B.Sc. Matej Gomboši Determining differences between two sets of polygons Laboratory for Geometric Modelling and Multimedia Algorithms Faculty of Electrical.

B.Sc. Matej Gomboši

Determining differences between two sets of polygons

Determining differences between two sets of polygons

Laboratory for Geometric Modelling and Multimedia Algorithms

Faculty of Electrical Engineering

and Computer Science

University of Maribor

www.uni-mb.si/~gemma

IntroductionIntroduction

Parcel records on paper - cadastre Computer supported cadastre Database changes Keeping database up-to-date Finding and analyzing changes Working with changes in geometry and attributes Lack of appropriate commercial solutions (ESRI, ArcView) Integrated solution for GIS environments

IntroductionIntroduction

Difference ?

FormulationFormulation

1. Let P be a polygon made up of vertices v1, v2, ..., vn and edges e1, e2, ..., en connecting them.

2. Let S be a set of polygons P1, P2, ..., Pn. Each Pi can have arbitrary shape and number of vertices.

3. Find a set of polygons D, which represents the difference between S1 and S2. D contains changed polygons P1, P2, ..., Pm, which belong to S1 or S2.

StrategiesStrategies

Brute force approach Localized search approch Speed and stability considerations Separate aplications for different problems (need for

integration)

Basic ideaBasic idea

Comparison of S1 and S2

based on polygon edges Removing equal edges What remains represents

changes Analyzing remaining edges

Polygon• Sets of polygons from ESRI files (SHP)

• Organized data structures in memory

• Edge as main object

“Work table”• Uniform plane subdivision

• Binary search tree in cells

• Sorted edges

Edge• p1,p2

• Polygon info

• Hole info

Data objectsData objects

“Work table”“Work table”

• binary search tree in each cell• pointers to tree roots

Polygon edge information

Polygon edge information

1. Coordinates - p1(x1,y1), p2(x2,y2)

2. Polygon info

polygon index

set indicator (S1 or S2)

index of the surrounding polygon

• Counter

• Hole info

hole index (locally inside a polygon)

Edge clasification

Edge clasification

O uter border edge

Interio r edge

1

12

Counter values!

1. Acquiring polygon sets from ESRI database

2. Inserting edges into uniform plane subdivison

3. Updating already existing edges

4. Removing of equal edges

5. Analyzing remaining edges

6. Storing changes

AlgorithmAlgorithm

Finding differences (1)

Finding differences (1)

Finding differences (1)

Finding differences (1)

Finding differences (2)Finding differences (2)

Finding differences (2)Finding differences (2)

Problems at comparing attributesProblems at comparing attributes

Non-simple polygon

Contains regular(green) and non-regular(gray) holes

Finding correct polygon index to compare attributes

Arithmetic problems Arithmetic problems

Possible errors of overlaping edges

Measuring error (+/- 12cm) Epsilon tolerance at comparing

the vertices

Time complexityTime complexity

1. Inserting edgesO(n*log m)n – total num. of edgesm – average num. of edges in a cell

2. Analyzing changesO(n*log m)n – number of cellsm - average num. of edges in a cell

Practical resultsPractical results

20.000 edges8.000 polygons1.000 changes

5 seconds with database access

ConclusionsConclusions

• New efficient algorithm for specific geometric problem• Works on large sets of polygons as found in GIS application• Simple implementation• Efficient use of known speed-up techniques • Easy integration into other GIS environments (dll)• Robust (no problems with geometric boundary cases)• Succesfully used in practice