Computational Geometry Introduction Line intersections Polygon

1
Computational Geometry
Course outline
Introduction
Line intersections
Polygon triangulation
Geometric search
Voronoï diagrams
Delaunay Triangulations
Binary Space Partition Trees

2
Computational Geometry
Line intersections
Line segments intersections
Polygonal zones intersections
Plane sweeping / DCEL

3
Computational Geometry
Line intersections
Classical problem in GIS
Example :
One has access to several independent maps :
Forestry
Wildlife
etc...
One wishes to know every homogeneous zones for
every tuple of characteristics :
e.g. deciduous forest & deers
pine forest & deers
pne forest & bears … and so forth.

4
Computational Geometry
Line intersections
Types of data that are contained in maps :
Towns (as points or polygons)
Rivers, highways (networks, graphs)
Wooden areas, or of a given climate (polygones)
One needs to combine 2 or more of these maps,
therefore compute intersections
Two maps with networks → points (bridges ?)
Two maps with areas (zones) → new polygons
Any combination...
One common task (elementary task) is the
intersection between two sets of line segments.

5
Computational Geometry
Line intersections
Line segments intersections