Taiwan 衛星定位系統 GPS and 座標轉換 TWD67, TWD97, WGS84 coordinate transformations

ENGLISH ONLY auto-stripped version of
中英版 Chinese+English version.

本頁不應由老化糊塗外行之我維護。 This page should not be maintained by aging confused amateur me.

現代台灣地圖只能出現下列座標： Modern Taiwan maps will only have the following coordinates, if any:

TWD67
1. 經緯度 longitude/latitude
2. 二度分帶 2-degree transverse Mercator
TWD97/WGS84
1. 經緯度 longitude/latitude
2. 二度分帶 2-degree transverse Mercator

上河文化：座標系統與二度分帶座標

How can I tell if a map is 怎判斷某圖為 TWD67 vs. TWD97?

TWD67 例 examples:

台北市復興南路為 Taibei City's Fuxing S. Rd. lies upon 304000m E.
國道一號新竹公道五交流道為 Expressway 1's Gongdaowu interchange lies upon 121.00 deg. E. == 250000m E.
豐原火車站前為 221000m E. lies in front of Fengyuan railway station.

若以上偏約 If the above are off by about 828 meters 公尺，該圖則 then the map is TWD97.

混淆ＴＷＤ６７，ＴＷＤ９７易耽誤救援 TWD67, TWD97 confusion can delay rescues

If you mix up TWD67 and TWD97, your results could be off by a kilometer -- dangerous [Chinese].

我們來請教洪本善老師ＴＷＤ６７，ＴＷＤ９７，ＷＧＳ８４。它們若弄錯，測的結果可能差一公里，會釀成新聞如：

總統限航區座標烏龍事件，錯用舊座標系統！民航局將公告正確位置（２００３．７．１５）

甚至有危險。那末，今日除了東經、北緯外，必加個ＴＷＤ６７或ＴＷＤ９７始有意義。 So, these days, beside longitude and latitude, one must also mention "TWD67" or "TWD97" for the data point to be useful. 一個負責任的地圖出版社應同時載ＴＷＤ６７及ＴＷＤ９７才對。建議如公里方格前者用黑，後者用籃，而兩者之經緯度於邊遠用短線。一看 TWD97 是用籃方格，或至少邊緣短線。 A responsible map publisher should print both grids...

２００３。８。２６朋友寄給我：

建議你新增一個網頁詳細介紹目前台灣地區ＴＷＤ６７╱ＴＭ２及經緯度，ＴＷＤ９７╱ＴＭ２及經緯度，ＷＧＳ８４╱經緯度的使用現況，釐清許多人對此的錯誤觀念，同時我也與消防署詢問搜救地點坐標通報的規範時，對方告知只要求以經緯度通報，但是沒有要求是以ＷＧＳ８４為ｄａｔｕｍ，追問下竟然他們根本不知道原來還有ＴＷＤ６７，ＴＷＤ９７，ＷＧＳ８４的差別，我就舉上次三貂角雷達為例，他們才恍然大悟，我給了Ｇａｒｍｉｎ何經理電話請他們聯絡，因此你真的必須要建立此一網頁，如果最高搜救機關都沒有規定通報規則（最好以ＷＧＳ８４為ｄａｔｕｍ的經緯度），更何況下屬警察機關，搜救單位（民間或是消防隊），以及對登山人員的宣導，徒增搜救成本。對了何經理提到ＴＷＤ９７╱ＴＭ２及經緯度已經使用於新出版的航照圖，只是不知道何時民間登山常用的經建版１╱２５０００及１╱５００００地形圖會改變ｄａｔｕｍ，或許你也可以以此向相關單位詢問未來推廣ＴＷＤ６７改為ＴＷＤ９７的轉變時程，因為這對全台灣的坐標通報實在有很大的影響，相信你是此中專家，一定知道相關影響層面。
因少出們，我只能猜國內三分之一的人已用ＷＧＳ８４╱ＴＷＤ９７。大約需經某難發生，單位們才懂得三種ｄａｔｕｍ之別。反正，今日光報個ｘ，ｙ不夠，必須加註用的是哪個基準（ｄａｔｕｍ）才安全。

2007/3 總而言之，救難者應尋三處 To sum it up, rescuers should check three places:

他報的是 They report	我拿的圖是 Our map is	我應查 We should check
WGS84	WGS84	原報的 original X,Y
WGS84	TWD67	X-828m, Y+207m
TWD67	WGS84	X+828m, Y-207m
TWD67	TWD67	原報的 original X,Y

正如病人說他是ＡＢ血型，仍必測試始能輸血，無法確定報的人搞清什麼ＷＧＳ８４╱ＴＷＤ６７，又支派的人員圖堆亦然搞不清，故建議直昇機飛上述三處，成西北西東南東狀，過程中指揮中心千萬不要替人家轉換座標，以免混淆極增。註：本人無實際救難經驗，以上屬猜測理論。

Recommendation to rescuers: just like medical workers still will test the patient's blood type before giving them a transfusion even though they insist they are type AB etc., we shouldn't trust the reporting public's vague notions of datums, if any. Nor should we trust various rescue teams with piles or PDAs of various maps. Therefore the helicopter should check in the above three places, which form a west-northwest - east-southeast line. During the process the coordination center should not "help" anybody by converting the original reported coordinates, lest confusion increase exponentially. Note however that I have no rescue experience and the above is all a guess as to how things should operate.

Basic facts for both TWD67 and TWD97

Latitude origin	0 degrees
Central meridian	121 degrees E
Scale factor	0.9999
False easting	250000 m
False northing	0 m

They are both 2 degree wide transverse Mercator projections. They differ in their ellipse.

有沒有所謂的原點 Is there an origin (0,0)?

至赤道與東經１２１度，頭再往西，往前２５０公里。此時已離地面相當高。此點好像是原點。

Go to the junction of the equator and 121 degrees east longitude, then point one's head west and go straight 250 km. When one stops one will be considerably above the earth's surface. I'm pretty sure that is the "origin".

ＴＭ２兩個緯度Ｅ、Ｎ，是不是往正北方，Ｎ就會增加；往正東方，Ｅ就會增加？ If I go due east or north, will that increase TM2's E and N values?

不完全一致。拿地圖仔細看，唯一ＴＭ方格線與經、緯線完全平行就是２５０ｋｍＥ即東經１２１度那條，其他有多少歪斜。

Not exactly. Take a good look at a map. The only place where the longitude and latitude grid lines are parallel to the TM2 grid lines is 250 km E., i.e., 121 east longitude, that single line. All other lines are more or less askew.

座標轉換 Coordinate Transformation

經緯度與二度橫麥卡脫投影之間 Between latitude/longitude and 2-degree transverse Mercator projection

proj is free software:

GNU/Linux example, 東郡大山 Dongjundashan TWD67: given x and y, compute longitude and latitude (and store them in variable LL):
$ LL=$(echo 258566.571 2613894.788 |
proj -I +proj=tmerc +ellps=aust_SA +lon_0=121 +x_0=250000 +k=0.9999)
$ echo $LL
121d5'2.255"E 23d37'42.655"N
Now convert back to x and y:
$ echo $LL |
proj +proj=tmerc +ellps=aust_SA +lon_0=121 +x_0=250000 +k=0.9999
258566.57 2613894.80
(If we were using TWD97 instead of TWD67, we would instead use:)

$ proj +proj=tmerc +ellps=GRS80 +lon_0=121 +x_0=250000 +k=0.9999

The ellipses we use can be seen with "proj -le":
For TWD97 use 用:

GRS80 a=6378137.0 rf=298.257222101 GRS 1980(IUGG 1980)
For TWD67 用:

Use:
aust_SA a=6378160.0 rf=298.25 Australian Natl & S.Amer. 1969

不要用 DON'T use:
GRS67 a=6378160.0 rf=298.2471674270 GRS 67 (IUGG 1967)

I.e. the TWD67 spheroid is NOT the International 1967. 名字會亂，參數才算。 Names get confused; parameters are what count.
Q: the HTZ (Hu Tzu Shan) datum predefined in ArcInfo/ArcGIS is set to Int/Hayford 1909. Have ESRI (Arc perpetrators) made a mistake?
A: Try the aust_SA parameters instead. 「虎子山」此名充滿了危機，定義已多。只能談其ａ＝、ｆ＝。 The name "Hu-tzu-shan" is full of danger, as it has accrued several definitions. One must instead talk in terms of a=, f=.

/usr/share/proj/epsg has a
# Hu Tzu Shan
<4236> +proj=longlat +ellps=intl +towgs84=-637,-549,-203,0,0,0,0 +no_defs  <>
which is suspect too. 頗質疑。

另參 Also see perl module Geography::NationalGrid::TW.

Q: 是否可以提供經緯度轉二度ＴＭ座標公式？ Where can I see the formula for latitude longitude to TM conversion?: A: 那麼，既然是自有軟體，也許看 Well, since it is Free Software, perhaps see the source code to proj 的原始碼? Also note freegis.org .

GPSFUN 有如下之比較 has a comparison like:

大地基準 Datum	參考橢球 Reference spheroid	長半徑 major axis "a"	扁率 flattening "f"
see note 註*	see note 註*	6378388	1/297
TWD67	GRS67	6378160	1/298.25
TWD97	GRS80	6378137	1/298.257222101
WGS84	WGS84	6378137	1/298.257223563

*註解 note: the names 所謂 "hu-tzu-shan", and even 甚至 "International 19xx", 此兩名字經多年已累積多重定義 have been given many definitions here in Taiwan, so are dangerous to use. One must speak in terms of 故用之危險，只好直接講 a, f !

甚至 "hu-tzu-shan" 有時 sometimes even means 拿來稱 TWD67.

台灣經緯度及二度ＴＭ座標轉換 Online TM to lat/long transformation (for TWD67 to TWD67, TWD97 to TWD97 will be off by .0001 degree), 但無原始碼，無千分之一度之下數字，無清楚網站名。 [Chinese] but no source code, no decimals below 0.0001 degrees, no clear website name.

TWD97 vs. WGS84

TWD97 is very close to 幾乎等於 WGS84, at least where I live,

$ a="120d51'58.2\"E 24d10'54.2\"N"; echo $a #(just see what it looks like)

120d51'58.2"E 24d10'54.2"N

$ echo $a | proj +proj=tmerc +ellps=GRS80 +lon_0=121 +x_0=250000 +k=0.9999 -f %.5f

236402.76293 2675155.08596

$ echo $a | proj +proj=tmerc +ellps=WGS84 +lon_0=121 +x_0=250000 +k=0.9999 -f %.5f

236402.76293 2675155.08604

$ echo 2675155.08604 - 2675155.08596 | bc

.00008

Zones

+lon_0=125 # Chiwei Is. 赤尾島
+lon_0=123 # Diaoyutai, Pengjia Is... 釣魚台、彭佳嶼
+lon_0=121 # Taiwan Island 台灣本島
+lon_0=119 # Penghu Is. 澎湖, Jinmen 金門
+lon_0=117 # Dongsha Is. 東沙群島
+lon_0=115 # Nansha Is. 南沙群島

gpsman author "M" == Miguel Filgueiras writes:

M> As far as I understand from your description these 2 degree zones centered from 115 to 125 will cover longitudes from 114 to 126. Does these cover all Taiwan territory?

yes, everything that Taiwan owns or still claims to own.

M> I also take it that these zones cover all the latitude range, that is, for each central meridian there is a single zone for all the possible latitudes in Taiwan.

Yes, and each has Y=0 at the equator, and X=250000 at the central meridian.

M> Another point: could you please confirm that the correct scale factor is k0=0.9999.

yes, that's right, 0.99990 And note that these 6 zones can be used with both the TWD67 or TWD97 datums.

I discovered many maps of Jinmen 金門, at least as late as the 1990's still use an older system:)

$ proj +proj=utm +ellps=intl +lon_0=117
# intl a=6378388.0 rf=297. International 1909 (Hayford)

TWD67 -- TWD97 轉換 transformation:徵碼：我們來寫個公開版 let's write a public version

每天很多人到敝站找答案，不知道有無一位願意寫開放原始碼程式給大家用？ (3/2008: 政府的封閉版本 Government's closed-source version: .PDFs, .ZIPs. 不理之而自己弄如下 Anyways, ignoring them we do it by hand:)

目前我只能全省以

x67 = x97 - 828 meters
y67 = y97 + 205 meters

臨時土法，含幾公尺誤差 This is the best I can do at present, for all of Taiwan, with its few meters of error. (828: 但下邊都 Odd, all the few formula I have below give approximately 841, 為什麼 why?)

另 Also john at thl.ncku.edu.tw 8/2003 捐的 contributed:

A = 0.00001549
B = 0.000006521
X67 = X97 - 807.8 - A * X97 - B * Y97
Y67 = Y97 + 248.6 - A * Y97 - B * X97
X97 = X67 + 807.8 + A * X67 + B * Y67
Y97 = Y67 - 248.6 + A * Y67 + B * X67
Perl implementation

「以四參數法（平移加旋轉因子）來統計，此算法比七參數法來得簡單！結果誤差應在２公尺內！」

2/2006: 今生 Now there is Perl Geography-NationalGrid-TW 那麼，也許解決本頁很多問題。 which perhaps solves many problems discussed by this page. 2007/10: xylonlat 採之為例 is an example program I wrote using it.

Minstrel made programs, 6/2004.

2007: note http://www.mobile01.com/topicdetail.php?f=130&t=374120

高程轉換 Vertical transformations

我不清楚６７╱９７的高程轉換法。 I'm not sure what the official Z axis transformation is for TWD67--TWD97.

轉換程式很少公開 Few open transformation programs

本來應該能夠由內政部地政司衛星測量中心取多些點做６７，９７比較，但因其成果供應要點：「…以公尺為單位，且其個位數值以零替代」，故休想。所謂「公」佈和「公」告ＴＷＤ９７的「公」字程度就這樣。

雖然ＴＷＤ６７與ＴＷＤ９７轉換程式都已經有人寫好，如林務局ＭＴＷＤＣＯＮ等等，但作者或單位不願意開放。另外，這多數是專為了微軟系統。故希望有一位懂得座標轉換的人，願意採自有軟體版權，寫個ＴＷＤ６７與ＴＷＤ９７轉換程式，原始碼也放網。說不定以後大家都用我們的。

There are various programs here in Taiwan to convert from TWD67 to TWD97, but their authors or organizations are not willing to release them. Also most are for Micro$oft. Therefore, I wish there would be someone who understands coordinate transformations to step forth and under the free software license write a TWD67 -- TWD97 transformation program and also put its source code on the web. Who knows, perhaps in the future everybody will use ours!

研究支援工具 Tools 可能只是 might only be for Windows.

From a 從人家送我的 fortran program I was given, I guess 我猜 proj's 的 cs2cs parameters might be 參數如

$ cs2cs +proj=tmerc +ellps=aust_SA \
+towgs84=-764.558,-361.229,-178.374,-.0000011698,\
.0000018398,.0000009822,.00002329 +lon_0=121 +x_0=250000 \
+k=0.9999 +to +proj=tmerc +datum=WGS84 +lon_0=121 +x_0=250000 +k=0.9999

The results and 所得與 transfer.for's are close 近: 即全島約 for the whole island around x: -841, y: 207, (z: varies a lot). 也許懂的人能幫忙做更好的。 Maybe someone who understands this could lend a hand.

某公司蒐集了各縣市平均值，但：

「因此檔案是屬公司的智慧財產，積多年經驗及智慧所得，所以不方便給您，請您諒解！」

Note that the above is a seven parameter transformation different than:

dx, dy, dx, da, df; Garmin GPS

Chatting with 與何明興 M.H. Ho of Taiwan Garmin, in 2000 年對話:

Q: I need dx,dy,dz,da,df for Taiwan Hu-tzu-shan datum (note: "Hu-tzu-shan datum" is Garmin's name for TWD67 故又一「虎子山」定義)

A: For GARMIN GPS:

dx: -767 m

dy: -358 m

dz: -176

da: -18.00

df: -0.00081204

[Note from Eino Uikkanen.]

Ｑ：Ｇａｒｍｉｎ牌ＧＰＳ，到２０００年為止的小問題是選ＴａｉｗａｎＧｒｉｄ時，它會顯示「Ｔ６７」但此與Ｈｕ－ｔｚｕ－ｓｈａｎｄａｔｕｍ才有關。若選ＷＧＳ８４ｄａｔｕｍ怎麼能還要顯示「Ｔ６７」呢？當然這不妨礙功能只是難看。 Q: Garmin's GPS units, at least to the year 2000, have the flaw that when we select "Taiwan Grid", the unit displays "T67". Note that that should be related to the "Hu-tzu-shan datum" [Garmin's name for TWD67]. How could one show a "67" when one selects WGS84? [The "67" has nothing to do with the grid. We use the same grid (X shifted 250000m etc.) for both TWD67 and WGS84 datums.] Of course we can still use the unit, it just looks bad.

Ａ：謝謝您的來信，確實若改成ＷＧＳ８４後，仍以Ｔ６７做為標題是比較容易讓人誤解，此問題會反應給公司，謝謝您！ A: Thanks for your letter. Indeed when one switches to WGS84, still showing T67 can create confusion. I will report this to our company. Thanks.

可能至今未改。難看又危險。 Perhaps Garmin still hasn't fixed this. Not only does it look bad, but it also creates danger on the trail.

2003.6.26 Cygnet said: 本來Ｇａｒｍｉｎ的ＧＰＳ都還標「Ｔ６７」，那是經積丹尼兄、小弟等屢次反應才改為「ＴＭ２」。 After bugging them about it so long, new Garmins now say "TM2".

故Ｇａｒｍｉｎ舊、新機種儀表面即 So, new Garmin models display:

Old/New		Grid
Old/New		Lat,Lon	TM-2
Datum	TWD67	N,E/N,E	T67/TM2
Datum	WGS84	N,E/N,E	T67/TM2

今不再用一個ｄａｔｕｍ的名字稱呼一個ｇｒｉｄ，但仍無法由此儀表面知到所選之ｄａｔｕｍ。 They no longer use the name of a datum for a grid. However one still can't tell what datum has been chosen from this display.

2004/3: Ｇａｒｍｉｎ長了一個新「ＴＡＩＷＡＮ」大地基準選項，好像只是略修其所謂Ｈｕ－Ｔｚｕ－Ｓｈａｎ基準，更貼近ＴＷＤ６７。 Garmin products now have an additional "TAIWAN" datum now along with their original so-called "Hu-tzu-shan" datum. Apparently this new "TAIWAN" datum is supposed to be just a minor correction to their so-called "Hu-tzu-shan" datum. The instruction books apparently say this "TAIWAN" means TWD67, which would be apparently correct. (Why doesn't Garmin just name it directly "TWD67"?)

便宜非正版 unofficial Garmin GPS 接頭 cheap connector [Taiwan]

Regarding DA, DF, DX, DY, DZ (but beware of any 但小心那兒的任何 1924 based Hu-tzu-shan datums listed there).

地籍座標 Cadastral coordiantes

若在地政事務所看到以六台尺為單位之老座標，就是所謂的地籍座標。

If in a land office you stumble upon an old grid that uses 20/11 meters per unit, that is the so called Cadastral coordinates.

轉換程式 Programs: cad2twd67

將ＴＭ或經緯度換成台灣地圖編號 Turn TM or longitude/latitude into Taiwan map numbers

$ echo 120.85788 24.18347|./longlat2taiwanmapno
#1> 120.85788 24.18347
9521-2-025 9521-2-09 9521-2-NW
$ echo 9521-2-025|./taiwanmapno2longlat
#1> 9521-2-025
120.850 24.175

問：台灣官方地圖的圖號的訂定，是以東經７３度３０分和北緯１４度為標準分幅線，每３０分＊３０分為一幅，即以台中區圖號９５２１為例，為距東經７３度３０分的第９５張圖及距北緯１４度第２１張圖，這個算法我明瞭。但不明瞭的是，為什麼訂出東經７３度３０分和北緯１４度為標準分幅線呢？我是猜想這分幅線是否為中國的邊疆？

積：看起來如此。

台灣三角點的座標 Taiwan Triangulation Points' Coordinates

台灣三角點ＴＷＤ６７座標表（TWD67 Taiwan Triangulation Points' Coordinates）

台灣地圖有趣的地方 Taiwan map curiosities

像片基本圖１：５０００版尾編號００１至１００以三位數與二位數的１：１００００版來區別；但本來若用００至９９好處多多：簡短又不造成右一排開頭數位不規則５１…５９、６０

Orthophotomaps are labeled from 1-100 instead of the more systematic 0-99. See Chinese version.

圓圈 Circles

我很好奇，台中僑光商專周圍有一個直徑一公里的圓形小馬路， Odd, on maps from the 1980's there is traces of a 1 km. diameter circular road centered at 中心點在 TWD67 213230 mE, 2676040 mN, (north of Fengjia Univ., Taizhong). 很多政府的圖看得到其北端，但快被都市計劃磨滅。那是什麼東西？國際上看到大規模圓形東西為核子加速器… Traces of an old cyclotron?

My friend guesses it might be a 朋友猜可能是個 high frequency direction finder, like the ones in 林口湖北村 Linkou, TWD67: 2776.5 km N 289 km E, used in cooperation with the USA in coordination with others in Asia to triangulate signals from China. However the diameter of the largest Linkou one is only 1/3 km.

大雅交流道偏移 Daya Interchange distortion

大雅交流道沒建在原中清路正上方，而另繞旁路，看地圖令我很好奇，不是只增加紅路燈？

Why isn't Taizhong's Daya Interchange on Zhongqing Rd. but instead on an extra side road? Looks so curious on a map. Doesn't that just increase the number of red lights? See Chinese version.

黃立夫說是原水湳機場跑道衝突。
網友ｅ０１６５則試算水湳機場跑道的限建範圍及高度：
1. 因交流道距跑道約９００米，所以限建高度＝９００∕５０＝１８米，以一般高速公路路堤高度約１０米以下，所以應該沒有影響（以機場跟高速公路地面同高估計）
2. 限建範圍是梯形，所以交流道往北移還是在限建範圍。
3. 所以我認為原中清路正上方建築物太多了，所以交流道往北移。

其他 Etc.

The finder of 24N 121E reassures me he was using WGS84 and not TWD67...

朋友２００３年８月寄來緊張的話：

今天收到民航局的每月通告，提到三貂角新近安裝啟用航路搜索雷達，ＷＧＳ８４經緯度是Ｎ２５度０分２７．５秒，Ｅ１２２度０分３．９秒，高度１２８．４公尺（４２１英尺），馬上查對上河文化的北島地圖發現居然這地點是在海裡面，再看看其他地圖發現政經版１╱２５０００地圖的，戶外生活〔方格而已〕的全部都是如此，因此判斷這應該是這些國內地圖都是使用ＴＷＤ６７所致，也就是全部都是以虎子山為基準算出來的。如果你要再確認，不妨用松山機場報道中心點位置（Ｎ２５度０４分１０秒，Ｅ１２１度３３分６秒）確認就知道了！！

更讓我訝異的是與ｘｘｘｘ聯繫時，技術人員告訴我ｙｙｙｙ。看來ｄａｔｕｍ與ｐｏｓｉｔｉｏｎｆｏｒｍａｔ讓許多人暈頭轉向了！！！如果用這地圖來判斷搜救地點（假設都用ＷＧＳ８４告知國家搜救中心），差距接近１公里，可有的找了！！

註：雷達位置應該是在萊萊山東方山麓才對。

另外， Working with Coordinates and Units 對於座標ｃｏｏｒｄｉｄａｔｅ及基準ｄａｔｕｍ有極清楚且簡單的說明，非常容易讓一般人理解。

２００６年９月：積丹尼：台灣軍方地圖使用座標格式應該是ＴＷＤ６７為基準，格式則是ＵＴＭ或是ＭＧＲＳ（尚待確認是哪一種！），提供你鍵入〔本頁〕作為補充，

反正見其圖例細文為準，正規圖均註之。

此外，近日告知國家搜救中心的馬科長詢問有關座標格式轉換的問題時，他們告知現在可以用電腦轉換了，當然也不會有航空航海與地面人員使用座標溝通不良的問題，提供給你參考。－Ｍｉｌｌｅｒ

反正多看ＲＩＳＫＳ

bnpcoa2shp: 台灣地籍 Taiwan cadastral .coa, .bnp 格式轉成 format conversion to Shapefile.

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積丹尼（Dan Jacobson）

Last modified: 2008-05-15 12:02:41 +0800