This presentation describes three geometric ideas and then addresses their usefulness in the corporate world
Computational Geometry Algorithms
Their uses in GIS/Molecular Biology/CAD/Robotics
Three Examples
Voronoi Diagram and Delaunay Triangulation
Use of the Voronoi Diagram in Product mix for stores
Use of Delaunay Triangulation in finding Steiner Tree
Convex Hull algorithms
Use in range and gap detection
Segment Intersection
Use of segment intersection in overlaid maps
4.
Voronoi Diagram for a set of vertices in the plane
For a given set of vertices the Voronoi Diagram gives us cells identified with each vertex
All points in the Voronoi cell are closer to the vertex than to any other vertex
5.
Voronoi Diagram for Hardware Stores in a neighbourhood What sort of items should a Home Store have in stock? That depends on the modernity of houses in a sub-area. The colour gives some idea of the age of houses in an area. Darker greens indicate more recent houses. Source of map: Altavision Geographics
6.
Stacked barchart for sub-areas Source of map: Altavision Geographics
We can use discs of various diameters instead of vertices
x x x x x x x If the discs represent broadcast range, this picture shows the gaps in the overall range.
14.
Segment Intersection and Subregion Intersection
Given a map of roads and a map of rivers one may be interested in the intersection points, as possible locations for bridges
Overlay of two or more geographical maps can be as helpful as querying a relational database
15.
References 1. Voronoi Diagrams and Delaunay Triangulations, Steven Fortune, Computing in Euclidean Geometry, pp. 193-233 2. Computational Geometry, Mark de Berg, Cheong, Marc Van Kreveld and Mark Overmars, 1997, Third edition Springer Verlag.
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