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From: James Gentles <jdg@hpqtdla.sqf.hp.com>
Subject: v04i003: mercator_jg - Transverse Mercator Projections v1.0, Part01/01
Newsgroups: comp.sources.hp48
Followup-To: comp.sys.hp48
Approved: spell@seq.uncwil.edu
Checksum: 3542956383 (verify with brik -cv)
Submitted-by: James Gentles <jdg@hpqtdla.sqf.hp.com>
Posting-number: Volume 4, Issue 3
Archive-name: mercator_jg/part01
BEGIN_RDM mercator.rdm
Posted below are HP48 programs for performing Transverse Mercator Projections.
They are accompanied by documentation, so should be self-explanitory.
Mercator: Transverse Mercator Projections, for cartographers and others,
including radio amateurs!
Comments & Queries to me at the above address.
Regards
James
---------------------------------------------------------------------
I have no professional connection with Hewlett-Packard's
calculator operations other than as a user of their products.
---------------------------------------------------------------------
Opinions expressed are my own, and are not intended to be an official
statement by Hewlett-Packard Company
---------------------------------------------------------------------
To strive, to seek, to find, and not to yield. Tennyson, "Ulysses".
---------------------------------------------------------------------
James Gentles Hewlett Packard, Amateur: GM4WZP
Queensferry Telecoms Division QTD, Email: jdg@hpsqf.sqf.hp.com
Station Road, South Queensferry, HPDESK: James Gentles / HP1400
West Lothian, Scotland, EH30 9XR. Phone: + 44 31 331 7663 DDI
---------------------------------------------------------------------
END_RDM
BEGIN_DOC mercator.doc
ROUTINES and PROCEDURES for PERFORMING
TRANSVERSE MERCATOR PROJECTIONS.
James Gentles
jdg@hpsqf.sqf.hp.com
February 1992
1. Introduction
2. Basics
3. Pseudo Code for Main Routines
4. HP48 Routines: Descriptions
5. HP48 Routines: Programs (ASCII DIR object)
1. Introduction
This file contains a collection of HP48 programs used for translation
between Latitude/Longitude and Transverse Mercator Projection. The programs
were written specifically to translate between the Great Britain and Ireland
"National Grid" systems, however they could be used for translation between
latitude/longitude and ANY mapping system that uses this projection by
altering the constants used to define the projection conveniently contained
in a list.
These programs were written for Amateur Radio use in the UK. Some amateurs
use positioning reference systems based on Latitude and Longitude, where
others use a system based on the UK National Grid which is a Transverse
Mercator Projection. This file only contains the projection translation part
of this work and as such may be useful to a wider audience.
2. Basics
"Mercator Projection" is one of the projections commonly used to show the
whole world in atlases. It's main disadvantage for 'whole world' maps is the
distortion near the poles, making Antartica and Greenland appear much larger
than they actually are. For small parts of the globe (e.g. the UK) this
projection provides a very accurate model.
This system allows a map to contain a regular grid for reference and short
distance calculations. However, because the map is a projection of the surface
of a shape approximating to an oblate spheroid onto a plane (or cylindrical
shaped) piece of paper then these grid lines have a very complex relationship
to latitude and longitude. In "Mercator" projection the map of the world is
projected onto a cylinder of paper from the globe, where the only point of
contact between the two is the equator. Transverse Mercator uses the same
principle, except a line of latitude is used. Absolute accuracy is only
achieved where the globe touches the map, however by choosing scalings and
sphere models correctly these errors can be minimised.
Although the National Grid Systems are peculiar to the British Isles, the
"Transverse Mercator Projection" system is used elsewhere. The constants
required for the translation are all included in a list, in this case called
AIRY or IRISH, substitute the constants for your local projection if desired.
It should be possible to use the formulae for "Mercator Projection" by simply
swapping the Latitude and Longitude entries and providing the appropriate
list of constants.
The programs are written specially for the British and Irish Grids, and their
Grid Numbering scheme. This may not be the same as other systems, again
however the programs are structured for the easy removal or modification of
the numbering scheme. The basic translation provides an output of X and Y
coordinates called eastings and northings. The complication in the UK systems
is that 100Km squares are given grid letters, rather than numbers. In addition
the accuracy is truncated to 100m.
The origin of the UK grid is off the SW corner of England, and there are 4
main squares, each with 500Km sides. The square nearest the origin is called
S (South?), and covers most of England. The square north of that is N (North?)
and covers mostly Scotland. The square north of that again is H (Highland?)
and covers the most northerly islands of Scotland. Finally the eastern
extremity of England just pokes into square T to the east of square S. These
letters appear to be named arbitrarily. A pictorial representation follows:
1500Km --------------
| |
| H . |
| / | (Northern Isles)
| . |
1000Km ---------/----
| ./---- |
| | / N /. | (Scotland)
| / /| ./_ |
| //| | |
500Km ------|----\--------------
| ._| \| |
| |_ S |_ T | (England)
| __- | | |
| _-__________/ |
0 --------------------------
0 500Km 1000Km
Each of these 500Km squares is divided into 25 100Km squares as follows:
A B C D E
F G H J K
L M N O P
Q R S T U
V W X Y Z
Note that this is A to Z from top left to bottom right with letter "I"
omitted. So for example I live at "NT119779" to the nearest 100metres.
The full reference from datum for this is Eastings 311900, Northings
677900. The program XX6-> is used to do the translation from "NT119779"
to the eastings and northings in metres.
The Irish grid only covers one of the above described 500Km squares, so
it is identical to the British system except the leading N, S, H or T is
not required.
This file contains programs written for a HP48SX calculator, but they were
originally developed on a HP28S. In translating my code from the HP28 I
have taken the opportunity of reducing their size slightly, reducing their
execution time by 40%, and taking advantage of some of the HP48's features,
including TAGing. I have also corrected an error in the original HP28 code
that limited the accuracy to approximately 10m. The routines are now accurate
to better than 0.01 seconds of a degree, the oblate spheroid model is now
the limiting factor.
For those more interested in the mathematics of the projection, I have
included psudo-code descriptions of the routines to aid understanding. The
routines are all based on Reference Transverse Mercator Projection Constants,
Formulae and Methods, Ordnance Survey Information March 1983
3. Pseudo Code for Main Routines
This pseudo-code is based on the following calculator routines and on the
Ordnance and Survey Document, Transverse Mercator Projection, March 1983.
The routines use mostly two letter variable names, this does not aid
readability however these are the calculator variables. Leaving the
variables like this means that no errors have been introduced in the
translation to pseudo-code from HP48 code.
Latitude/Longitude to National Grid Reference
Note: All calculations performed in radians
k = Latitude of point
l = Longitude of point
Constants for AIRY Spheriod for Great Britain National Grid
a = 6377563.396 Major semi-axis m
b = 6356256.91 Minor semi-axis m
k0 = .855211333477 True Origin 49 deg N for
l0 = -3.490658E-2 2 deg W GREAT BRITAIN
n0 = -100000 False Origin in m E of true origin
e0 = 400000 m N of true origin
f0 = .9996012717 Scale factor on Central meridian Fo
Constants for AIRY Spheriod for Irish National Grid
a = 6377563.396 Major semi-axis m
b = 6356256.91 Minor semi-axis m
k0 = .933751149817 True Origin 53.5 deg N for
l0 = -.139626340159 8 deg W IRELAND
n0 = 250000 False Origin in m E of true origin
e0 = 200000 m N of true origin
f0 = 1.000035 Scale factor on Central meridian Fo
p = l - l0
k3 = k - k0 difference in latitude
k4 = k + k0 sum of latitudes
call subroutine ABNE, uses a b f0 and returns a1 b1 n1 e2
call subroutine AOM, uses n1 k3 k4 b1 and returns m
call subroutine VRH2, uses a1 e2 k and returns v r h2
J3 = 'm+n0' Formula 1
J4 = 'v/2*SIN(k)*COS(k)' Formula 2
J5 = 'v/24*SIN(k)*COS(k)^3*(5-TAN(k)^2+9*h2)' Formula 3
J6 = 'v/720*SIN(k)*COS(k)^5*(61-58*TAN(k)^2+TAN(k)^4)' Formula 3a
northings = 'J3+p^2*J4+p^4*J5+p^6*J6' COMPUTE NORTHINGS
(answer in metres from origin)
J7 = COS(k) * v Formula 4
J8 = 'v/6* COS(k)^3*(v/r-TAN(k)^2)' Formula 5
J9 = 'v/120*COS(k)^5*(5-18*TAN(k)^2+TAN(k)^4+14*h2-58*TAN(k)^2*h2)' Formula 6
eastings = 'e0+p*J7+p^3*J8+p^5*J9' COMPUTE EASTINGS
(answer in metres from origin)
Grid reference can now be easily obtained from eastings and northings.
National Grid Reference to Latitude/Longitude
Note: All calculations performed in radians
Initially decode grid reference into metres from origin, to obtain
e = eastings of point (in metres from origin)
n = northings of point (in metres from origin)
Constants for AIRY Spheriod for Great Britain National Grid
a = 6377563.396 Major semi-axis m
b = 6356256.91 Minor semi-axis m
k0 = .855211333477 True Origin 49 deg N for
l0 = -3.490658E-2 2 deg W GREAT BRITAIN
n0 = -100000 False Origin in m E of true origin
e0 = 400000 m N of true origin
f0 = .9996012717 Scale factor on Central meridian Fo
Constants for AIRY Spheriod for Irish National Grid
a = 6377563.396 Major semi-axis m
b = 6356256.91 Minor semi-axis m
k0 = .933751149817 True Origin 53.5 deg N for
l0 = -.139626340159 8 deg W IRELAND
n0 = 250000 False Origin in m E of true origin
e0 = 200000 m N of true origin
f0 = 1.000035 Scale factor on Central meridian Fo
y1 = e - e0
call subroutine ABNE, uses a b f0 and returns a1 b1 n1 e2
call subroutine PHI, uses n n0 n1 k0 a1 b1 and returns k k3 k4
call subroutine VRH2, uses a1 e2 k and returns v r h2
J3 = TAN(k)/(2*r*v) Formula 7
J4 = 'TAN(k)/(24*r*v^3)*(5+3*TAN(k)^2+h2-9*TAN(k)^2*h2)' Formula 8
J5 = 'TAN(k)/(720*r*v^5)*(61+90*TAN(k)^2+45*TAN(k)^4)' Formula 9
Latitude = 'k-y1^2*J3+y1^4*J4-y1^6*J5' COMPUTE LATITUDE
J6 = 1/(COS(k)*v) Formula10
J7 = '1/(COS(k)*6*v^3)*(v/r+2*TAN(k)^2)' Formula11
J8 = '1/(COS(k)*120*v^5)*(5+28*TAN(k)^2+24*TAN(k)^4)' Formula12
J9 = '1/(COS(k)*5040*v^7)*(61+662*TAN(k)^2+1320*TAN(k)^4+720*TAN(k)^6)' 12a
Longitude = 'l0+y1*J6-y1^3*J7+y1^5*J8-y1^7*J9' COMPUTE LONGITUDE
Finally translate Latitude and longitude back into degrees, minutes and seconds
SUBROUTINES used in National Grid Ref / Latitude & Longitude TRANSFORMS
VRH2 (uses a1 e2 k and returns v r h2)
v = 'a1/SQRT(1-e2*SIN(k)^2)'
r = 'v*(1- e2)/(1-e2*SIN(k)^2)'
h2 = '(v/r)-1'
AOM (uses n1 k3 k4 b1 and returns m), Compute Developed Arc of Meridian
J3 = '(1+n1+5/4*n1^2+ 5/4*n1^3)*k3'
J4 = '(3*n1+3*n1^2+21/8*n1^3)*SIN(k3)*COS(k4)'
J5 = '(15/8*n1^2+15/ 8*n1^3)*SIN(2*k3)*COS(2*k4)'
J6 = '35/ 24*n1^3*SIN(3*k3)*COS(3*k4)'
m = 'b1*(J3 - J4 + J5 - J6)'
PHI (uses n n0 n1 k0 a1 b1 and returns k k3 k4) Iteratively Calc Latitude k
k = '(n-n0)/a1+k0' First approximation to Latitude
REPEAT
k3 = 'k-k0'
k4 = 'k+k0'
call subroutine AOM, uses n1 k3 k4 b1 and returns m
Test= 'n-n0-m'
k = 'k+(n-n0-m)/a1'
UNTIL ABS(Test)<0.001
k = Test
ABNE (uses a b f0 and returns a1 b1 n1 e2)
a1 = 'a*f0'
b1 = 'b*f0' Scale Major & Minor axes by f0
n1 = '(a1-b1)/(a1+b1)' calculate n from scaled axes
e2 = '(a1^2-b1^2)/a1^2' calculate e^2 (e2) from scaled axes
4. HP48 Routines: Descriptions
Transverse Mercator Projection Routines, to change to Latitude and Longitude,
all latitude and longitude numbers are entered, and returned in DD.MMSSsss
format.
->NGR Lat and Long to National Grid Reference (Great Britain). Put
Latitude on stack (north is +ve), then Longitude on stack
(east is +ve), returns a string of format "NT119779". The bottom
left corner of the 100m square defined.
NGR-> National Grid to Lat and Long. The inverse of ->NGR. Returns the
Lat and Long of the centre of the 100m square defined.
->IGR Lat and Long to Irish Grid Reference. Put Latitude on stack
(north is +ve), then Longitude on stack (east is +ve), returns
a string of format "T119779". The bottom left corner of the 100m
square defined.
IGR-> Irish Grid to Lat and Long. The inverse of ->IGR. Returns the
Lat and Long of the centre of the 100m square defined.
->XX6 Used by ->NGR and ->IGR to translate eastings and northings in metres
to a national grid reference, e.g. 311900 677900 become "NT119799".
Truncates accuracy to 100m, so result refers to the bottom left corner
of the grid reference 100metre square produced. If the coordinates do
not fall into one of the 4 500Km squares a "#" is returned in the
first character of the string.
XX6-> Performs the inverse process of ->XX6. Returns the full eastings and
northings of the square centre refered to in metres, i.e. +50m is
added to the eastings and northings.
->TMP Performs the Transverse Mercator Projection. On entry the stack should
contain Lat, Long (both in radians), then all the constants in list
AIRY or IRISH depending on what projection is being used. The routine
returns eastings and northings on the stack in metres.
TMP-> Performs the inverse Transverse Mercator Projection. On entry the
stack should contain eastings, northings, then all the constants in
list AIRY or IRISH depending on what projection is being used. The
routine returns latitude and longitude on the stack in radians.
VRH2 Used by ->TMP and TMP-> routines. Calculates v r & h2.
AOM Used by ->TMP and PHI routines. Calculates Arc of Meridian, m.
PHI Used by TMP-> routine. Iteratively calculates k k3 & k4.
ABNE Used by ->TMP and TMP-> routines. Calculates a1 b1 n1 & e2.
PAD0 Used by ->XX6 routine
AIRY List of constants used by TMP routines for Great Britain. See following
listing of object for comments on what individual elements are.
IRISH List of constants used by TMP routines for Ireland. See following
listing of object for comments on what individual elements are.
External programs used (included in the listing for completeness):
PRESERVE Returns flags to initial state on program exit. Used in ->TMP TMP->
and ->XX6 routines. See HP48SX Manual II page 555.
5. HP48 Routines: Programs (ASCII DIR Object) 4256bytes #25FEhex
END_DOC
BEGIN_RPL mercator.rpl
%%HP: T(3)A(D)F(.);
DIR
\->NGR
\<< HMS\-> D\->R SWAP HMS\-> D\->R @ Change to degs decimal then rads
AIRY OBJ\-> DROP @ Put projection consts on stack
\->TMP @ Do projection, returns E&N on stack
\->XX6 @ translate to grid letters + 6 nums
"NGR" \->TAG @ tag output
\>>
@
NGR\->
\<< XX6\-> @ translate grid to full coordinates
AIRY OBJ\-> DROP @ put projection consts on stack
TMP\-> @ do projection, returns Lat and Long
SWAP R\->D \->HMS "Lat\^o" \->TAG @ translate to degrees decimal
SWAP R\->D \->HMS "Long\^o" \->TAG @ and tag output
\>>
@
\->TMP @ Reference Transverse Mercator Proj'n
\<< @ Constants, Formulae and Methods.
\<< RAD \-> l k a b k0 l0 n0 e0 f0 @ Ordnance Survey Information March 83
\<< l l0 - k k0 - k k0 + \-> p k3 k4
\<< a b f0 ABNE \-> a1 b1 n1 e2
\<< n1 k3 k4 b1 AOM a1 e2 k VRH2
l l0 - k SIN k COS k TAN @ Compute SIN(k) COS(k) & TAN(k) once
\-> m v r h2 p s c t
\<< m n0 + @ Formula I
s c v 2 / * * p SQ * @ Formula II *p^2
'v/24*s*c^3*(5-t^2+9*h2)'
\->NUM p 4 ^ * @ Formula III *p^4
'v/720*s*c^5*(61-58*SQ(t)+t^4)'
\->NUM p 6 ^ * @ Formula IIIA*p^6
+ + + @ compute northings
c v * p * @ Formula IV *p
'v/6*c^3*(v/r-SQ(t))' \->NUM p 3 ^ * @ Formula V *p^3
'v/120*c^5*(5-18*SQ(t)+t^4+14*h2
-58* SQ(t)*h2)' \->NUM p 5 ^ * @ Formula VI *p^5
+ + e0 + @ compute eastings
SWAP
\>>
\>>
\>>
\>>
\>> PRESERVE @ Return to original flag settings
\>> @ See HP48 Manual II page 555
@
TMP\-> @ Reference Transverse Mercator Proj'n
\<< @ Constants, Formulae and Methods.
\<< RAD \-> e n a b k0 l0 n0 e0 f0 @ Ordnance Survey Information March 83
\<< a b f0 ABNE e e0 - \-> a1 b1 n1 e2 y1
\<< n n0 n1 k0 a1 b1 PHI \-> k k3 k4
\<< a1 e2 k VRH2 k COS k TAN @ Calculate COS(k) & TAN(k) for use later
\-> v r h2 c t
\<< k t 2 r v * * / y1 SQ * @ Formula VII *y1^2
't/(24*r*v^3)*(5+3*SQ(t)+h2
-9*SQ(t)*h2)' \->NUM y1 4 ^ * @ Formula VIII *y1^4
't/(720*r*v^5)*(61+90*SQ(t)
+45*t^4)' \->NUM y1 6 ^ * @ Formula IX *y1^6
- - - @ Compute Latitude
c v * INV y1 * @ Formula X *y1
'1/(c*6*v^3)*(v/r+2*SQ(t))'
\->NUM y1 3 ^ * @ Formula XI *y1^3
'1/(c *120*v^5)*(5+28*SQ(t)+24
*t^4)' \->NUM y1 5 ^ * @ Formula XII *y1^5
'1/(c*5040*v^7)*(61+662*SQ(t)+1320
*t^4+720*t^6)' \->NUM y1 7 ^ * @ Formula XIIA *y1^7
- - - l0 + @ Compute Longitude
\>>
\>>
\>>
\>>
\>> PRESERVE @ Return to original flag settings
\>> @ See HP48 Manual II page 555
@
\->IGR
\<< HMS\-> D\->R SWAP HMS\-> D\->R @ Same as \->NGR but since Irish grid
IRISH OBJ\-> DROP @ is only one 500Km square then the
\->TMP \->XX6 @ initial grid letter "S" is dropped.
2 8 SUB "IGR" \->TAG
\>>
@
IGR\->
\<< DTAG "S" SWAP + @ Same as NGR\-> but since Irish grid
XX6\-> IRISH OBJ\-> DROP @ is only one 500Km square then an
TMP\-> @ extra "S" is added so the standard
SWAP R\->D \->HMS "Lat\^o" \->TAG @ routines can be used.
SWAP R\->D \->HMS "Long\^o" \->TAG
\>>
@
\->XX6
\<<
\<< STD 100 / IP SWAP 100 / IP @ throw away accuracy better than 100m
DUP2 5000 / IP SWAP 5000 / IP @ break eastings and northings into
\-> n e es ns @ 100 metre units and 500Km units
\<<
IF es 0 ==
THEN @ for eastings 0 to 500000
CASE ns 2 == @ for northings 1000K to 1500K square H
THEN "H"
END
ns 1 == @ for northings 500K to 1000K square N
THEN "N"
END
ns 0 == @ for northings 0 to 500K square S
THEN "S"
END
"#" @ else illegal square denoted by a #
END
ELSE
ns 0 == es 1 == AND @ for eastings 500K to 1000K AND
"T" @ northings 0 to 500K square T
"#" @ else illegal square denoted by a #
IFTE
END
e 1000 / IP 5 MOD 1 + @ Compute a number for each 100Km square
4 n 1000 / IP 5 MOD - @ within the 500Km square in the range
5 * + DUP @ 1 to 25 top left to bottom right
IF 8 \<= @ skip the number 8, gives 0-7,9-25
THEN 1 -
END 65 + CHR + @ translate to A to Z with I missing
e PAD0 n PAD0 @ use PAD0 to pad e & n with leading 0's
+ +
\>>
\>> PRESERVE @ Return to original flag settings
\>> @ See HP48 Manual II page 555
@
XX6\->
\<< DUP 3 5 SUB @ Split incoming string into 4 parts
SWAP DUP 6 8 SUB @ and put them on stack
SWAP DUP NUM @ e.g. "NJ123456"
SWAP 2 2 SUB NUM 66 - @ "123" "456" NUM(N) NUM(J)-66
DUP @ e n f s
IF 7 < @ NUM(J)-66 are translated to be
THEN 1 + @ contiguous top left to bottom right
END
CASE OVER 72 == @ H square msdigits
THEN 0 2
END
OVER 78 == @ N square msdigits
THEN 0 1
END
OVER 83 == @ S square msdigits
THEN 0 0
END
OVER 84 == @ T square msdigits
THEN 1 0
END
"XX Error" DOERR @ else display error
END
3 PICK 5 MOD 4 5 PICK 5 / IP 5 MOD -
\-> e n f s e1 n1 e2 n2
\<< e OBJ\-> e1 5000 *
e2 1000 * + + 100 * 50 +
n OBJ\-> n1 5000 * @ recombine elements into full N&E
n2 1000 * + + 100 * 50 + @ adding 50 metres to return square ctr
\>>
\>>
@
VRH2 @ Compute v r and h2
\<< \-> a1 e2 k
\<< 'a1/\v/(1-e2* SIN(k)^2)' \->NUM
DUP
'(1-e2)/(1-e2*SIN(k)^2)' \->NUM *
DUP2 / 1 -
\>>
\>>
@
AOM @ Compute Developed Meridian Arc m
\<< 4 PICK DUP SQ SWAP 3 ^ @ Compute n1^2 and n1^3 only once
\-> n1 k3 k4 b1 n2 n3
\<< '(1+n1+5/4*n2+5/4*n3)*k3' \->NUM
'(3*n1+3*n2+21/8*n3)*SIN(k3)*COS(k4)' \->NUM
'(15/8*n2+15/8*n3)*SIN(2*k3)*COS(2*k4)' \->NUM
'35/24*n3*SIN(3*k3)*COS(3*k4)' \->NUM
- - - b1 * @ on exit m is on stack
\>>
\>>
@
PHI @ iteratively calculate Latitude k
\<< \-> n n0 n1 k0 a1 b1 @ stack to local variables
\<< '(n-n0)/a1+k0' \->NUM @ first approximation to Latitude
0 0
DO
DROP2 DUP DUP k0 - SWAP k0 +
\-> k k3 k4
\<< n1 k3 k4 b1 AOM \-> m @ re-compute arc of meridian
\<< n n0 - m - DUP
IF .001 <
THEN k
ELSE n n0 - m - a1 / k +
END
k3 k4
\>>
\>> 4 ROLL
UNTIL .001 < @ until error is less than 0.001
END
\>> @ returns k k3 k4 on stack
\>>
@
ABNE
\<< DUP ROT * 3 ROLLD * \-> b1 a1 @ scale a & b by f0 and call a1 and b1
\<< a1 b1 DUP2 - a1 b1 + / @ calculate n from scaled axes
a1 SQ b1 SQ - a1 SQ / @ calculate e^2 (e2) from scaled axes
\>>
\>>
@
PAD0
\<< 1000 MOD \->STR @ take string from stack and
WHILE @ while it is shorter than 3 characters
DUP SIZE 3 <
REPEAT "0" SWAP + @ add a leading "0"
END
\>>
@
@ Constants defining Transverse Mercator
AIRY { @ Projection for Airy Spheroid
6377563.396 @ Major semi-axis m
6356256.91 @ Minor semi-axis m
.855211333477 @ True Origin 49 deg N for
-3.490658E-2 @ 2 deg W GREAT BRITAIN
-100000 @ False Origin in m E of true origin
400000 @ m N of true origin
.9996012717 } @ Scale factor on Central meridian Fo
@
@ Constants defining Transverse Mercator
IRISH { @ Projection for Airy Spheroid
6377563.396 @ Major semi-axis m
6356256.91 @ Minor semi-axis m
.933751149817 @ True Origin 53.5 deg N for
-.139626340159 @ 8 deg W IRELAND
250000 @ False Origin in m E of true origin
200000 @ m N of true origin
1.000035 } @ Scale factor on Central meridian Fo
@
PRESERVE @ See HP48SX Manual II page 555.
\<< RCLF \-> f @ May be more suitably located in HOME
\<< EVAL f STOF
\>>
\>>
END
END_RPL
BEGIN_ASC mercator.asc
%%HP: T(3)A(D)F(.);
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BYTES: #6E70h 4255
BEGIN_UU mercator.uue
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end
END_UU
