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Preserving Incidence and Coincidence Topologies in Saalfeld’s Polyline Simplification Algorithm

Preserving Incidence and Coincidence Topologies in Saalfeld’s Polyline Simplification Algorithm. da Silva, Adler C. G. Wu, Shin-Ting {acardoso,ting}@dca.fee.unicamp.br. Department of Computer Engineering and Industrial Automation (DCA) School of Electrical and Computer Engineering (FEEC)

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Preserving Incidence and Coincidence Topologies in Saalfeld’s Polyline Simplification Algorithm

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

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

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

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

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

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

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

  8. Polyline Simplification • White, 1985 • Ramer, 1972; Douglas and Peucker, 1973 RDP algorithm • Visvalingam and Whyatt, 1993 Distance Adjacent distance • McMaster, 1986 Adjacent Angle Adjacent Area GEOINFO 2005

  9. Polyline Simplification: RDP • Maximum tolerable distance ()  GEOINFO 2005

  10. Polyline Simplification: Problems  GEOINFO 2005

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

  12. Topological Properties • Geometrical properties that are invariant under continuous deformations GEOINFO 2005

  13. Topological Properties Side crossings Coincidence Incidence GEOINFO 2005

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

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

  16. State-of-the-art: Saalfeld’s Simplification from RDP algorithm 1) Necessity for inconsistencies subpolyline simplification 2) Point sidedness 3) Triangle inversion GEOINFO 2005

  17. State-of-the-art: Saalfeld’s  First step: RDP algorithm until condition is satisfied  Second step: further insertions until sidedness and conditions are satisfied GEOINFO 2005

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

  19. State-of-the-art: Saalfeld’s crossings Incidence Coincidence GEOINFO 2005

  20. State-of-the-art: Saalfeld’s GEOINFO 2005

  21. State-of-the-art Incidence of P2 in P1 without the insertion of the incident vertex in P1: http://maps.google.com GEOINFO 2005

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

  23. Objective • General context: to develop a topologically consistent map simplification algorithm • Contribution of this work: to enhance Saalfeld’s algorithm such that it also preserves topological consistency of the redundant data GEOINFO 2005

  24. Objective: Improving Saalfeld’s • RDP • Saalfeld • Saalfeld for maps    GEOINFO 2005

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

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

  27. Map Vertices Time (s) Amazonas 168.000 3,718 Minas Gerais 88.000 1,729 São Paulo 47.000 0,899 Santa Catarina 25.000 0,528 Rio de Janeiro 11.000 0,254 Alagoas 7.000 0,001 Proposal: Coincidence • Preserving coincidence by using the essential vertices Essential Vertices = extreme overlapping vertices • Pre-processing time required GEOINFO 2005

  28. Proposal: Coincidence • Processing of the in-between vertices: Original polylines First step: RDP Simplifications Second step Second step One simplification is adjusted The other is a copy GEOINFO 2005

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

  30. Proposal: Stop Conditions • From RDP algorithm: condition • From Saalfed’s algorithm: sidedness condition • Our proposal: nearness condition  GEOINFO 2005

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

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

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

  34. Results Saalfeld’s Our GEOINFO 2005

  35. Results Saalfeld’s Our GEOINFO 2005

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

  37. Concluding Remarks • 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. • The visual results make us to believe that our proposal is promising. • As further work, • To integrate this algorithm with one-line diagram algorithm to be presented on Wedneday. • To extend it to be multiresolution. GEOINFO 2005

  38. Thank You! GEOINFO 2005

  39. Objective: Improving Saalfeld’s • To simplify each polyline until condition is satisfied. • To process each convex hull until and sidedness conditions are satisfied.   GEOINFO 2005

  40. State-of-the-art: Saalfeld’s • RDP with a new stop condition ( + sidedness) GEOINFO 2005

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