1

Rujukan Kami: JUPEM 18/7/2.148 Jld. 3 ( 17 ) Tarikh: 25 Mei 2009

Semua Pengarah Ukur dan Pemetaan Negeri

PEKELILING KETUA PENGARAH UKUR DAN PEMETAAN BILANGAN 1 TAHUN 2009

GARIS PANDUAN MENGENAI SISTEM RUJUKAN KOORDINAT DI DALAM PENGGUNAAN

GLOBAL NAVIGATION SATELLITE SYSTEM (GNSS) BAGI TUJUAN UKUR DAN PEMETAAN

1. TUJUAN

Pekeliling ini bertujuan untuk memberikan garis panduan mengenai

sistem rujukan koordinat dalam kontek penggunaan Global Navigation

Satellite System (GNSS) bagi kerja-kerja ukur dan pemetaan di

Malaysia.

2. LATAR BELAKANG

2.1 Sistem rujukan koordinat Malayan Revised Triangulation 1948

(MRT48) dengan Bukit Kertau sebagai titik asalan (origin) telah

digunakan bagi aktiviti pemetaan dan ukur kadaster sejak tahun

1948 di Semenanjung Malaysia. Datum rujukan geodetik bagi

sistem ini adalah Datum Kertau yang menggunakan elipsoid

Modified Everest (Kertau). Bagi Sabah, Sarawak dan Labuan

pula, aktiviti ukur dan pemetaan telah dijalankan dengan

2

menggunakan sistem rujukan koordinat Borneo Triangulation

1968 (BT68) dengan Bukit Timbalai sebagai titik asalan. Datum

rujukan geodetik bagi BT68 adalah Datum Timbalai yang

menggunakan elipsoid Modified Everest (Timbalai).

2.2 Penggunaan teknologi GNSS bagi kerja-kerja ukur dan pemetaan

di Malaysia telah bermula sejak tahun 1989. Dalam hal ini,

Jabatan Ukur dan Pemetaan Malaysia (JUPEM) telah

menghasilkan sistem-sistem rujukan koordinat dengan

menggunakan teknik Global Positioning System (GPS), iaitu

Peninsular Malaysia Geodetic Scientific Network (PMGSN94)

pada tahun 1994, diikuti dengan East Malaysia Geodetic

Scientific Network (EMGSN97) pada tahun 1997. Seterusnya

dalam tahun 2003, kerangka rujukan geodetik GPS pasif tersebut

telah diperkukuhkan bagi menghasilkan Malaysia Primary

Geodetic Network (MPGN2000).

2.3 Dalam pada itu, antara tahun 1998 dan 2008, JUPEM telah

membangunkan rangkaian-rangkaian GPS/GNSS aktif, iaitu

Malaysia Active GPS System (MASS) antara tahun 1998 dan

2001 dan diikuti dengan penubuhan Malaysia Real-Time

Kinematic GNSS Network (MyRTKnet) antara tahun 2002 dan

2008.

2.4 Bagi memenuhi tuntutan semasa yang menjurus kepada

penggunaan datum rujukan global yang bersifat geosentrik,

JUPEM telah selanjutnya melancarkan datum rujukan geodetik

baru yang seragam bagi kerja-kerja ukur dan pemetaan di

Malaysia pada 26 Ogos 2003. Datum ini dikenali dengan nama

Geocentric Datum of Malaysia (GDM2000), di mana elipsoid

rujukan adalah Geodetic Reference System 1980 (GRS80). Titik

asalan bagi sistem-sistem rujukan koordinat yang berasaskan

GDM2000 ini adalah di pusat jisim bumi (geosentrik).

3

2.5 Pada tahun 2004 dan 2005 telah berlaku gempa bumi besar,

masing-masingnya bermagnitud 9.2 dan 8.7 pada skala Ritcher di

Sumatra, Indonesia dan kejadian ini telah menyebabkan anjakan

yang signifikan terhadap sistem koordinat GDM2000.

Sehubungan itu, pemantauan anjakan keatas sistem-sistem

rujukan koordinat telah dilakukan oleh JUPEM secara berterusan

melalui analisis anjakan ke atas stesen-stesen MyRTKnet.

Analisis mendapati bahawa sistem-sistem rujukan koordinat yang

berasaskan GDM2000 perlu disemak dan dihitung semula,

terutamanya bagi kerja-kerja pengukuran yang memerlukan

penggunaan sistem rujukan koordinat yang berkejituan tinggi

seperti di dalam bidang geodesi dan geodinamik.

2.6 Hasil daripada semakan dan hitungan semula tersebut yang

menggunakan produk data GPS bermula 1 Januari 2006 hingga

30 April 2009, siri set koordinat baru yang dikenali sebagai

GDM2000 (2009) bagi rangkaian-rangkaian GNSS/GPS aktif dan

pasif telah diterbitkan oleh JUPEM.

3. GARIS PANDUAN PENGGUNAAN SISTEM RUJUKAN KOORDINAT

Penerangan lebih lanjut tentang amalan penggunaan sistem rujukan

koordinat terkandung di dalam dokumen Technical Guide to the

Coordinate Reference Systems seperti di Lampiran ‘A’ yang disertakan.

Intisari kandungan garis panduan tersebut adalah seperti berikut:

4

Perenggan Perkara

1. INTRODUCTION

2. OLD TRIANGULATION NETWORKS

2.1 MALAYAN REVISED TRIANGULATION 1968 (MRT68)

2.2 BORNEO TRIANGULATION 1968 (BT68)

3. GPS-BASED NETWORKS

3.1 PENINSULAR MALAYSIA GEODETIC SCIENTIFIC

NETWORK 1994 (PMGSN94)

3.2 EAST MALAYSIA GEODETIC SCIENTIFIC NETWORK

1997 (PMGSN97)

4. GEOCENTRIC DATUM OF MALAYSIA (GDM2000)

4.1 INTRODUCTION

4.2 MALAYSIA ACTIVE GPS SYSTEM (MASS)

4.3 MALAYSIA PRIMARY GEODETIC NETWORK 2000

(MPGN2000)

4.4 MALAYSIA REAL-TIME KINEMATIC GNSS NETWORK

(MyRTKnet)

5. REVISION OF GDM2000

5.1 MAJOR SUMATRAN EARTHQUAKES IN 2004, 2005

AND 2007

5.2 MyRTKnet IN GDM2000 (2009)

5.3 MPGN200 IN GDM2000 (2009)

6. CONCLUSION

4. PEMAKAIAN

4.1 Sistem-sistem rujukan koordinat yang dinyatakan di dalam

pekeliling ini hendaklah digunakan berdasarkan tarikh-tarikh

tertentu seperti yang dinyatakan dalam Jadual 1 dan Jadual 2 di

bawah:

5

Jadual 1 : Jaringan GPS/GNSS Pasif Malaysia

Sistem Rujukan Koordinat Bil

Sistem Koordinat Datum Geodetik

Tarikh Penggunaan

1 Peninsular Malaysia Geodetic Scientific Network 1994 (PMGSN94)

WGS84 Ellipsoid: WGS84 Reference Frame: WGS84 Epoch: 1987.0

1 Januari 1994 hingga

22 Ogos 2003

2 East Malaysia Geodetic Scientific Network 1997 (EMGSN97)

WGS84 Ellipsoid: WGS84 Reference Frame: WGS84 (G783) Epoch: 1997.0

1 Januari 1997 hingga

22 Ogos 2003

GDM2000 Ellipsoid: GRS80 Reference Frame: ITRF2000 Epoch: 2000.0

23 Ogos 2003 hingga

30 April 2009 3

Malaysia Primary Geodetic Network 2000 (MPGN2000) GDM2000 (2009)

Ellipsoid: GRS80 Reference Frame: ITRF2000 Epoch: 2000.0

Mulai 1 Mei 2009

Jadual 2 : Jaringan GPS/GNSS Aktif Malaysia

Sistem Rujukan Koordinat Bil

Sistem Koordinat Datum Geodetik

Tarikh Penggunaan

1 Malaysia Active GPS System (MASS)

GDM2000 Datum: GRS80 Reference Frame: ITRF2000 Epoch: 2000.0

1 Januari 1999 hingga

30 April 2009

GDM2000 Datum: GRS80 Reference Frame: ITRF2000 Epoch: 2000.0

12 Mei 2004 hingga

30 April 2009 2

Malaysia Real-Time Kinematic GNSS Network (MyRTKnet) GDM2000 (2009)

Datum: GRS80 Reference Frame: ITRF2000 Epoch: 2000.0

Mulai 1 Mei 2009

4.2 Bagi pengguna-pengguna yang terlibat di dalam kerja-kerja ukur

yang memerlukan ketepatan dan kejituan yang tinggi, khususnya

bidang geodesi dan geodinamik, tarikh penggunaan sistem-

6

sistem rujukan koordinat berasaskan GDM2000 adalah sehingga

31 Disember 2005, manakala tarikh penggunaan sistem-sistem

rujukan koordinat berasaskan GDM2000 (2009) adalah mulai

1 Januari 2006.

4.3 Pengguna-pengguna boleh mendapatkan nilai-nilai koordinat dan

maklumat lokasi bagi setiap stesen trigonometri dan stesen

GPS/GNSS dengan menghubungi Ibu Pejabat JUPEM, Kuala

Lumpur atau dengan melayari Laman Web JUPEM, iaitu

http://www.jupem.gov.my. Selain itu, JUPEM juga turut

menyediakan maklumat dan perkhidmatan penukaran koordinat

dan transformasi datum bagi semua sistem rujukan koordinat

serta unjuran peta kepada para pengguna.

5. TARIKH BERKUATKUASA Pekeliling ini adalah berkuatkuasa mulai tarikh ianya dikeluarkan. Sekian, terima kasih. “BERKHIDMAT UNTUK NEGARA”

( DATUK HAMID BIN ALI ) Ketua Pengarah Ukur dan Pemetaan Malaysia

7

Salinan kepada: Timbalan Ketua Pengarah Ukur dan Pemetaan Pengarah Ukur Bahagian (Pemetaan) Pengarah Ukur Bahagian (Kadaster) Pengarah Bahagian Geospatial Pertahanan Setiausaha Bahagian (Tanah, Ukur dan Pemetaan) Kementerian Sumber Asli dan Alam Sekitar Pengarah Institut Tanah dan Ukur Negara (INSTUN) Kementerian Sumber Asli dan Alam Sekitar Pengarah Pusat Infrastuktur Data Geospatial Negara (MaCGDI) Kementerian Sumber Asli dan Alam Sekitar Ketua Penolong Pengarah Unit Ukur Tanah, Cawangan Pengkalan Udara dan Maritim Ibu Pejabat Jabatan Kerja Raya Malaysia Penolong Pengarah Unit Ukur Tanah, Bahagian Kejuruteraan Awam Ibu Pejabat Jabatan Perumahan Negara Setiausaha Lembaga Jurukur Tanah Semenanjung Malaysia Setiausaha Lembaga Jurukur Tanah Sabah Setiausaha Lembaga Jurukur Tanah Sarawak

Technical Guide to the

Coordinate Reference Systems

JABATAN UKUR DAN PEMETAAN MALAYSIA2009

Lampiran ‘A’

i

TABLE OF CONTENTS 1. INTRODUCTION 1

2. OLD TRIANGULATION NETWORKS 2

2.1 MALAYAN REVISED TRIANGULATION 1968 (MRT68) 2

2.2 BORNEO TRIANGULATION 1968 (BT68) 5

3. GPS-BASED NETWORKS 7

3.1 PENINSULAR MALAYSIA GEODETIC SCIENTIFIC NETWORK 1994 (PMGSN94) 7

3.2 EAST MALAYSIA GEODETIC SCIENTIFIC NETWORK 1997 (EMGSN97) 10

4. GEOCENTRIC DATUM OF MALAYSIA (GDM2000) 12

4.1 INTRODUCTION 12

4.2 MALAYSIA ACTIVE GPS NETWORK (MASS) 12

4.3 MALAYSIA PRIMARY GEODETIC NETWORK 2000 (MPGN2000) 14

4.4 MALAYSIA REAL-TIME KINEMATIC GNSS NETWORK (MyRTKnet) 17

5. REVISON OF GDM2000 19

5.1 MAJOR SUMATRAN EARTHQUAKES IN 2004, 2005 AND 2007 19

5.2 MyRTKnet IN GDM2000 (2009) 24

5.3 MPGN2000 IN GDM2000 (2009) 25

6. CONCLUSION 26

REFERENCES 27

1

1. INTRODUCTION

1.1 Coordinate reference systems have been established in many regions

around the world by national mapping authorities since the 19th

century, using conventional surveying techniques and procedures.

Most of them use local datums that are confined to small areas of the

globe, fit to limited areas to satisfy national mapping requirements.

This is also the case with Malaysia where it has in place two

old/classical triangulation networks, namely the Malayan Revised

Triangulation 1968 (MRT68) for Peninsular Malaysia and the Borneo

Triangulation 1968 (BT68) for Sabah and Sarawak.

1.2 With the recent advances in space-based positioning technology,

many countries have begun to implement and subsequently adopted a

global geocentric coordinate reference system. In relation to this,

JUPEM itself has embraced in the early 1990s the Global Positioning

System (GPS) technology with the eventual objective of adopting a

global unified datum for Peninsular Malaysia, Sabah and Sarawak.

This later led to the establishment of the Peninsular Malaysia GPS

Scientific Network 1994 (PMGSN94) and East Malaysia GPS Scientific

Network 1997 (EMGSN97), comprising of 238 stations and 171

stations respectively.

1.3 Subsequently, JUPEM established the permanent GPS tracking

stations known as Malaysia Active GPS System (MASS) at the end of

1998, with eighteen (18) stations making up the whole MASS

infrastructure. Coupled with the GPS data obtained from the

International Global Navigational Satellite System (GNSS) Service

(IGS) stations, the coordinates of MASS stations were derived from 4-

years of continuous GPS data (1999 - 2002). Collectively, these

coordinates represent the basis for the determination of the Geocentric

Datum of Malaysia (GDM2000), which was launched on 26 August

2003.

2

1.4 Between 2002 and 2008, JUPEM further developed a modern active

GNSS network with the latest state-of-the-art technology to establish

the Malaysia Real-Time Kinematic GNSS Network or MyRTKnet. The

new MyRTKnet system is able to provide real-time positioning services

at centimeter-level accuracy to users in the field.

1.5 However, there were significant displacements of positions of the

aforementioned Malaysian geodetic infrastructure as a result of two

major Indonesian earthquakes that occurred in 2004 and 2005.

Nevertheless, due to the relatively stable conditions that followed in the

past four years (albeit still quite unpredictable), JUPEM has taken

further steps to revise the coordinate reference systems, using GPS

data from the years 2006 to 2008 of MyRTKnet and IGS stations. The

resultant coordinates obtained through this endeavour are known as

GDM2000 (2009).

1.6 This technical guide then is produced to give an overview of the

coordinate reference systems that are available in Malaysia and to

assist users in understanding the concept, strategies and procedures

involved in the move towards the adoption of GDM2000 in 2003 and its

subsequent revision carried out in 2009.

2. OLD TRIANGULATION NETWORKS 2.1 MALAYAN REVISED TRIANGULATION 1968 (MRT68)

2.1.1 JUPEM could trace its origin to way back in 1885. The 1880s marked

an important phase with the commencement of widespread

trigonometrical works in various parts of Malaya, including a

triangulation survey in Penang in 1832.

2.1.2 The trigonometrical survey in Perak together with the Penang and

Province Wellesley triangulations as well as Malacca Triangulation

3

(1886 - 1888) laid the foundation for the existing control framework.

This was followed by the commencement of other trigonometrical

surveys in various parts of the country that included Selangor and

Negeri Sembilan.

2.1.3 However, the early works were so inconsistent and of questionable

quality that it was decided to re-observe the principal triangles of the

general triangulation with the object of bringing it up to modern

standards of that time. This triangulation scheme in Peninsular

Malaysia which was completed in 1916 is known as the Primary or

Repsold Triangulation.

2.1.4 The Primary or Repsold Triangulation was later replaced by a new

system known as the Malayan Revised Triangulation 1948 (MRT48).

This was subsequently followed by a lengthy process of additional

measurements and re-computation until 1968, which eventually

resulted in a system referred to as MRT68.

2.1.5 The MRT68 network consists of 77 geodetic, 240 primary, 837

secondary and 51 tertiary stations. It is based on conventional

observations with many of the triangulation points dated as far back

as 1885. The MRT68 has been adopted as a result of the re-

computations of the earlier network together with the Primary or

Repsold Triangulation (Figure 1) carried out between 1913 and 1916.

The reference ellipsoid used for MRT68 is in Table 1 below. The map

projection used for mapping in Peninsular Malaysia is Rectified Skew

Orthomorphic (RSO) and Cassini Soldner for cadastral surveying.

Table 2 tabulates the parameters for map projection used in

Peninsular Malaysia.

4

Table 1 Reference Ellipsoids for MRT68 and BT68

No. Parameter MRT68 BT68

1. Reference Ellipsoid Modified Everest Modified Everest

2. Origin Kertau, Pahang Timbalai, Labuan

3. Semi-major axis ( a ) 6 377 304.063 6 377 298.556

4. Semi-Minor Axis ( b ) 6 356 103.039 6 356 097.550

5. Flattening ( f ) 1/300.8017 1/300.8017

G001

G003

G004

G005

G007

G008

G009

G010

G011

G012

G013

G015

G016

G017

G018

G019

G020

G021

G022

G023

G024

G025

G026

G027

G028G029

G030G031

G032G033

G034

G035

G036

G037

G038 G039

G040

G041

G042

G043

G044

G045

G046

G047

G048

G049

G050

G051

G052

G053

G054

G055

G056

G057

G058

G059

G060

G061

G062

G063

G064

G065

G066

G067

G068

G069

G070

G071

G072

G073

G074G075

G076

G077

99.50 100.00 100.50 101.00 101.50 102.00 102.50 103.00 103.50 104.00

Longitude

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

Latit

ude

G002

G014

G084

P4

P075

Figure 1: Malayan Revised Triangulation 1968 (MRT68)

5

2.2 BORNEO TRIANGULATION 1968 (BT68)

2.2.1 Sabah started its primary triangulation work in a project known as the

Borneo West Coast Triangulation between 1930 and 1942. In around

1935, Sarawak and Brunei also began their primary triangulation

projects.

2.2.2 The Directorate of Overseas Survey (DOS) undertook the task of

readjusting the whole primary triangulation of Borneo. The adjusted

results for the Primary Triangulation of Borneo 1948 were then

published in terms of Timbalai Datum and Modified Everest ellipsoid.

2.2.3 The East Coast Triangulation was later introduced and initiated by

DOS and observations were carried out in the year 1955 to 1960.

The aim of this triangulation was to extend the Primary Triangulation

of Borneo to the eastern side of Sabah. EDM traversings were also

carried out in 1961 to 1968 to supplement the work.

2.2.4 The combined geodetic networks in Sabah and Sarawak, known as

the Borneo Triangulation 1968 (BT68), was established with the

station at Bukit Timbalai (in the island of Labuan) as the origin. BT68

consequently resulted from the readjustment of the primary control of

East Malaysia (Sabah, Sarawak and Brunei) made by the DOS.

2.2.5 The BT68 network consists of the Borneo West Coast Triangulation

of Brunei and Sabah (1930-1942), Borneo East Coast Triangulation

of Sarawak and extension of the West Coast Triangulation in Sabah

(1955-1960) as well as some new points surveyed between 1961

and 1968. This geodetic network is shown in Figure 2 with the

reference ellipsoid used given in Table 1. The map projection

employed for mapping and cadastral surveys is RSO and Table 2

shows the various parameters used.

6

Table 2: Map Projections for Peninsular Malaysia, Sabah and Sarawak

110.0 111.0 112.0 113.0 114.0 115.0 116.0 117.0 118.0 119.0

Longitude

1.0

2.0

3.0

4.0

5.0

6.0

7.0

Latit

ude

INDONESIA

SABAH

SARAWAK

SOUTH CHINA SEA

Figure 2: Borneo Triangulation 1968 (BT68)

No. Parameter Peninsular Malaysia Sabah & Sarawak

1. Projection Name Malayan RSO Borneo RSO

2. Datum Kertau Timbalai

3. Conversion Factor

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

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

4. Origin of Projection N 4° 00’ , E 102° 15’ N 4° 00’ , E 115° 00’

5. Scale Factor (Origin) 0.99 984 0.99 984

7

3. GPS-BASED NETWORKS

3.1 PENINSULAR MALAYSIA GEODETIC SCIENTIFIC NETWORK 1994 (PMGSN94)

3.1.1 As stated earlier, old triangulation networks such as MRT68 and

BT68 are regional in nature and are thus not aligned with global

geocentric coordinate frames. On the other hand, earth-centered

geocentric system is difficult to define - not until the recent

development of space-based positioning systems. This was made

possible over the last decade or so because the space-based

positioning satellites revolve around the center of mass of the earth

and are therefore related to an earth-centered or geocentric datum.

3.1.2 The World Geodetic System of 1984 or WGS84 is one such system,

which is maintained by the United States Department of Defense for

GPS-based positioning. Another is the International Terrestrial

Reference Frame (ITRF) and it is reported to be compatible with

WGS84 at the centimeter level.

3.1.3 In an effort to harness the full prowess of the space-based

technology, JUPEM has established a GPS network of 238 stations

in Peninsular Malaysia, called the Peninsular Malaysia Geodetic

Scientific Network 1994 (PMGSN94), as in Figure 3. The main

objectives of setting up PMGSN94 are to establish a new geodetic

network based on GPS observations and to analyse the existing

geodetic network. The network has been observed using four

Ashtech LX II dual frequency GPS receivers and the acquired data

was processed and adjusted in 1994.

3.1.4 In the network adjustment, a minimally constrained adjustment was

made with Kertau, Pahang, held fixed. The coordinates of Kertau are

in approximate WGS84 and derived from Doppler coordinates of

NSWC 9Z-2 reference frame. The Ashtech GPS Post-Processing

8

Software (GPPS) with broadcast ephemeris was used for the

determination of the baseline solutions. The relative accuracy of the

network is between 1-2 ppm for the horizontal coordinates and

between 3-5 ppm for the vertical coordinates. The summary of the

results of the network adjustment using Geolab network adjustment

software is tabulated in Table 3.

DOP1

DOP2

DOP3

DOP4

DOP5

GP02

G003GP04

GP05GP06

GP07

GP08

GP09GP10

GP11 GP12 GP13

GP14

GP15GP16

GP17

GP18

GP19 GP20

GP21

GP22

GP23

GP24GP25

GP26 GP27GP28

GP29 GP30 GP31 GP32GP33

GP34GP35

GP36 GP37

GP38

GP39GP40

GP41 GP42

GP43

GP44

GP45

GP47

GP48

GP49GP50

GP51

GP52

GP53

GP54

GP55

GP56GP57

GP58

GP59

GP60

GP61

GP79

GP80

GP81

GP82

P083

GP84GP85

GP86

GP87GP88

GP89

GP90GP91

GP94

GP95

GP98

GP99

G100

J416

TD01

TG01

TG03

TG04

TG05

TG06

TG07

TG09

TG10

TG11

TG13

TG14

TG15

TG18

TG19

TG20

TG24TG25

TG26

TG27TG28

TG31

TG33

TG35

TG36

TG38

TG42

TG56

TG57TG58

TG59

TG61

T190

T200

T283

13DJ

149B

251.00

P101

P102

P105

P106

P107

P201

P202

P203

P204

P205

P207

P209

P210P211

P212

P213

P214

P215

P216P217

P218

P219

P220

P221

P222

P223

P224

P225

P226

P227

P228

P229

P230

P231

P232

P233

P234P235

P236P237

P238

P239

P240

P241

P242

P243

P244P245

P246

P247

P248

P249P250

P251P252

P253

P254

P255 P256

P257

P258

P259P260

P261

P263

P264

P265

P267

P268

P269

P270

P271P272

P273P274

P275

P276

P277

P278

P279

P280P281

P282

P283 P285 P286

P287

P288

P289P290

P291

P292

P293

P295

P296

P297

P298

P299

P304

P305

P306P307

P308P309

P310

P311

P313

P314

P351

P352

P500

P808P809

S136

S290

K350

M331

99.00 99.50 100.00 100.50 101.00 101.50 102.00 102.50 103.00 103.50 104.00 104.50 105.00

Longitude

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

7.00

Latit

ude

Figure 3: Peninsular Malaysia GPS Scientific Network 1994

(PMGSN94)

9

Table 3: Results of Minimally Constrained Adjustment for PMGSN94

Network Adjustment Software Used

Geolab Network Adjustment

Fixed Point in 3D Kertau, Pahang

Approximate Positions 237

Number of Parameters 711

No. of Observations 3594

Redundancy 2883

Weights Used σN = 5mm ± 0.5 ppm σE = 5mm ± 0.7 ppm σU = 7mm ± 1.1 ppm

Variance Factor Used 0.9952

Chi-Square Test Passed

Station Error Ellipses Hort: 0.038 – 0.094 Vert: 0.032 – 0.080

Relative Error Ellipses Hort: 0.013 – 0.031 Vert: 0.011 – 0.030

Average Baseline Accuracies Hort: < 1.5 ppm Vert: < 2.0 ppm

10

3.2 EAST MALAYSIA GEODETIC SCIENTIFIC NETWORK 1997 (EMGSN97)

3.2.1 Following the successful completion of PMGSN94 in Peninsular

Malaysia, JUPEM began making plans to establish a similar type of

GPS-derived geodetic network in Sabah and Sarawak. For this

purpose, GPS observations were made using Trimble 4000SSE

L1/L2 receivers to establish the East Malaysia Geodetic Scientific

Network 1997 (EMGSN97) that comprises a total of 171 GPS

stations as shown in Figure 4.

3.2.2 In the network adjustment, a constrained adjustment was made with

coordinates from the Special Technical Royal Engineer (STRE) GPS

campaign fixed. Broadcast ephemeris was used for the baseline

determinations. The relative accuracy of the network is found to be

better than 1 ppm for the horizontal coordinates and 2-3 ppm for the

vertical coordinates. The summary of the results of the network

adjustment using Geolab network adjustment software is tabulated in

Table 4.

110.00 111.00 112.00 113.00 114.00 115.00 116.00 117.00 118.00 119.00

Longitude

0.50

1.50

2.50

3.50

4.50

5.50

6.50

Latit

ude

T002

M510

T006

T004

T003

M511

M502

D001

T007

T008

T005

4122

5101

T001

D002

42428045

8047

4044

T010

T009

8048T012

8028

T013

3074

3032

3046

T014T016

T015

3021

T020T019

3010

T021

6008

4127

4114

4118

2200

2011

T022

2038T029

9900

T030

T031

T026

R027

T0252005

T018

T017

6047

T045

708570866052

J01

70847082

7083

D003

T038

T037

7080

T039

4119T043

4120T042

T041

T0407079

2015

T032

1009

T034

T036

T035

1019

M501T004

M502

T101

T102

M503

M505

M504

T103

M507

M506M508

M402M403

M404

M405M509

M401

M407

M408

T114

M406

D004

M413

M412

M414M415

T108

M409

T106M410

M411

T107

T109

M416

M316

M417

M317

M315

M314

M418

T128

M313

M306T127

M419M422

M421

M420

M305

M307 M312

M311M310

T125

M304

M303

M302

M105

T124

M424

M423

T113T116

M104

M202

M301

M201

M203

T122A102

T123

T121D006

M204

T120

D005

T118

T119

T117

M102

T110

T112

M103

A101

T115M101

T111T100

T104

T105

Figure 4: East Malaysia Geodetic Scientific Network 1997 (EMSGN97)

11

Table 4: Results of Constrained Adjustment for EMGSN97

Network Adjustment Software Used

Geolab Network Adjustment

Fixed Points in 3D Five (5) Stations from STRE GPS Campaign

Approximate Positions 166

Number of Parameters 498

No. of Observations 1218

Redundancy 720

Weights used σN = 2mm ± 0.2 ppm σE = 2mm ± 0.2 ppm σU = 2.5mm ± 0.5 ppm

Variance Factor Used 0.9600

Chi-Square Test Passed

Station Error Ellipses Hort: 0.009 – 0.044 Vert: 0.010 – 0.055

Relative Error Ellipses Hort: 0.007 – 0.040 Vert: 0.008 – 0.052

Average Baseline Accuracies Hort: 0.6 ppm Vert: 0.8 ppm

12

4. GEOCENTRIC DATUM OF MALAYSIA (GDM2000)

4.1 INTRODUCTION 4.1.1 The Geocentric Datum of Malaysia or GDM2000 is the new national

geodetic datum for Malaysia and it replaces the old datum of MRT48

and BT68. It was officially launched nationwide on 26 August 2003.

4.1.2 The development of GDM2000 began firstly by the establishment of

the zero-order network of permanent GPS stations known as the

Malaysia Active GPS System (MASS). This was followed by the

establishment of the Malaysia Primary Geodetic Network 2000 or

MPGN2000 by strengthening the PMGSN94 and EMGSN97

networks via a GPS observation campaign performed at selected

stations to form a connection to the MASS network. Subsequently,

the MASS network is replaced by another network of active GNSS

stations known as the Malaysia Real-Time Kinematic GNSS Network

or MyRTKnet.

4.2 MALAYSIA ACTIVE GPS NETWORK (MASS)

4.2.1 Malaysia Active GPS Network or MASS is a permanent network of

active GPS stations that was established in 1999 and formed a

homogeneous and coherent geodetic infrastructure, covering the

whole of Malaysia. The MASS station’s GPS data were used along

with those from the International GNSS Service (IGS) stations for the

realization of the zero-order geodetic network for Malaysia.

4.2.2 GPS data from seventeen (17) MASS stations (Figure 5) and eleven

(11) IGS stations (Figure 6) from 1999 to 2002 have been processed

to establish the zero-order geodetic network. The eleven (11)

permanent GPS tracking stations of the IGS world-wide network in

ITRF2000 Epoch 1997 were used as fiducial points in the processing

to obtain the MASS set of station coordinates.

13

GUAM

SHAO

WUHNKUNM

PIMO

BAKO

LHAS

IISC

COCOKARR

NTUSGUAM

SHAO

WUHNKUNM

PIMO

BAKO

LHAS

IISC

COCOKARR

NTUS

98 100 102 104 106 108 110 112 114 116 118 120

Longitude

0

2

4

6

8La

titud

e

Kuch

KinaLabu

Bint

Miri

Sand

Tawa

Arau Geti

Kual

Utmj

KuanKtpk

Ipoh

Usmp

Sega

Figure 5: Distribution of MASS stations

Figure 6: IGS stations used to derive MASS coordinates in ITRF2000

Sibu

14

4.2.3 The reference IGS station coordinates which are in ITRF2000 at

epoch 1997.0 were transformed to the same epoch as the adjusted

MASS station coordinates, i.e. ITRF 2000 at epoch 2000.00. From

the free network adjustment, the resulting accuracy of the MASS

stations with respect to the ITRF2000 reference frame at epoch

2000.0 is between 9 to 15 mm in the horizontal component and

between 12 to 19 mm in vertical component.

4.2.4 In the heavily constrained adjustment, a specific reference frame in

ITRF2000 was adopted and results indicated that the accuracy of

station coordinates is between 3 to 16 mm in the horizontal

component and between 8 to 13 mm for the vertical component.

Thus, the coordinates of the heavily constrained adjustment was

adopted as the final coordinates in ITRF2000 at epoch 2 January

2000. These new set of coordinates are known as the Geocentric

Datum of Malaysia or GDM2000 and was officially adopted on

26 August 2003.

4.3 MALAYSIAN PRIMARY GEODETIC NETWORK 2000 (MPGN2000)

4.3.1 Following the availability of MASS network in GDM2000 coordinates,

JUPEM carried out further efforts to transform the PMGSN94 and

EMGSN97 networks into the newly adopted datum. Both networks

formed the new Malaysia Primary Geodetic Network 2000

(MPGN2000) and were strengthened by connecting them to the

MASS network. This was achieved by carrying out GPS campaigns

to re-observe thirty-six (36) stations of PMGSN94 in 2000 and thirty

(30) stations of EMGSN in 2002 for a period of 48 hours to form the

strengthening network (Figures 7 and 8). The outcome defines a

new Malaysia Primary Geodetic Network 2000 (MPGN2000) for the

whole of Malaysia (Figure 9) based on the GDM2000 reference

frame.

15

4.3.2 Heavily constrained adjustment with MASS stations held fixed was

made to adjust the observed baseline vectors and obtain the link

station’s coordinates, which conform to GDM2000. The accuracy of

stations in horizontal and vertical components is less than 14 mm.

The adjustment of the MPGN2000 using the old vectors has

eventually achieved the primary target of obtaining 3 cm accuracy

station coordinate, referred to the ITRF2000 Epoch 1 Jan 2000.

99.50 100.00 100.50 101.00 101.50 102.00 102.50 103.00 103.50 104.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

GP50

GP58

GP84

GP18

GP24

P102

P281

P310

P247

GP36

P219

P258

P221

P238

P229

GP32

P290

P298

P299

GP02

P213

GP47

GP43

GP52

GP37

GP21

P297

P244

P263P274

P255

GP28

GP06

M331

GP98

GP54

KUAL

GETI

KUAN

UTMJ

ARAU

USMP

IPOH

KTPK

Mass Station

Main Station

Check Station

Figure 7: Link Stations Distribution in Peninsular Malaysia

16

109.00 110.00 111.00 112.00 113.00 114.00 115.00 116.00 117.00 118.00 119.00 120.00

Longitude

1.00

2.00

3.00

4.00

5.00

6.00

7.00

Latit

ude

T 004M503

T112M302

M111

4119

4114

T008

T006

T001

M309

D006

D005

M305

M202

3046

7083

T041

7080

4242

M509

M416

M424

M405 M410

9900

70861009

2011

T021Kuch

Kina

Labu

Bint

Miri

Sand

Tawa

Main Station

Check Station

MASS Station

Figure 8: Link Stations Distribution in East Malaysia

100 102 104 106 108 110 112 114 116 118 120

Longitude

2

4

6

Latit

ude

Figure 9: MPGN2000 Stations in Peninsular Malaysia, Sabah & Sarawak

17

4.4 MALAYSIA REAL-TIME KINEMATIC GNSS NETWORK (MyRTKnet)

4.4.1 Beginning 2002, JUPEM has established a network known as the

Malaysia Real-Time Kinematic GNSS Network or MyRTKnet that

uses a new generation of RTK solution known as Virtual Reference

Station (VRS). MyRTKnet is based on a network of GPS reference

stations continuously connected via tele-communication network to

the control centre, situated at JUPEM headquarters in Kuala Lumpur

(Figures 11 and 12).

4.4.2 By the end of 2008, Malaysia has seventy-eight (78) RTK reference

stations for the network with fifty (50) stations covering the whole

Peninsular Malaysia, apart from fourteen (14) stations each covering

Sabah and Sarawak. The spacing between stations ranges from 30

to 100 km. Each station is equipped with either a Trimble 5700 or a

NetR5 GPS receiver, antenna, power supply and modem to

communicate with the central facility via Internet Protocol Virtual

Private Network (IPVPN) communication infrastructure.

4.4.3 The central facility at JUPEM headquarters in Kuala Lumpur

continuously gathers the information from GPS receivers at all

MyRTKnet stations and creates a living database of regional area

corrections. With MyRTKnet, a virtual reference station will be

established for any single roving GPS user near the survey area. It

also models the spatial errors that limit GPS accuracy through a

network solution and in turn generates corrections for the roving GPS

users to be positioned anywhere inside the network with an accuracy

better than a few centimetres to a few decimetres in real-time. A web

site is also available to enable downloading of GPS data for post-

processing solutions.

18

99.00 99.50 100.00 100.50 101.00 101.50 102.00 102.50 103.00 103.50 104.00 104.50 105.00

Longitude

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

7.00

Latit

ude

ARAU

BABH

BANT

BEHR

GETI

GMUS

GRIK

JHJY

JUML

KLAW

KUAL

KUKP

LGKW

MERS

MERU

PEKN

PUPK

SGPT

TGPG

TLOH

UPMS

USMP

UUMK

AYER

BAHA

BENT

CAME

CENE

GAJA

JRNT

KRAI

KROM

LASA

LIPI

MUAD

MUKH

PASP

PDIC

PRTS

PUSI

SBKB

SEG1

SETI

SIK1

SPGR

SRIJ

TERI

TGRH

TLKI

TOKA

Figure 11: MyRTKnet Stations in Peninsular Malaysia

109.00 110.00 111.00 112.00 113.00 114.00 115.00 116.00 117.00 118.00 119.00 120.00

Longitude

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

Latit

ude

MRDUBELU

RANA

TMBNKENIBEAU

TENM DATU

SEMA

SEMP

TEBE

SERAKAPI

BELA

NIAHMRDI

LAWS

AMAN

KUDA

UMSS

UMAS

SAND

TAWA

LAB1

SIB1

MIRI

BIN1

MUKH

Figure 12: MyRTKnet Stations in East Malaysia

19

5. REVISION OF GDM2000

5.1 MAJOR SUMATRAN EARTHQUAKES IN 2004, 2005 AND 2007

5.1.1 On 26 December 2004, 28 March 2005 and 12 September 2007,

three major earthquakes occurred in Sumatra, Indonesia with

magnitude 9.2, 8.7 and 7.9 on the Richter scale respectively. When

these natural catastrophes occurred, three types of motions were

generated:

a) Pre-seismic motion: earth movement before the earthquake.

b) Co-seismic motion: earth movement at the time of

earthquake.

c) Post-seismic motion: earth movement after the earthquake.

5.1.2 The earlier two aforementioned earthquakes have generated motions

and caused significant displacements to the geodetic infrastructures

in Malaysia which need to be modelled. The post-seismic motion is

the most difficult to model and the task can only be made after the

velocity and the rotating pole of the motion have been determined.

5.1.3 The co-seismic motion was deduced by comparing the coordinates of

MyRTKnet stations computed using GPS data during the first week

before the earthquake with those during the second week after the

event. Results indicate that the displacement of MyRTKnet stations

due to the co-seismic motion from the 2004 earthquake in Sumatra

was between 1.5 to 17 cm, occurring predominantly in the south-west

direction. Similarly, the results from 2005 and 2007 earthquakes

indicate displacements of between 1.0 to 6.5 cm and

1.0 to 3 cm respectively, also in the south-west direction.

5.1.4 Figures 13, 14 and 15 show the displacements of MyRTKnet stations

associated with the co-seismic motions from the 26 December 2004,

28 March 2005 and 12 September 2007 Sumatran earthquakes

respectively.

20

Figure 13: Co-seismic motion during the 26 December 2004 earthquake

Figure 14: Co-seismic motion during the 28 March 2005 earthquake

21

Figure 15: Co-seismic motion during the 12 September 2007 earthquake

5.1.5 Consecutively, the rate of the post-seismic motion was also deduced.

This was carried out by comparing the GDM2000 coordinates of

MyRTKnet stations with those computed after the 2005 earthquake

using GPS data from April to December 2005. Results indicate that

the MyRTKnet stations had experienced post-seismic motion from

the two earlier Sumatran earthquakes and moving at a rate of about

8 cm/year in the south-west direction.

5.1.6 Further computation of MyRTKnet station coordinates for the years

2006, 2007, 2008 and 2009 show that their displacement vectors

from the post-seismic motions continuously demonstrate an anti-

clockwise rotation, thus indicating a possible return to the effect of

tectonic plate motion. These yearly post-seismic motions for the

years 2006 to 2008 are illustrated in Figures 16, 17 and 18.

22

Figure 16: Post-seismic motion in 2006

Figure 17: Post-seismic motion in 2007 (January to August)

23

Figure 18: Post-seismic motion in 2008

5.1.7 The accumulated displacement of MyRTKnet stations from

26 December 2004 until 30 April 2009 is shown in Figure 19. In

carrying out data adjustments, the GDM2000 coordinates of

MyRTKnet stations in Sabah and Sarawak were held fixed, as the

displacement of the coordinates in Sabah and Sarawak were found

to be very minimal.

5.1.8 From the magnitude of the displacements, which range from 1.0 to

25.8 cm, it can be concluded that the resultant displacement of

MyRTKnet stations, as a result of the co-seismic and post-seismic

motions associated with the 2004, 2005 and 2007 Sumatran

earthquakes, were significant. Consequently, their GDM2000

coordinates cannot be further utilised for high precision survey and

that they need to be revised.

24

Figure 19: Accumulated displacement of MyRTKnet stations from

26 December 2004 to 30 April 2009

5.2 MyRTKnet IN GDM2000 (2009)

5.2.1 GPS data from seventy-eight (78) MyRTKnet stations and fifty-six

(56) IGS stations in ITRF2005 from 1 January 2006 to 30 April 2009

as well as GPS data from an observation campaign conducted in

January 2009 on three (3) MASS stations (KUCH, BINT and KINA)

were used in the data processing to re-establish the zero order

geodetic network. However, in the case of Sabah and Sarawak, only

thirty-three (33) IGS stations were used as fiducial points in the

processing to obtain the MyRTKnet set of station coordinates. These

IGS stations which are in ITRF2005 at epoch 2007.67 were then

brought to ITRF2000 at epoch 2000.00 using published velocity

models.

5.2.2 Subsequently, the combined adjustment for the aforementioned data

was fixed at epoch 1 January 2000 and the resulting coordinates

named as GDM2000 (2009). Comparison with the original GDM2000

coordinates was then carried out using three parameter Helmert

25

transformation process and results indicate that the RMS fitting for

the coordinates of four (4) reference stations (KUCH, BINT, KINA

and MIRI) were less than one (1) cm in the north and east as well as

in the height components. Other stations saw large displacements

which were possibly caused by the earthquakes or seasonal

environmental effects.

5.2.3 The final combined adjustment, involving MyRTKnet and MASS

stations only, used the 2009 data and employed the original

GDM2000 reference frame as the reference by holding the

coordinates of the four (4) aforementioned reference stations fixed.

With this adjustment, the resulting coordinates of the MyRTKnet

stations were obtained and are labelled as GDM2000 (2009).

5.3 MPGN2000 IN GDM2000 (2009)

5.3.1 Apart from producing MyRTKnet stations in GDM2000 (2009)

coordinates, similar efforts were also made for the MPGN2000

stations. In order to establish MPGN2000 with GDM2000 (2009)

coordinates, it is necessary to firstly ascertain the thirty-six (36) link

stations between PMGSN94 and MASS (refer to Section 4.3.1) in

GDM2000 (2009). This approach requires adjustment to be

performed using the October to November 2000 GPS vectors of

those link stations and ten (10) MASS stations, by fixing them to the

GDM2000 (2009) coordinates of the MASS stations. With the link

stations in GDM2000 (2009), the next step taken is to perform the

adjustment using the GPS vectors of the remaining PMGSN94

stations. Similar process is carried out for EMGSN97 using thirty (30)

link stations (refer to Section 4.3.2).

5.3.2 Results indicate that the coordinate displacement of the MPGN2000

network in Peninsular Malaysia is not linear and displays elastic

properties. In addition, the displacements also differ from one station

to another. Thus, any type of modelling of the actual displacement

26

needs a long period of monitoring in order to produce precise

parameters. As an alternative, a multiple regression model was

subsequently produced to provide a relationship between the

MPGN2000 in GDM2000 and MPGN2000 in GDM2000 (2009). In

order to validate the accuracy of the multiple regression model, GPS

observations were carried out at selected MPGN2000 stations and

results showed that the coordinates of MPGN2000 in GDM2000

(2009) stations are at cm-level accuracy.

6. CONCLUSION

6.1 JUPEM has successfully established both active and passive GNSS

networks to replace the old triangulation networks in Malaysia. These

new networks will facilitate the development and enhancement of

various surveying and mapping activities and meet the requirements of

all types of users, ranging from the novice to the scientists.

6.2 The GDM2000 supersedes the classical geodetic datums in Malaysia

and has been established with respect to a geocentric reference frame

defined in ITRF system at ITRF2000 epoch 2 January 2000 at an

accuracy of 1 cm. On the other hand, with the reference frame and

epoch maintained, the new GDM2000 (2009) coordinates have taken

into account the displacements and movements resulting from the

Sumatran earthquakes in 2004, 2005 and 2007. This new

GDM2000 (2009) would be continuously maintained and managed

through the use of MyRTKnet permanent tracking stations to ensure

the availability of a highly accurate, homogeneous and up-to-date

datum for Malaysia.

27

REFERENCES Abu et al. (1998), Towards the Next Millienium: Current Status, Preliminary

Results and Applications of Malayssian Active GPS System), Paper presented

at the Directors of Surveys Conference, Kuala Lumpur, October 8-9.

Abu, S. (2002), Determination of Malaysian Geodetic GPS Network in the

ITRF2000, Universiti Teknologi Malaysia

Abu, S & Mohamed, A.B. (1997), Sea Level Monitoring System (Proposed

Malaysian Active Control System), Paper presented at the Departmental

Management Meeting, Riviera Bay Resort, Melaka, July 21-22.

Altamimi, Z., P. Sillard, and C. Boucher (2002), ITRF2000: A new release of the

International Terrestrial Reference Frame for earth science application, J.

Geophys. Res., 107(B10), 2214,doi:10.1029/2001 JB000561.

Bitwise Ideas Inc. (1998), Geolab 3.9 Reference Manual, 89 Auriga Drive

Nepean, Ontario Canada

Bowring, B.R. (1985), The accuracy of geodetic latitude and height equations,

Survey Review 28(218): 202-206.

Burford, B.J. (1985), A further examination of datum transformation parameters

in Australia The Australian Surveyor, vol.32 no. 7, pp. 536-558.

Bursa, M. (1962), The theory of the determination of the non-parallelism of the

minor axis of the reference ellipsoid and the inertial polar axis of the Earth, and

the planes of the initial astronomic and geodetic meridians from observations of

artificial Earth Satellites, Studia Geophysica et Geodetica, no. 6, pp. 209-214.

Defence Mapping Agency (DMA), (1987), Department of defence World

Geodetic System 1984: its definition and relationship with local geodetic

28

systems (second edition). Technical report no. 8350.2, Defence Mapping

Agency, Washington.

Department of Survey and Mapping Malaysia, 2000, Malaysia Reference

Frame System: Current Study and GDM2000 Revision (Sistem Kerangka

Rujukan: Kajian Semasa dan Semakan GDM2000).

Department of Survey and Mapping Malaysia, 2007, Malaysia Reference

Frame System: Current Study and GDM2000 Revision (Sistem Kerangka

Rujukan: Kajian Semasa dan Semakan GDM2000).

Directorate of Colonial Surveys, 1948, Primary Triangulation of Borneo

Directorate of Colonial Surveys, 1968, Report on the Adjustment of the Primary

Control in East Malaysia and Brunei

Heiskanen and Moritz (1967), Physical Geodesy, W. H Freeman and

Company, San Francisco, USA.

Hamid Ali, Ahmad Fauzi Nordin, Samad Abu, Chang Leng Hua (2006),

MyRTKnet: Get Set and Go, Coordinates, Issues 6, 6-13

Hugentobler, U., Schaer, S., and Fridez, P. (2001), Bernese GPS Processing

Software Version 4.2, Astronomical Institute University of Berne, Switzerland.

Jamil, H et al (2002), Geocentric Datum of Malaysia, 4th Malaysia Survey

Congress, Subang aya, June 13-14.

Krakiwsky, E.J. and Thomson, D.B. (1974), Mathematical models for the

combination of terrestrial and satellite networks, the Canadian Surveyor, vol.

28, no. 5, pp. 606-615.

Richardus, Peter, and Adler, R. K., (1974), Map Pprojetions for Geodesists,

Cartographers and Geographers: Amsterdam, North-Holland Pub. Co.

29

Rothacher, M., and Mervart, L. (1996), Bernese GPS Processing Software

Version 4.0, Astronomical Institute University of Berne, Switzerland.

Shahabuddin (1978), Msc Thesis, University of Oxford, United Kingdom.

Simons W. J. F., A. Socquet, C. Vigny, B. A. C. Ambrosius, S. Haji Abu,

Chaiwat Promthong, C. Subarya, D. A. Sarsito, S. Matheussen, P. Morgan, and

W. Spakman (2007), A decade of GPS in Southeast Asia: Resolving

Sundaland motion and boundaries, J. Geophys. Res., 112, B06420,

doi:10.1029/2005JB003868

Simons W.J.F., D.L.F. van Loon, A. Walpersdolf, B.A.C. Ambrosius, J. Kahar,

H.Z. Abidin, D.A. Sarsito, S.H. Abu, and P. Morgan (2000), Geodynamics of

S.E. Asia: Final Results of the Sulawesi 1998 GPS campaign, IAG: Geod.

Beyond 2000, 121 271-277

Snyder, J.P. (1984), Map projections used by the U.S. Geological Survey.

Geological Survey Bulletin 1532, U.S. Geological Survey.

Wolf, H. (1963), Geometric connection and re-orientation of three-dimensional

triangulation nets. Bulletin Geodesique. No, 68, pp165-169.