Determining differences between two sets of polygons

1. B.Sc. Matej Gomboši Determining differences between two sets of polygons Laboratory for Geometric Modelling and Multimedia Algorithms Faculty of Electrical Engineering and Computer Science University of Maribor www.uni-mb.si/~gemma

2. Introduction • Parcel records on paper - cadastre • Computer supported cadastre • Database changes • Keeping database up-to-date • Finding and analyzing changes • Working with changes in geometry and attributes • Lack of appropriate commercial solutions (ESRI, ArcView) • Integrated solution for GIS environments

3. Introduction Difference ?

4. Formulation • Let P be a polygon made up of vertices v1, v2, ..., vn and edges e1, e2, ..., en connecting them. • Let S be a set of polygons P1, P2, ..., Pn. Each Pican have arbitrary shape and number of vertices. • Find a set of polygons D, which represents the difference between S1 and S2. D contains changed polygons P1, P2, ..., Pm, which belong to S1 or S2.

5. Strategies • Brute force approach • Localized search approch • Speed and stability considerations • Separate aplications for different problems (need for integration)

6. Basic idea • Comparison of S1 and S2 based on polygon edges • Removing equal edges • What remains represents changes • Analyzing remaining edges

7. Data objects Polygon Edge • Sets of polygons from ESRI files (SHP) • Organized data structures in memory • Edge as main object • p1,p2 • Polygon info • Hole info “Work table” • Uniform plane subdivision • Binary search tree in cells • Sorted edges

8. “Work table” • binary search tree in each cell • pointers to tree roots

9. Polygon edge information • Coordinates - p1(x1,y1), p2(x2,y2) • Polygon info • polygon index • set indicator (S1 or S2) • index of the surrounding polygon • Counter • Hole info • hole index (locally inside a polygon)

10. Edge clasification Counter values!

11. Algorithm • Acquiring polygon sets from ESRI database • Inserting edges into uniform plane subdivison • Updating already existing edges • Removing of equal edges • Analyzing remaining edges • Storing changes

12. Finding differences (1)

13. Finding differences (1)

14. Finding differences (2)

15. Finding differences (2)

16. Problems at comparing attributes Non-simple polygon Contains regular(green) and non-regular(gray) holes Finding correct polygon index to compare attributes

17. Arithmetic problems • Possible errors of overlaping edges • Measuring error (+/- 12cm) • Epsilon tolerance at comparing the vertices

18. Time complexity • Inserting edges • O(n*log m) • n – total num. of edges • m – average num. of edges in a cell • Analyzing changes • O(n*log m) • n – number of cells • m - average num. of edges in a cell

19. Practical results 20.000 edges 8.000 polygons 1.000 changes 5 seconds with database access

20. Conclusions • New efficient algorithm for specific geometric problem • Works on large sets of polygons as found in GIS application • Simple implementation • Efficient use of known speed-up techniques • Easy integration into other GIS environments (dll) • Robust (no problems with geometric boundary cases) • Succesfully used in practice