preserving incidence and coincidence topologies in saalfeld’s polyline simplification algorithm

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


Topics

Motivation Polyline simplification Topological Properties State-of-the-art Objective Proposal Results Concluding remarks


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


Motivation

Geographical context in different levels of detail

Maps in different resolutions

Simplification of a set of polylines


Topics



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)


Polyline Simplification

Visvalingam and Whyatt, 1993

White, 1985

McMaster, 1986

Ramer, 1972;Douglas and Peucker, 1973RDP algorithm

Distance Adjacent distance

Adjacent Angle Adjacent Area


Polyline Simplification: RDP Maximum tolerable distance ()


Polyline Simplification: Problems


Topics



Topological Properties

Geometrical properties that are invariant under continuous deformations


Topological Properties

Coincidence

Side crossings

Incidence


Topics



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)


State-of-the-art: Saalfeld’s1) Necessity for inconsistencies

3) Triangle inversion2) Point sidedness

Simplification from RDP algorithm

simplification

subpolyline


State-of-the-art: Saalfeld’s First step: RDP algorithm until condition is satisfied

Second step: further insertions until sidedness and conditions are satisfied


State-of-the-art: limitations

WITH redundancies(Fast visualization)

WITHOUT redundancies(Easy edition)

Data structures:


State-of-the-art: Saalfeld’s

Coincidence

crossings Incidence


State-of-the-art: Saalfeld’s


State-of-the-art

Incidence of P2 in P1 without the insertion of the incident vertex in P1:

http://maps.google.com


Topics



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


Objective: Improving Saalfeld’s RDP Saalfeld Saalfeld for maps


Topics



Proposal

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


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


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


Proposal: Incidence Preserving Incidences:

1 – nearness tolerance in numerical resolution

2 – nearness tolerance in device resolution

= max(1, 2)


Proposal: Stop Conditions

From RDP algorithm: condition From Saalfed’s algorithm: sidedness

condition Our proposal: nearness condition


Proposal: IncidenceNearness classification

Feature distance monitoring

Close

Close


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.


Topics



ResultsSaalfeld’s Our


Topics



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.


Thank You!


Objective: Improving Saalfeld’s

To simplify each polyline until condition is satisfied.

To process each convex hull until and sidedness conditions are satisfied.


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

preserving incidence and coincidence topologies in saalfeld’s polyline simplification algorithm

Documents

saalfelds geoinfo

satisfied geoinfo

saalfelds algorithm

redundant data geoinfo

simplified map

different levels of

topological consistency

satisfiedsecond step