Introdução to Geoinformatics: vector geometries
Vector geometries
Vector geometries Arcs and nodes Polygons
Vector geometries fonte: Universidade de Melbourne
Vector Model: Lines vertex node Lines start and end at nodes line #1 goes from node #2 to node #1 Vertices determine shape of line Nodes and vertices are stored as coordinate pairs
Vector Model: Polygons Polygon #2 is bounded by lines 1 & 2 Line 2 has polygon 1 on left and polygon 2 on right
Types of topology source: ESRI
Planar enforcement All the space on a map must be filled Any point must fall in one polygon alone Polygons must not overlap
Vector geometries Island Points
Topology: polygon-polyline source: ESRI
Topology: polygon-polyline Shapefile polygon spatial data model less complex data model polygons do not share bounding lines
Topology: the OGC model source: John Elgy
What’s the use of a polygon? Census tracts in São José dos Campos
Topology: arc-node-polygon source: ESRI
Topology: arc-node-polygon source: GIS Basics (Campbell and Chin, 2012)
Vectors and table Duality between entre location and atributes Lots geoid owner address cadastral ID 22 Guimarães Caetés 768 250186 23 22 23 Bevilácqua São João 456 110427 24 271055 Ribeiro Caetés 790
Duality Location - Attributes Praia de Boiçucanga Praia Brava Exemplo de Unidade Territorial Básica - UTB
Geometrical operations Point in Polygon = O(n)
Geometrical operations Line in Polygon = O(n•m)
Topological relationships
Topological relationships Disjoint Point/Point Line/Line Polygon/Polygon
Topological relationships Touches Point/Line Point/Polygon Line/Line Line/Polygon Polygon/Polygon
Topological relationships Crosses Point/Line Point/Polygon Line/Line Line/Polygon
Topological relationships Overlap Point/Point Line/Line Polygon/Polygon
Topological relationships Within/contains Point/Point Point/Line Point/Polygon Line/Line Line/Polygon Polygon/Polygon
Topological relationships Equals Point/Point Line/Line Polygon/Polygon
Topological relations Interior: A◦ Exterior: A- Boundary: ∂A
Topological Concepts Interior, boundary, exterior Green is A interior Let A be an object in a “Universe” U. Green is A interior Red is boundary of A Blue –(Green + Red) is A exterior U A
4-intersections disjoint contains inside equal disjoint contains inside equal meet covers coveredBy overlap
OpenGIS: 9-intersection dimension-extended topological operations Relation disjoint meet overlap equal 9-intersection model
Example Consider two polygons A - POLYGON ((10 10, 15 0, 25 0, 30 10, 25 20, 15 20, 10 10)) B - POLYGON ((20 10, 30 0, 40 10, 30 20, 20 10))
9-Intersection Matrix of example geometries I(B) B(B) E(B) I(A) B(A) E(A)
Specifying topological operations in 9-Intersection Model Question: Can this model specify topological operation between a polygon and a curve?
9-Intersection Model
Examples of functions defined by SFSQL
DE-9IM: dimensionally extended 9 intersection model
9-Intersection Matrix of example geometries I(B) B(B) E(B) I(A) B(A) E(A)
DE-9IM for the example geometries I(B) B(B) E(B) I(A) 2 1 B(A) E(A)