poorly-defined

12. Importance of topology  Topology enables operations like connectivity and contiguity analysis.  Searching a shortest path  Finding a service area by using a road network  Finding adjacent areas  Topology enables spatial analysis without using a coordinate set,  Apply spatial analysis using topological definitions alone  Major difference from CAD or computer-aided cartography

13. Topology and GIS analysis Searching a shortest path 2.5 2 3 1 2 2 The shortest path from the blue point to the yellow point is through the red point and then the orange point (2+1+2.5=5.5 map units). However, if the topology of the red point is not defined clearly, which means the two yellow lines are consider as one and the two orange lines are considered as one, the resulting answer will be wrong (2+2+2=6 map units). 2 Finding adjacent areas The overlapped two polygons have to be cut into three in order to clearly defined the spatial topology. Otherwise \ there will be difficulties finding an adjacent polygon of either.

14. Summary for today  Relationships between GIS objects  Spatial relationships  Relationships as attributes  Object pairs  GIS topology  What is GIS topology  Importance of GIS topology  Topology and GIS analysis