Transformation Projection Parameters

8/18/2019 Transformation Projection Parameters

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Geocentric RSO Projection Parameters

Peninsular

RSO

East Malaysia

BRSO

Remark

Ellipsoid Parameters

Ellipsoid GRS 80 GRS 80

Semi-major axis, (a) 6378137.000 Meters 6378137.000 Meters

Flattening, f 1/298.2572221 1/298.2572221

Defined Parameters.

Latitude of Origin, φo 4o 00’ 00” N 4o 00’ 00” N

Longitude of Origin, λ 102o 15’ 00” E 115o 00’ 00” E

Rectified to Skew Grid,γ o

sin-1 (-0.6) sin-1 (0.8)

Azimuth of Central Line,αc

323o 01’ 32.86728” 53o 18’ 56.91582”

Scale factor, k 0.99984 0.99984

False Origin (Easting) 804,671 Meters E 0

False Origin (Northing) 0 0

Basic Longitude. λo 105o 14’ 10.58664” 109o41' 08.95525”


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PROJECTION PARAMETERPENINSULAR MALAYSIA

1 Projection Malayan Rectified Skew Orthomorphic (MRSO)old2 Ellipsoid Modified Everest

3 Semi-major axis (a) 6,377,304.063

4 Flattening (f) 1/300.8017

5 Whence e² = 0.00663784630200

6 Datum Kertau ( N 3° 27’ 50.71” ; E 102° 37’ 24.55” )

7 Conversion Factor 1 chain = 20.11678249 m (Chaney & Benoit, 1896)

8 Origin of projection 4o 00’ N ; 102o 15’ E of Greenwich

9 Scale factor at Origin 0.99984

10 False Coordinates of Projection ( 804671.2996 Meters E ; 0.00 N )

11 Initial line of projectionPasses through the Skew Origin at an azimuth of

Sin (-0.6) or 323° 01’ 32”.8458 from North

12Limit of table

North-parallel of 8o N

East-Meridian of 104o 30’ E

South-parallel of 1o N

West-Meridian of 99o 30’ E


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PROJECTION PARAMETEREAST MALAYSIA

1 Projection Borneo Rectified Skew Orthomorphic (BRSO)old 2 Ellipsoid Borneo (Modified Everest)

3 Semi-major axis (a) 6,377,298.556

4 Flattening (f) 1/300.8017

5 Whence e² = 0.00663784630200

6 Datum Timbalai 1968 ( N 5° 17’ 03.55” ; E 115° 10’ 56.41” )

7 Conversion Factor 1 chain= 20.11676512m (Sears, Jolly & Johnson, 1927)

8 Origin of projection 4o 00’ N ; 115o 00’ E of Greenwich

9 Scale Factor at Origin 0.99984

10 Coordinates of Origin ( 590476.8723 meters E ; 442857.6537 meters N )

11 Initial line of projectionPasses through the origin in an azimuth of 53° 18’

56”.9537 east of True North

12Limit of table

North-parallel of 8o N

East-Meridian of 109o 30’ E

South-parallel of 0o 50’ N

West-Meridian of 119o 30’ E

13 False Origin0 N

0 E


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TRANSFORMATION PARAMETERS USED IN PENINSULAR MALAYSIA

GDM2000 – Geocentric Datum of Malaysia

PMGSN94 - Peninsular Malaysia Geodetic and Scientific Network

( Previous WGS84 Datum adopted by JUPEM)

GDM2000 TO PMGSN94

Num Parameter

1 Translation X (dX) 1.69276 m

2 Translation Y (dX) - 1.92994 m

3 Translation Z (dX) 2.07108 m

4 Rotation X (Rx) 0.03515 "

5 Rotation Y (Ry) - 0.02858 "

6 Rotation Z (Rz) - 0.00617 "

7 Scale Factor 0.24859 ppm

8 SD of Transformation 0.025 m

PMGSN94 TO GDM2000

Num Parameter

1 Translation X (dX) - 1.69276 m

2 Translation Y (dX) 1.92994 m

3 Translation Z (dX) - 2.07108 m

4 Rotation X (Rx) -0.03515 "

5 Rotation Y (Ry) 0.02858 "

6 Rotation Z (Rz) 0.00617 "

7 Scale Factor -0.24859 ppm8 SD of Transformation 0.025 m


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PMGSN94 - Peninsular Malaysia Geodetic and Scientific Network

MRT48 – Malaysian Revised Triangulation 1948 (MRT48) – Kertau Datum

GDM2000 TO MRT48

Num Parameter


2 Translation Y (dX) -777.31353 m




6 Rotation Z (Rz) -12.11994 "


MRT48 TO GDM2000

Num Parameter

1 Translation X (dX) -381.42407 m2 Translation Y (dX) 777.33682 m

3 Translation Z (dX) -88.66677 m

4 Rotation X (Rx) -2.63177 "

5 Rotation Y (Ry) -2.07370 "

6 Rotation Z (Rz) 12.11991 "

7 Scale Factor -0.24859 ppm


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PMGSN94 TO MRT48

Num Parameter

1 Translation X (dX)379.77603 m





6 Rotation Z (Rz) - 12.11377 "


MRT48 TO PMGSN94

Num Parameter

1 Translation X (dX) -379.73137 m



4 Rotation X (Rx) - 2.59662 "

5 Rotation Y (Ry) - 2.10228 "

6 Rotation Z (Rz) 12.11374 "



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PENUKARAN KOORDINAT DARI GEOGRAFIKAL KE CASSINI-SOLDNER

E = FE + v[A – T(A3/6) - (8 –T + 8C)T * A5/120]

N = FN + M – Mo + v*tanφ[A2/2 + (5 – T + 6C)A4/24]

di mana,

E, N = Koordinat Cassini-Soldner Hitungan

FE, FN = Koordinat Cassini-Soldner asalan

A = (λ - λo)Cosφ di mana,

λ = Longitud titik hitungan

λo = Longitud titik asalan

φ = Latitud titik hitungan

T = tan2φ

C = (e2 / (1-e2))cos2φ

V = Jejari lengkung bumi di Pugak Utama

= a / (1-e2sin2φ)1/2

M = Jarak lengkung di meridian

= a[(1 – e2/4 – 3e4/64 – 5e6/256-..)φ - (3e2/8 + 3e4/32 +

45e6/1024 + …)sin2φ + (15e4/256 + 45e6/1024 +…)sin4φ

- (35e6/3072 + …)sin6φ ..]

dengan φ dalam unit Radians.

Mo = Nilai M dihitung di latitud origin pilihan.


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PENUKARAN KOORDINAT DARI CASSINI-SOLDNER KE GEOGRAFIKAL

φ = φ1 – (v1tanφ1 / ρ1) [D

2/2 – (1 + 3T 1) D4/24]

λ = λo + [D –T 1.D3/3 + (1 + 3T 1) T1.D

5/15] / cosφ1

di mana,

φ1 = µ1 + (3e1/2 – 27e13/32+ ..)Sin2µ1 +(21e1

2/16 -

55e14/32 + ..)Sin4µ1 + (151e1

3/96 + …)Sin6µ1 +

(1097e14/512 - …)Sin8µ1 + …

ρ1 = a(1-e2) / (1 – e2sin2φ1)

3/2

v1 = a / (1 – e2sin2φ1)1/2

di mana,

e1 = 1 – (1-e2)1/2 / 1 + (1-e2)1/2

µ1 = M1 / a(1- e2/4 - 3e4/64 - 5e6/256 - ……)

M1 = Mo + (N – FN)

= Mo adalah nilai M dihitung di latitud titik origin

T1 = tan2φ1

D = (E – FE)/v1


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Koordinat Muktamad Titik-Titik Asalan

GDM2000

Stesen

Latitud (N) Longitud (E)

Ketinggian

Ellipsoidal, h (m)

Ketinggian

Geoid, N

WMGeoid04

(m)

Ketinggian

MSL

(h-N)

(m)

Gunung Belumut 2° 02’ 33.20196” 103° 33’ 39.83730” 1016.308 6.918 1009.390

Gun Hill 2° 42’ 43.63383” 101° 56’ 22.92969” 118.583 -0.668 119.251

Gunung Sinyum 3° 42’ 38.69263” 102° 26’ 04.60772” 486.453 0.445 486.008

Bukit Asa 3° 40’ 48.37778” 101° 30’ 24.48581” 263.480 -3.544 267.024

Gunung Gajah Trom 4° 56’ 44.97184” 102° 53’ 37.00496” 1205.442 -0.289 1205.731

Fort Cornwallis 5° 25’ 15.20433” 100° 20’ 40.76024” -5.722 -11.523 5.801

Gunung Perak 5° 57’ 52.82155” 100° 38’ 10.93860” 852.235 -11.387 863.622

Gunung Hijau Larut 4° 51’ 32.64488” 100° 48’ 55.47038” 1439.089 -8.335 1447.424

Bukit Panau 5° 53’ 37.07975” 102° 10’ 32.24529” 226.388 -5.697 232.085

Bukit Kertau 3° 27’ 49.89150” 102° 37’ 18.93931” 269.258 1.383 267.875

Koordinat Rujukan Cassini-Soldner

Koordinat Titik-Titik Asalan Negeri

GDM2000 Cassini-SoldnerNegeri Nama Stesen

Latitud, (N) Longitud, (E)Utaraan

(m)

Timuran

(m)

Johor Gunung Belumut 2° 02’ 33.20196” 103° 33’ 39.83730” 0.000 0.000

N.Sembilan & Melaka Gun Hill 2° 42’ 43.63383” 101° 56’ 22.92969” 0.000 0.000

Pahang Gunung Sinyum 3° 42’ 38.69263” 102° 26’ 04.60772” 0.000 0.000

Selangor Bukit Asa 3° 40’ 48.37778” 101° 30’ 24.48581” 0.000 0.000

TerengganuGunung Gajah

Trom4° 56’ 44.97184” 102° 53’ 37.00496” 0.000 0.000

P.Pinang &

S. PeraiFort Cornwallis 5° 25’ 15.20433” 100° 20’ 40.76024” 0.000 0.000

Kedah & Perlis Gunung Perak 5° 57’ 52.82155” 100° 38’ 10.93860” 0.000 0.000

PerakGunung Hijau

Larut4° 51’ 32.64488” 100° 48’ 55.47038” 0.000 0.000

KelantanBukit Panau

(Baru)5° 53’ 37.07975” 102° 10’ 32.24529” 0.000 0.000


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TRANSFORMATION PARAMETERS USED IN EAST MALAYSIA

GDM2000 – Geocentric Datum of Malaysia

EMGSN97 - East Malaysia Geodetic and Scientific Network

- (Previous WGS84 Datum adopted by JUPEM)

1. GDM2000 TO EMGSN97

Num Parameter





5 Rotation Y (Ry) - 0.03471 "




2. EMGSN97 TO GDM2000

Num Parameter




4 Rotation X (Rx) - 0.01102 "


6 Rotation Z (Rz) - 0.02865 "7 Scale Factor 0.01934 ppm



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BT68 – Borneo Triangulation 1968 (Timbalai Datum)

3. GDM2000 TO BT68 (SABAH)

Num Parameter




4 Rotation X (Rx) -1.44639 "

5 Rotation Y (Ry) -0.88308 "6 Rotation Z (Rz) 1.82849 "


4. BT68 TO GDM2000 (SABAH)

Num Parameter

1 Translation X (dX)-596.09491 m





6 Rotation Z (Rz) -1.82849 "



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5. EMGSN97 TO BT68 (SABAH)

Num Parameter




4 Rotation X (Rx) -1.45741 m

5 Rotation Y (Ry) -0.84837 "


7 Scale Factor -10.43577ppm


6. BT68 (SABAH) TO EMGSN97

Num Parameter






6 Rotation Z (Rz) -1.79984 "

7 Scale Factor 10.43582ppm



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BT68 – Borneo Triangulation 1968 (Timbalai Datum)

7. GDM2000 TO BT68 (SARAWAK)

Num Parameter





5 Rotation Y (Ry) -0.51514 "



8. BT68 TO GDM2000 (SARAWAK)

Num Parameter


2 Translation Y (dX)676.11908 m


4 Rotation X (Rx) -1.28439 "


6 Rotation Z (Rz) -4.79004 "



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9. EMGSN97 TO BT68 (SARAWAK)

Num Parameter





5 Rotation Y (Ry) -0.48043 "




10. BT68 (SARAWAK) TO EMGSN97

Num Parameter




4 Rotation X (Rx) -1.27337 "


6 Rotation Z (Rz) -4.76139 "




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FAKTOR PENUKARAN KOORDINAT DARI RSO KE CASSINI-SOLDNER

DAN SEBALIKNYA

JOHOR

ORIGIN CASSININ = 0.0 E = 0.0

ORIGIN RSON = 11227.927 E = 30745.124

R1 = -0.0098: A1 = -2.0871: A2 = -5.27113: A3 = -0.47547: A4 = -0.64384: A5 = 0.58805R2 = 0.021: B1 = 5.29886: B2 = -1.83579: B3 = -0.74017: B4 = 0.17978: B5 = -0.66614

NS/MELAKA

ORIGIN CASSININ = -47.152 E = -12.03

ORIGIN RSON = 14918.998 E = 21786.154

R1 = -0.0132: A1 = 0.04887: A2 = -19.7519: A3 = -5.29544: A4 = -1.48678: A5 = 1.39966R2 = -0.011: B1 = 19.88167: B2 = -0.08787: B3 = -3.60882: B4 = 2.40011: B5 = -1.63052

SELANGOR

ORIGIN CASSININ = 2781.802 E = -1081.656

ORIGIN RSO

N = 20245.21 E = 19407.061

R1 = 0.00454: A1 = -1.05487: A2 = -26.99523: A3 = -4.56972: A4 = -2.38486: A5 = 1.43565R2 = -0.01114: B1 = 27.09565: B2 = -0.88007: B3 = -4.10737: B4 = 2.26095: B5 = -.38064


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PERAK UTARA


ORIGIN RSON = 26737.765 E = 15613.508

R1 = 0.0097: A1 = -1.26936: A2 = -38.99859: A3 = -2.48409: A4 = -0.09546: A5 = 0.38284R2 = -0.0085: B1 = 38.94896: B2 = -1.195: B3 = -0.4236: B4 = 1.13201: B5 = -0.44895

PERAK SELATAN


ORIGIN RSON = 26737.765 E = 15613.508

R1 = 0.0164: A1 = -0.94169: A2 = -39.34054: A3 = -4.55691: A4 = -1.11538: A5 = 1.7355

R2 = 0.0098: B1 = 39.34524: B2 = -0.98511: B3 = -2.53941: B4 = 2.35634: B5 = -1.56404

PULAU PINANG


ORIGIN RSON = 29837.058 E = 13032.613

R1 = 0.0035: A1 = -0.70331: A2 = -48.434: A3 = -7.83333: A4 = 0: A5 = 0R2 = -0.002: B1 = 47.88313: B2 = -0.97433: B3 = 0: B4 = 0: B5 = 0


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KEDAH/PERLIS


ORIGIN RSON = 32818.535 E = 14652.327

R1 = 0.0229: A1 = -1.67791: A2 = -43.47877: A3 = -0.78177: A4 = -0.71284: A5 = -0.00789R2 = -0.0139: B1 = 43.48222: B2 = -1.60907: B3 = 0.02231: B4 = 0.28692: B5 = -0.05668

KELANTAN


ORIGIN RSON = 32402.468 E = 23123.367

R1 = -0.0055: A1 = 0.09802: A2 = -16.90028: A3 = 3.08499: A4 = 1.30902: A5 = -0.43245R2 = 0.0093: B1 = 16.79903: B2 = 0.03457: B3 = 2.12603: B4 = -1.83988: B5 = 1.14088

TERENGGANU


ORIGIN RSO

N = 27187.737 E = 27071.372

R1 = 0.0023: A1 = 0.12995: A2 = -8.66038: A3 = 4.4369: A4 = 1.61249: A5 = -1.96429R2 = 0.0022: B1 = 8.65674: B2 = 0.21035: B3 = 3.95148: B4 = -2.29659: B5 = 2.52198


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PAHANG TIMUR LAUT


ORIGIN RSON = 20402.611 E = 24530.257

R1 = 0.0074: A1 = -1.85804: A2 = -15.531: A3 = -0.26344: A4 = 0.6903: A5 = -0.80353R2 = 0.0167: B1 = 15.74953: B2 = -1.98886: B3 = 1.13755: B4 = -0.37557: B5 = 0.92214

PAHANG TENGGARA


ORIGIN RSON = 20402.611 E = 24530.257

R1 = 0.1201: A1 = -0.65021: A2 = -15.75245: A3 = -3.5823: A4 = 0.62127: A5 = -0.85946R2 = -0.1127: B1 = 15.98562: B2 = -1.29342: B3 = 1.27091: B4 = 1.81814: B5 = 0.1889

PAHANG BARAT DAYA


ORIGIN RSON = 20402.611 E = 24530.257

R1 = -0.019: A1 = -2.0555: A2 = -15.85: A3 = -0.87963: A4 = -0.85008: A5 = 0.51332R2 = 0.0142: B1 = 15.96743: B2 = -1.75774: B3 = -0.77691: B4 = 0.84104: B5 = -0.57895


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PAHANG BARAT LAUT

ORIGIN CASSINI

N = 0.00 E = 0.00

ORIGIN RSON = 20402.611 E = 24530.257

R1 = -0.0402: A1 = -1.17721: A2 = -15.97246: A3 = 2.36266: A4 = -0.47438: A5 = 0.31267R2 = -0.0392: B1 = 16.45555: B2 = -1.60681: B3 = 0.79414: B4 = -1.33406: B5 = 0.56153


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RSO KE CASSINI - SOLDNER

Anggaran Pertama

N(CASS)1 = ∆N(RSO) - (R1+X1A1+Y1A2+X1Y1A3+X1²A4+Y1²A5)E(CASS)1 = ∆E(RSO) - (R2+X1B1+Y1B2+X1Y1B3+X1²B4+Y1²B5)

N(CASS)1 : Koordinat Cassini Utara/Selatan – Anggaran 1E(CASS)1 : Koordinat Cassini Timur/Barat – Anggaran 1∆N(RSO) : Koordinat Utara RSO Stesen – Koordinat Utara Origin∆E(RSO) : Koordinat Timur RSO Stesen – Koordinat Timur OriginX1 : ∆N (RSO)/10000

Y1 : ∆E (RSO)/10000

Anggaran Kedua :

N(CASS)Final = ∆N(RSO) - (R1+X2A1+Y2A2+X2Y2A3+X2²A4+Y2²A5)E(CASS)Final = ∆E(RSO) - (R2+X2B1+Y2B2+X2Y2B3+X2²B4+Y2²B5)

X2 : N(CASS)1) /10000Y2 : E(CASS)1) /10000


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CONTOH PENGIRAAN DARI RSO KE CASSINI SOLDNER

Negeri : Johor

Origin : G. Belumut

Koordinat Origin Negeri Johor

CASS-U: 0.00 Rantai = 0.00 MeterCASS-T: 0.00 Rantai = 0.00 Meter

Koordinat Origin dalam RSO

RSO-U : 11227.927 rantai

RSO-T: 30745.124 rantai

Unit rantai didarab dengan factor penukaran

RSO-U : 11227.927 X 20.11678249 = 225869.7653 meterRSO-T : 30745.124 X 20.11678249 = 618492.9721 meterFaktor

R1 -0.0098 A5 0.58805R2 0.021 B1 5.29886

A1 -2.0871 B2 -1.83579A2 -5.27113 B3 -0.74017A3 -0.47547 B4 0.17978A4 -0.64384 B5 -0.66614

Contoh Koordinat Stesen yang hendak dikira:

RSO-U: 14168.94900 Rantai

RSO-T: 29246.11700 Rantai

Anggaran Pertama

Dari formula

N(CASS)1 = ∆N(RSO) - (R1+X1A1+Y1A2+X1Y1A3+X1²A4+Y1²A5)


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E(CASS)1 = ∆E(RSO) - (R2+X1B1+Y1B2+X1Y1B3+X1²B4+Y1²B5)

∆N(RSO) = Perbezaan Koordinat Utara Stesen yang hendak dikira dengankoordinat Utara stesen origin (RSO)

= 14168.94900 - 11227.927 = 2941.02200 Rantai

∆E(RSO) = Perbezaan Koordinat Timur Stesen yang hendak dikira dengankoordinat Timur stesen origin (RSO)

= 29246.11700 - 30745.124 = -1499.00700 Rantai

X1: = ∆N(RSO)/10000 = 2941.02200/10000 = 0.2941022 Y1: = ∆E(RSO)/10000 = -1499.00700/10000 = -0.1499007

N(CASS)1 = 2941.02200 – [(-0.00980)+(-0.613820702)+0.790146077+0.02096163+-0.055689652+ 0.013213613]

2941.02200 - 0.14501 = 2940.87699

E(CASS)1 = -1499.00700 – [0.02100+1.558406383+0.275186206+0.032631228+0.01555027+(-0.014968312)]

-1499.00700 - 1.88781 = -1500.89481

Anggaran Kedua

Dari Formula

N(CASS)Final = ∆N(RSO) - (R1+X2A1+Y2A2+X2Y2A3+X2²A4+Y2²A5)E(CASS)Final = ∆E(RSO) - (R2+X2B1+Y2B2+X2Y2B3+X2²B4+Y2²B5)

X2 = Nilai N(Cass)1 dibahagi dengan 10000 = 2940.87699/10000 = 0.294087699Y2 = Nilai E(Cass)1 dibahagi dengan 10000 = -1500.89481/10000 = -0.150089481

N(CASS)Final = 2941.02200-[(-0.00980)+( -0.613790436)+ 0.791141164+0.020986994+(-0.05568416)+ 0.013246915]

= 2941.02200 - 0.14610 = 2940.8759 unit dalam rantai

E(CASS)Final = -1499.00700-[0.02100+1.558329544+0.275532768+0.032670711+0.015548736+(-0.015006037)]

= -1499.00700-1.88808 = -1500.89508 unit dalam rantai


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CASSINI-SOLDNER KE RSO

N(RSO) = ∆N(CASS) + N(ORSO)+(R1+XA1+YA2+XYA3+X²A4+Y²A5)E(RSO) = ∆E(CASS) + E(ORSO)+(R2+XB1+YB2+XYB3+X²B4+Y²B5)

∆N(CASS) : Koordinat Utara Cassini Stesen – Koordinat Utara Origin∆E(CASS) : Koordinat Timur Cassini Stesen – Koordinat Timur OriginN(ORSO) : Koordinat Utara Stesen Origin dalam RSOE(ORSO) : Koordinat Timur Stesen Origin dalam RSOX : ∆N(CASS)/10000Y : ∆E (CASS)/10000

Semua nilai adalah dalam unit rantai ( Guna nilai 20.11678249 sebagai faktor penukaran)


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GDM2000

RSO

GEOSENTRIK

CASSINIGEOSENTRIK

Transformation Projection Parameters

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