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) State University of Campinas (UNICAMP) GEOINFO 2005

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

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

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

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

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

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

Polyline Simplification: Problems  GEOINFO 2005

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

Topological Properties Side crossings Coincidence Incidence GEOINFO 2005

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Results Saalfeld’s Our GEOINFO 2005

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

Thank You! GEOINFO 2005

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

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

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