MOST COMMON STATE MAP PROJECTIONS FOR THE REPUBLIC OF KOSOVO

STATE UNIVERSITY OF TETOVAFaculty of Natural Sciences and Mathematics

MOST COMMON STATE MAP PROJECTIONS MOST COMMON STATE MAP PROJECTIONS FOR THE REPUBLIC OF KOSOVOFOR THE REPUBLIC OF KOSOVO

Prof.Dr.sc. Bashkim IDRIZI

15-19 November 2009, Santiago - CHILE

Prof.Dr.sc. Bashkim IDRIZI, [email protected] “Most common state map projections for the

Republic of Kosovo” ICC2009 – Santiago, CHILE , 15-21 November 2009


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Contents of presentation:Contents of presentation: Location and dimensions of the Republic of Kosovo Parameters of former and new state coordinate systems of the Republic of Kosovo Most common state map projections related to the form of territory Test model for testing of map projections in the area of the Republic of Kosovo Criteria‘s for analyzing of map projections Researching methodology Utilized map projections Projecting of territory of the Republic of Kosovo in Gauss-Krűger projection with several scale factors Projecting of territory of the Republic of Kosovo in Lambert conform conic projection with several

scale factors Projecting of territory of the Republic of Kosovo in stereographic projection with several scale factors Projecting of territory of the Republic of Kosovo in UTM projection Conclusions




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Location and dimensions of the Republic of KosovoLocation and dimensions of the Republic of Kosovo

Area 10908km2

Border line 744km

length of the northern parallel 144.1km

length of the southern parallel 147.5km

length of the meridian 186.6km

Number of cities 30

PointGeographic coordinates

in ETRS89-GRS80φ λ

North 43º16’07.5’’ N 20º49’01.9’’ ESouth 41º50’50.1’’ N 20º37’36.8’’ EEast 42º38’48.0’’ N 21º47’42.7’’ EWest 42º44’10.4’’ N 20º01’10.9’’ E

Center 42º33’28.8’’ N 20º54’26.8’’ E




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Parameters of former and new state Parameters of former and new state coordinate systems of the Republic of Kosovocoordinate systems of the Republic of Kosovo

Name: FryRef 30 KosovaREF01Year of defining: 1924 2001Period of utilization: 1924-2001 2001-ongoingDatum: Harmannskögel ETRS89Ellipsoid: Bessel 1841 GRS 80Map projection Gauss–Krüger Gauss–KrügerProjecting zone: 7th 7th Width of the zone: 30 30 Prime meridian: Greenwich GreenwichCentral meridian: 210 210 Origin of latitude: Equator EquatorFalse easting: 500000m 7500000mFalse northing: 0m 0mScale factor: 0.9999 0.9999Length units: Meter MeterOrigin of elevations: Mareograph “Molo

Sartorio” – Trieste, ItalyMareograph “Molo Sartorio” – Trieste, Italy




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- Gauss-Krüger projection - for countries lengthened along the meridians, - Lambert conform conic projection - for countries lengthened along the parallels, - Stereographic projection - for countries with the form nearness to circle, and - Mercator projection - for the countries along the equator.

Most common state map projections Most common state map projections related to the form of territoryrelated to the form of territory




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Test model for testing of Test model for testing of map projections in the area map projections in the area of the Republic of Kosovoof the Republic of Kosovo

- 108 points grid,- 10km distance between points,- defined in ETRS89-GRS80.




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Criteria‘s for analyzing of map projectionsCriteria‘s for analyzing of map projections

Basic criteria’s for choosing of the most common state map projection: the value of the largest linear deformation (main criteria), right dispersion of the linear deformations, and adopting of the mathematical module for geodetic calculations;

Extended criteria’s for choosing of the most common state map projection:

the value of mean linear deformations, sum of squares of linear deformations, mean value of linear deformations in 1km length, and the percent coverage with defined deformation.




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Researching methodologyResearching methodology

Analyzing of tangential variant. Analyzing of secant option with value of negative linear deformation equal to half of largest from the tangential variant Analyzing of secant option with value of negative linear deformation equal to average of extreme points from the

tangential variant




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Utilized map projectionsUtilized map projections Gauss-Krűger projection (because of lengthened along the meridians) Stereographic projection (because of the form nearness to circle) Lambert conform conic projection (because of lengthened along the

parallels) UTM (because of its international importance).

Geographic and orthogonal coordinates (false easting and northing) of central point in all variants of Stereographic and Lambert conform conic

projections




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Projecting of Kosovo in Gauss-KrProjecting of Kosovo in Gauss-Krűűger projectionger projection Gauss-Krűger within the KosovaREF 01 (scale factor 0.9999; -10cm/km) Gauss-Krűger in tangential variant Gauss-Krűger with secant cylinder (scale factor 0.99996; -4cm/km) Gauss-Krűger with secant cylinder (scale factor 0.999967; -3.3cm/km)

KosovaREF01 (mo=0.9999)

mo=1 mo=0.99996 mo=0.999967

Ɵ 8.7cm/km 1.3cm/km 2.93cm/km 2.46cm/km

Σ∆d∆d 8440.26 (cm/km)2 452 (cm/km)2 1055 (cm/km)2 746 (cm/km)2

m0 8.84cm/km 2.05cm/km 3.13cm/km 2.63cm/kmdmax -10cm/km 7.9cm/km -4cm/km 4.6cm/kmDispersion of deformations

-2.1 to -10cm/km 0 to 7.9cm/km -4 to 3.9cm/km -3.3 to 4.6cm/km

d positive - 87.30% 7.04% 10.85%d negative 100% - 92.45% 88.48%d without deformation

- 12.70% 0.51% 0.67%




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KosovaREF 01(Gauss-Krűger - 0.9999)

Gauss-Krűger – 1.0000




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Gauss-Krűger – 0.99996 Gauss-Krűger – 0.999967




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Linear deformationAreas

KosovaREF01 mo=1 mo=0.99996 mo=0.999967

0-1 cm/km - 6440km2 1081km2 1478km2

1-2 cm/km - 1997km2 1215km2 1887km2

2-3 cm/km40km2

(2.05-3cm/km)1022km2 2131km2 3977km2

3-4 cm/km 134km2 653km2 6480km2 3543km2

4-5 cm/km 193km2 428km2 -23km2

(4-4.65cm/km)

5-6 cm/km 428km2 193km2 - -

6-7 cm/km 653km2 134km2 - -

7-8 cm/km 1022km2 40km2

(7-7.95cm/km)- -

8-9 cm/km 1997km2 - - -

9-10 cm/km 6440km2 - - -

Map projection Area of Kosovo Border line of Kosovo

KosovaREF01 (mo=0.9999) 10906.05 km2 744.042 km

Gauss-Krüger (mo=1) 10908.23 km2 744.117 km

Gauss-Krüger (mo=0.99996) 10907.36 km2 744.087 km

Gauss-Krüger (mo=0.999967) 10907.51 km2 744.092 km




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Projecting of Kosovo in Lambert conform Projecting of Kosovo in Lambert conform conic projectionconic projection

Lambert conform conic projection in tangential variant

Lambert conform conic projection with secant cone (scale factor 0.999962; -3.8cm/km)

mo=1 mo=0.999962Ɵ 1.14cm/km 2.85cm/kmΣ∆d∆d 374 (cm/km)2 993 (cm/km)2

M0 1.86cm/km 3.03cm/kmdmax 7.69cm/km -3.8cm/kmDispersion of deformations 0 to 7.69 cm/km -3.8 to 3.79cm/kmd positive 84.34% 92.51%d negative - 7.11%d without deformation 15.66% 0.38%




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Lambert conform conic– 1.0000 Lambert conform conic – 0.999962




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Linear deformationAreas

mo=1 mo=0.999962

0-1 cm/km 6877km2 914km2

1-2 cm/km 1844km2 1292km2

2-3 cm/km 971km2 2345km2

3-4 cm/km 500km2 6356km2

(3-3.8cm/km)

4-5 cm/km 313km2 -

5-6 cm/km 191km2 -

6-7 cm/km 170km2 -

7-8 cm/km42km2

(7-7.69cm/km)-


Lambert conform conic projection (mo=1) 10908.20 km2 744.118 km

Lambert conform conic projection (mo=0.999962) 10907.38 km2 744.090 km




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Projecting of Kosovo in Stereographic projectionProjecting of Kosovo in Stereographic projection Stereographic projection in tangential variant Secant stereographic projection (scale factor 0.999979; -2.1cm/km) Secant stereographic projection (scale factor 0.999981; -1.9cm/km)

mo=1 mo=0.999979 mo=0.999981Ɵ 1.17cm/km 1.08cm/km 0.94cm/kmΣ∆d∆d 219 (cm/km)2 164 (cm/km)2 128 (cm/km)2

M0 1.42cm/km 1.23cm/km 1.09cm/kmdmax 4.18cm/km -2.1cm/km 2.28cm/kmDispersion of deformations

0 to 4.18 cm/km -2.1 to 2.08cm/km -1.9 to 2.28cm/km

d positive 97.67% 12.04% 16.46%d negative - 85.89% 80.91%d without deformation

2.33% 2.07% 2.63%




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Stereographic – 0.999979 Stereographic – 0.999981




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Linear deformation

Areas

mo=1 mo=0.999979 mo=0.999981

0-1 cm/km 5092km2 5024km2 5928km2

1-2 cm/km 4153km2 5374km2 4971km2

2-3 cm/km 1325km2 510km2

(2-2.08cm/km)9km2

(2-2.28cm/km)

3-4 cm/km 334km2 - -

4-5 cm/km4km2

(4-4.18cm/km)- -


Stereographic (mo=1) 10908.23 km2 744.118 km

Stereographic (mo=0.999979) 10907.77 km2 744.103 km

Stereographic (mo=0.999981) 10907.81 km2 744.104 km




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Projecting of Kosovo in UTM projectionProjecting of Kosovo in UTM projection

mo=0.9996Ɵ 38.7cm/kmΣ∆d∆d 161988 (cm/km)2

M0 38.73cm/kmdmax -40cm/kmDispersion of deformations

-32.11 to -40 cm/km

d positive -d negative 100%d without deformation

-


UTM 10899.50 km2 743.819 km




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Area and border line of Kosovo Area and border line of Kosovo in analyzed map projectionsin analyzed map projections

Map projection Area Border lineKosovaREF 01 (Gauss-Krüger, mo=0.9999) 10906.05 km2 744.042 kmGauss-Krüger (mo=1) 10908.23 km2 744.117 kmGauss-Krüger (mo=0.99996) 10907.36 km2 744.087 kmGauss-Krüger (mo=0.999967) 10907.51 km2 744.092 kmStereographic (mo=1) 10908.23 km2 744.118 kmStereographic (mo=0.999979) 10907.77 km2 744.103 kmStereographic (mo=0.999981) 10907.81 km2 744.104 kmLambert conform conic (mo=1) 10908.20 km2 744.118 kmLambert conform conic (mo=0.999962) 10907.38 km2 744.090 kmUTM 10899.50 km2 743.819 km




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… based on above results, most common state map

projection of the Republic of Kosovo for internal use is Stereographic projection

with scale factor 0.999979, and UTM projection for

international use.

ConclusionConclusion




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THANK YOU FOR YOUR ATTENTION!!!

CONTACTS:Prof.Dr. Bashkim IDRIZI, STATE UNIVERSITY OF TETOVA; Faculty of Natural Sciences and Mathematics.Address: str. Ilindenska, bb; 1200 Tetova; Macedonia.Home: str. Xhon Kenedi, 25-4/20; 1000 Skopje; Macedonia. Gsm: +389 75 712 998; Home: + 389 2 2612 492; Fax: + 389 44 334 222; e-mail: [email protected], [email protected] site: www.unite.edu.mk, www.geocities.com/hartografia/ut.html


MOST COMMON STATE MAP PROJECTIONS MOST COMMON STATE MAP PROJECTIONS FOR THE REPUBLIC OF KOSOVOFOR THE REPUBLIC OF KOSOVO

Prof.Dr.sc. Bashkim IDRIZI

15-19 November 2009, Santiago - CHILE

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MOST COMMON STATE MAP PROJECTIONS FOR THE REPUBLIC OF KOSOVO