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New method of creation data for natural objects in MRDB based on new simplification algorithm 1

New method of creation data for

natural objects in MRDB based on

new simplification algorithm

Krystian Kozioł, Stanisław Szombara

Department of Geomatics

Faculty of Mining Surveying and Environmental Engineering

Dresden, August 29th 2013.


Introduction

One of the main tasks of cartography in the 21st century is visualisation of

topographical objects in MRDBs in various scales. According to Sarjakoski

(2007), creating MRDB means use of generalisation model considering the

following criteria:

• most frequently used representation of objects,

• requirements of objects updating,

• level of automation that can be achieved in the process of creating the

representation of objects.

BDOT500, BDOT10k and BDOO (1:250k)


Simplification operator

• Point-reduction algorithms

• Scale-driven generalisation algorithms


Concept

The idea!

What if we develop a simplificationalgorithm that chooses the points on the real object rather then eliminates them?

Problems• How to get the real object?• How to place the points (vertices)

automaticaly according to the level of detail?


Protype

The stages of the algorithm are:

• Dividing

• Interpolation

• Determination extreme points

• Selection of new intermediate points

• Verification


Locating the characteristic vertices on apolyline (creating of surjection parts)


Creating curve using 3rd degree Hermite Interpolation

The chosen interpolation method should satisfy the following conditions for a curve:

• the curve should pass through all the points of a polyline – f(x) = H(x),

• the local extreme of a polyline should be preserved – f’(x) = H’(x).

We use the Hermite polynomial, compatible with f(xi) and with f’(xi) at points xi for i = 0,1,2…,n.

The form of the polynomial (Boor 1978) is as follows:

( ) ( ) ( ) ( ) ( )xHxfxHxfxH jnn

j jjn

n

j j,0,0 '

∧

== ∑+∑=


Arrangement of points on the original curve according to the standard drawing recognizability

In order to distinguish points on the original curve for a map in scale 1:Mk we used the recognisability normbased on the elementary triangle (Chrobak 2010):

• ε01 = 0,5[mm]*Mk b є [0,5mm – 0,7mm)*Mk],

• ε02 ≥ 0,5[mm]*Mk b є [0,4mm – 0,5mm)*Mk]


Verification of results

Piątkowski (1969) defined the accuracy norm ofacquiring curve-like objects and called it theprimitive generalization. This generalisation ideaconsists in use of line segments (chords) in place ofcorresponding curvilinear sections of a linearobject. Piątkowski determined empirically thelength of ordinate - e - between the chord and thearc of the curve, called the rise. Length of the risedepends on the scale of map as follows:

e ≥ 0,3[mm]*Mk,


Example results

Douglas-Peücker

Visvalingam - Whyatt

Wang

Chrobak

The new algorithm

Generalisation from 1:500 to 1:25000


Example results

10m

1:50001:10000

1:25000 1:50000

Reference scale: 1:500


Conclusions

• The conversion of a polyline into a curve allows arrangement of points on the original curve depending on the target map scale and not source map scale.

• The presented method can be implemented to any database of MRDB type under the assumption that the high-detail data will constitute the source data and the results will be used for the purpose of visualization at low level of detail.

• The drawing recognizability norm and Piątkowski normimplemented in the simplification process with this particular algorithm gives an unambiguous result and the opportunity for a measurable verification.


Thank you for your attention

[email protected]

Questions?

More details:

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