1. November 21GEOINFO 2005 Preserving Incidence and Coincidence Topologies in Saalfelds Polyline Simplification Algorithm Department of Computer Engineering and Industrial Automation (DCA) School of Electrical and Computer Engineering (FEEC) State University of Campinas (UNICAMP) da Silva, Adler C. G. Wu, Shin-Ting {acardoso,ting}@dca.fee.unicamp.br

2. November 21GEOINFO 2005 Topics l Motivation l Polyline simplification l Topological Properties l State-of-the-art l Objective l Proposal l Results l Concluding remarks

3. November 21GEOINFO 2005 Topics l Motivation l Polyline simplification l Topological Properties l State-of-the-art l Objective l Proposal l Results l Concluding remarks

4. November 21GEOINFO 2005 Motivation l Graphical User Interface for Pre-dispatches Pre-dispacth = Planned schedule of power dispatching One-line diagram Visual presentation in different levels of detail + + Geographical context

5. November 21GEOINFO 2005 Motivation Geographical context in different levels of detail Maps in different resolutions Simplification of a set of polylines

6. November 21GEOINFO 2005 Topics l Motivation l Polyline simplification l Topological Properties l State-of-the-art l Objective l Proposal l Results l Concluding remarks

7. November 21GEOINFO 2005 Polyline Simplification Original Map: 50.000 50.0001.800 Simplified Map: 1.800 Source: Digital Chart of the World Server (www.maproom.psu.edu/dcw)

8. November 21GEOINFO 2005 Polyline Simplification l Visvalingam and Whyatt, 1993 l White, 1985 l McMaster, 1986 l Ramer, 1972; Douglas and Peucker, 1973 RDP algorithm DistanceAdjacent distance Adjacent AngleAdjacent Area

9. November 21GEOINFO 2005 Polyline Simplification: RDP l Maximum tolerable distance ( )

10. November 21GEOINFO 2005 Polyline Simplification: Problems

11. November 21GEOINFO 2005 Topics l Motivation l Polyline simplification l Topological Properties l State-of-the-art l Objective l Proposal l Results l Concluding remarks

12. November 21GEOINFO 2005 Topological Properties l Geometrical properties that are invariant under continuous deformations

13. November 21GEOINFO 2005 Topological Properties Coincidence Sidecrossings Incidence

14. November 21GEOINFO 2005 Topics l Motivation l Polyline simplification l Topological Properties l State-of-the-art l Objective l Proposal l Results l Concluding remarks

15. November 21GEOINFO 2005 State-of-the-art Possible solutions: l To decrease the tolerance l To handle all polylines and features of a map as a whole l To handle the polyline, taking into account its vicinity (Saalfeld 1998)

16. November 21GEOINFO 2005 State-of-the-art: Saalfelds 1) Necessity for inconsistencies 3) Triangle inversion2) Point sidedness Simplification from RDP algorithm simplification subpolyline

17. November 21GEOINFO 2005 State-of-the-art: Saalfelds First step: RDP algorithm until condition is satisfied Second step: further insertions until sidedness and conditions are satisfied

18. November 21GEOINFO 2005 State-of-the-art: limitations WITH redundancies (Fast visualization) WITHOUT redundancies (Easy edition) Data structures:

19. November 21GEOINFO 2005 State-of-the-art: Saalfelds Coincidence crossings Incidence

20. November 21GEOINFO 2005 State-of-the-art: Saalfelds

21. November 21GEOINFO 2005 State-of-the-art Incidence of P 2 in P 1 without the insertion of the incident vertex in P 1 : http://maps.google.com

22. November 21GEOINFO 2005 Topics l Motivation l Polyline simplification l Topological Properties l State-of-the-art l Objective l Proposal l Results l Concluding remarks

23. November 21GEOINFO 2005 Objective l General context: to develop a topologically consistent map simplification algorithm l Contribution of this work: to enhance Saalfelds algorithm such that it also preserves topological consistency of the redundant data

24. November 21GEOINFO 2005 Objective: Improving Saalfelds l RDP l Saalfeld l Saalfeld for maps

25. November 21GEOINFO 2005 Topics l Motivation l Polyline simplification l Topological Properties l State-of-the-art l Objective l Proposal l Results l Concluding remarks

26. November 21GEOINFO 2005 Proposal l To integrate additional conditions in Saalfeld´s algorithm such that the topological consistencies may be ensured along the simplification process incidence coincidence

27. November 21GEOINFO 2005 Proposal: Coincidence l Preserving coincidence by using the essential vertices l Pre-processing time required MapVerticesTime (s) Amazonas168.0003,718 Minas Gerais88.0001,729 São Paulo47.0000,899 Santa Catarina25.0000,528 Rio de Janeiro11.0000,254 Alagoas7.0000,001 Essential Vertices = extreme overlapping vertices

28. November 21GEOINFO 2005 l Processing of the in-between vertices: Proposal: Coincidence Original polylinesFirst step: RDP Simplifications One simplification is adjustedThe other is a copy Second step

29. November 21GEOINFO 2005 Proposal: Incidence l Preserving Incidences: 1 – nearness tolerance in numerical resolution 2 – nearness tolerance in device resolution = max( 1, 2 )

30. November 21GEOINFO 2005 Proposal: Stop Conditions l From RDP algorithm: condition l From Saalfeds algorithm: sidedness condition l Our proposal: nearness condition

31. November 21GEOINFO 2005 Proposal: Incidence Nearness classification Feature distance monitoring Close

32. November 21GEOINFO 2005 Proposal: Enhanced Algorithm l Determine the first simplification consisting of the essential vertices l Apply RDP algorithm on each polyline until the condition is satisfied. l Determine the fat convex hull for each simplified segment. l Evaluate the sidedness, the coincidence, and the nearness of all features inside each convex hull. l Adjust coincidence geometry. l Apply RDP algorithm on each polyline until the sidedness, the, and the nearness conditions are satisfied.

33. November 21GEOINFO 2005 Topics l Motivation l Polyline simplification l Topological Properties l State-of-the-art l Objective l Proposal l Results l Concluding remarks

34. November 21GEOINFO 2005 Results Saalfelds Our

35. November 21GEOINFO 2005 Results Saalfelds Our

36. November 21GEOINFO 2005 Topics l Motivation l Polyline simplification l Topological Properties l State-of-the-art l Objective l Proposal l Results l Concluding remarks

37. November 21GEOINFO 2005 Concluding Remarks l We present a simple procedure to ensure coincidence and incidence topologies during the simplification of maps with redundant data. It is based on the essential vertices and the nearness tolerance. l The visual results make us to believe that our proposal is promising. l As further work, To integrate this algorithm with one-line diagram algorithm to be presented on Wedneday. To extend it to be multiresolution.

38. November 21GEOINFO 2005 Thank You!

39. November 21GEOINFO 2005 Objective: Improving Saalfelds l To simplify each polyline until condition is satisfied. l To process each convex hull until and sidedness conditions are satisfied.

40. November 21GEOINFO 2005 State-of-the-art: Saalfelds l RDP with a new stop condition ( + sidedness)