1. Principles of GIS Geocomputation – Part II Shaowen Wang
CyberInfrastructure and Geospatial Information Laboratory (CIGI)
Department of Geography and Geographic Information Science
Department of Computer Science
Department of Urban and Regional Planning
National Center for Supercomputing Applications (NCSA)
University of Illinois at Urbana-Champaign
November 5, 2013

2. Structure of Spatial Objects
Spaghetti
Node-arc-area (NAA)

3. Spaghetti Polygonal area For straightforward output
Boundary loop
Closed polyline (Douglas-Peucker)
For straightforward output
Graphical display
No explicit spatial relationships represented
Duplication

4. NAA
Directed arc
Node
Area
Rules

5. Representations of Field-based Models
Tessellation
Partition of a plane, or a portion of the plane, as the union of a set of disjoint areal objects
Regular
Irregular

6. Regular Tessellation Regular polygon Vertex figure
All edges have the same length
All internal angles are equal
Vertex figure
The polygon formed by joining in order the mid-points of all edges incident with the vertex
Polygon and vertex figure
Regular and equal

7. Irregular Tessellated Representations
TIN
Interpolation

8. I scanned this
What is it?

9. Delaunay Triangulations and Voronoi Diagrams
Dual graph
Delaunary triangulation and its dual
Voronoi diagram

10. Voronoi Diagrams Define proximal regions
For each point in P the area that is closest to it
Can be used to define service regions or as the basis for assigning measurements made at points to areas

11. Properties of Delaunary Triangulation
Unique
Convex hull of a particular point set
The circumcircle of any triangle contains no point
Triangles are closet to equilateral

12. Triangulations of Polygons
Constrained Delaunay triangulation
Greedy triangulation

13. Nested Tessellation

14. Fundamental Geometric Algorithms
Metric and Euclidean Algorithms
Topological Algorithms
Set-based Algorithms
Triangulation Algorithms

15. Metric and Euclidean Algorithms
Distance between points
Distance from point to line
Area of a simple polygon
Side operation
Centroid of a polygon

16. Topological Algorithms
Point-in-polygon
Convex
Side operation
Semi-line algorithm
Ray
Crossing
What is?
What is not?
Implementation
Complexity
Winding number algorithm

17. End of This Topic