Unformatted text preview: Topology and Vector data Topology and Vector data representation Spatial relationships Spatial relationships
• many GIS analysis types rely on relationships rather than coordinates • we don’t care how big the object is but rather that it borders another object • relationships: – geometry (if a common border is shared) – proximity (if we’re concerned about nearness)
question for DHS: which states border foreign nations? Spatial relationships Spatial relationships rules and models in GIS rules
• spatial relationships organized by rules in the vector data model • what rules govern the arrangement of the vector items (points, lines, polygons) on the following maps? some spatial relationship rules some spatial relationship rules
• computers like rules! • land parcels cannot intersect • there shouldn’t be space between countries (i.e. there should be a common border) • rivers can’t intersect • cities must be contained within their countries • roads must end at other roads • each parcel must have road frontage (parcels must share boundary with road polygon) • rivers have direction; must always go in direction of larger rivers Topology Topology
• • not topography the study of those properties of geometric objects that remain invariant under bending or stretching “like geometry on a rubber sheet”
Leonhard Euler (1700s): the Königsburg bridge problem • Topology in geoinfo representation Topology in geoinfo representation
• mental maps: store relationships, not real coordinates • basic elements of topological relationships:
– containment – adjacency – connectivity Containment Containment
• how might you tell a computer if the point is inside or outside the polygon? Think about the rule and come with ideas next time Adjacency, connectivity Adjacency, connectivity Vector topology in Vector topology in How does a computer GIS recognize a • polygons are stored as closed series of line segments (arcs) that meet (and end at) nodes
closed arc? 101
13 103 100 102 – arcs are made up of a series of connected (x,y) coordinates – arcs are directed graphs: they are oneway streets – direction matters as well as location – arcs go from fromnodes to tonodes arc # 10 11 12 x, y coordinates (4,3) (4,4) (3,4) (3, 7) (5, 7) (6, 6) (6, 6) (7, 5) (8, 5) (8, 1) (7, 1) (6, 2) (4, 2) (4, 3) (4, 3) (5, 3) (5, 5) (6, 6) (6, 4) (7, 4) (7, 5) (6, 5) (6,4) An arccoordinate list: nontopological – deals with coordinates 13 Arcnode topology Arcnode topology
• establishes connectivity • how does a computer know which arcs intersect? • what applications require arcnode topology?
Routefinding, river flow, subway lines... networks Polygonarc topology Polygonarc topology
• establishes containment and area definition • connected arcs can enclose a polygon • a polygon can have more than one boundary • a boundary can be only one arc Leftright topology Leftright topology
• establishes adjacency • arcs are directed, so each has a left side and a right side • how does a computer know that polygons C and D are adjacent? • which polygon is adjacent to only one other? Advantages of topological structures Advantages of topological structures
• data storage efficiency
– a shared boundary is stored only once – updating and editing is easier • make error detection easy – unclosed polygons, nodes that should meet but don’t – must be corrected for certain analyses to work Advantages of topological structures Advantages of topological structures
• enhance GIS analysis
– geocoding: what side of the street? what address ranges along this street (arc)? – habitat analysis: which habitats border others? What is the level of fragmentation of habitats? QDJ 8, part 1 QDJ 8, part 1
• on your card, draw a map of Canada using small boxes for each province, showing the province’s topological relationships to each other. (ignore the northern islands) ...
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 Spring '09
 RobEdsall
 Topology, Manifold, spatial relationships, topology Arcnode topology, topology Polygonarc topology

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