November 21GEOINFO 2005 Preserving Incidence and Coincidence Topologies in Saalfelds Polyline...
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Transcript of November 21GEOINFO 2005 Preserving Incidence and Coincidence Topologies in Saalfelds Polyline...
November 21 GEOINFO 2005
Preserving Incidence and Coincidence Topologies in Saalfeld’s 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
November 21 GEOINFO 2005
Topics
Motivation Polyline simplification Topological Properties State-of-the-art Objective Proposal Results Concluding remarks
November 21 GEOINFO 2005
Topics
Motivation Polyline simplification Topological Properties State-of-the-art Objective Proposal Results Concluding remarks
November 21 GEOINFO 2005
Motivation 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
November 21 GEOINFO 2005
Motivation
Geographical context in different levels of detail
Maps in different resolutions
Simplification of a set of polylines
November 21 GEOINFO 2005
Topics
Motivation Polyline simplification Topological Properties State-of-the-art Objective Proposal Results Concluding remarks
November 21 GEOINFO 2005
Polyline Simplification
Original Map: 50.000
50.000 1.800
Simplified Map: 1.800
Source: Digital Chart of the World Server (www.maproom.psu.edu/dcw)
November 21 GEOINFO 2005
Polyline Simplification
Visvalingam and Whyatt, 1993
White, 1985
McMaster, 1986
Ramer, 1972;Douglas and Peucker, 1973RDP algorithm
Distance Adjacent distance
Adjacent Angle Adjacent Area
November 21 GEOINFO 2005
Polyline Simplification: RDP Maximum tolerable distance ()
November 21 GEOINFO 2005
Polyline Simplification: Problems
November 21 GEOINFO 2005
Topics
Motivation Polyline simplification Topological Properties State-of-the-art Objective Proposal Results Concluding remarks
November 21 GEOINFO 2005
Topological Properties
Geometrical properties that are invariant under continuous deformations
November 21 GEOINFO 2005
Topological Properties
Coincidence
Side crossings
Incidence
November 21 GEOINFO 2005
Topics
Motivation Polyline simplification Topological Properties State-of-the-art Objective Proposal Results Concluding remarks
November 21 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)
November 21 GEOINFO 2005
State-of-the-art: Saalfeld’s1) Necessity for inconsistencies
3) Triangle inversion2) Point sidedness
Simplification from RDP algorithm
simplification
subpolyline
November 21 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
November 21 GEOINFO 2005
State-of-the-art: limitations
WITH redundancies(Fast visualization)
WITHOUT redundancies(Easy edition)
Data structures:
November 21 GEOINFO 2005
State-of-the-art: Saalfeld’s
Coincidence
crossings Incidence
November 21 GEOINFO 2005
State-of-the-art: Saalfeld’s
November 21 GEOINFO 2005
State-of-the-art
Incidence of P2 in P1 without the insertion of the incident vertex in P1:
http://maps.google.com
November 21 GEOINFO 2005
Topics
Motivation Polyline simplification Topological Properties State-of-the-art Objective Proposal Results Concluding remarks
November 21 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
November 21 GEOINFO 2005
Objective: Improving Saalfeld’s RDP Saalfeld Saalfeld for maps
November 21 GEOINFO 2005
Topics
Motivation Polyline simplification Topological Properties State-of-the-art Objective Proposal Results Concluding remarks
November 21 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
November 21 GEOINFO 2005
Proposal: Coincidence
Preserving coincidence by using the essential vertices
Pre-processing time required
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
Essential Vertices = extreme overlapping vertices
November 21 GEOINFO 2005
Processing of the in-between vertices:
Proposal: Coincidence
Original polylines First step: RDP Simplifications
One simplification is adjusted The other is a copy
Second step Second step
November 21 GEOINFO 2005
Proposal: Incidence Preserving Incidences:
1 – nearness tolerance in numerical resolution
2 – nearness tolerance in device resolution
= max(1, 2)
November 21 GEOINFO 2005
Proposal: Stop Conditions
From RDP algorithm: condition From Saalfed’s algorithm: sidedness
condition Our proposal: nearness condition
November 21 GEOINFO 2005
Proposal: IncidenceNearness classification
Feature distance monitoring
Close
Close
November 21 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.
November 21 GEOINFO 2005
Topics
Motivation Polyline simplification Topological Properties State-of-the-art Objective Proposal Results Concluding remarks
November 21 GEOINFO 2005
ResultsSaalfeld’s Our
November 21 GEOINFO 2005
ResultsSaalfeld’s Our
November 21 GEOINFO 2005
Topics
Motivation Polyline simplification Topological Properties State-of-the-art Objective Proposal Results Concluding remarks
November 21 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.
November 21 GEOINFO 2005
Thank You!
November 21 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.
November 21 GEOINFO 2005
State-of-the-art: Saalfeld’s RDP with a new stop condition ( + sidedness)