[Proj] Michigan Georef Projection Problems
Clever, Max
Maxc at spicergroup.com
Sun Jul 23 02:44:49 EDT 2006
Melita,
are you saying that since December of 2004 Proj has been corrected for the transformation of Michigan Georef? I have downloaded what I think is the most up-to-date version of Proj4 when I installed GRASS cvs 6.1, and it still did not correctly project my data that was in Michigan Georef.
Otherwise, just to refresh the subject, please read what you wrote 2 years ago on December 20th, 2004 to Gerald Evenden and others, where you basically provided manipulated parameters for the EPSG of Michigan Georef in order to make it translate to approximately the correct location.
Also, from what I have read in an email from Anthony Dunk dated May 18, 2006, the Alaska Zone 1, as defined in its EPSG, is not being transformed properly either. It sounded like someone got the correct answer when they set a flag called "no_ofs". Is this a setting that can be added to the EPSG file?
-----Original Message-----
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Today's Topics:
1. Re: Michigan GeoRef (Melita Kennedy)
2. Michigan Georef Projection Problems (Clever, Max)
3. Re: FW: [Proj] First attempt of porting PROJ.4 to Windows CE
(Mateusz Loskot)
4. Michael P Finn of the USGS/ National Geospatial Technical
Operations Center is out of the office. (Michael P Finn)
----------------------------------------------------------------------
Message: 1
Date: Fri, 21 Jul 2006 14:30:26 -0700 (GMT-07:00)
From: Melita Kennedy <mkennedy2 at earthlink.net>
Subject: [Proj] Re: Michigan GeoRef
To: proj at lists.maptools.org
Message-ID:
<4898027.1153517426540.JavaMail.root at elwamui-karabash.atl.sa.earthlink.net>
Content-Type: text/plain; charset=ISO-8859-1
Michigan GeoRef uses the same projection as State Plane Alaska zone 1.
I don't know which projection this is in PROJ. We shouldn't need to implement
another implementation of Hotine oblique Mercator to support Michigan GeoRef.
These are the official parameters from the Michigan DNR:
Projection: Oblique Mercator
Datum: NAD83
Ellipsoid: GRS80
Standard Units: Meters
Scale factor at projection's center: 0.9996
Longitude of projection's origin: 86° 00' 00" W
Latitude of projection's origin: 45° 18' 33" N
Azimuth at center of projection: 337.25556
False Easting: 2546731.496
False Northing: -4354009.816
Please note the azimuth value. The value in decimal degrees is not equal to the original
definition of 337d 15m 20s. Michigan GeoRef was originally defined to work with ArcInfo
workstation which had a limitation in how many decimal places were allowed in the azimuth
parameter. We've changed the ArcGIS version of the definition to match this--when we
added the definition to the projection engine library, we used the DMS value--because
Michigan clients were complaining that data wasn't lining up properly.
Melita
--
Melita Kennedy
ESRI Product Specialist
mkennedy at esri.com (but posting from mkennedy2 at earthlink.net)
-----Original Message-----
>Date: Thu, 20 Jul 2006 10:23:22 -0400
>From: "Clever, Max" <Maxc at spicergroup.com>
>Subject: [Proj] Michigan Georef projection support?
>To: <proj at lists.maptools.org>
>
>Hello Proj Developers,
>
>I've read a few posts and it looks like Gerald has already developed support for RSO's. In the previous emails shown below, I have code written for Hotine Oblique Mercators that uses the Michigan Georef Parameters. Hopefully the code you have written is more accurate. I could not get the Northing accurate enough. If you want the parameters for Michigan Georef they are available online if you google "Michigan Georef Projection". This projection is very important for any Michigan Proj users since most freely available data is provided in Michigan Georef. I think the last time I saw it in a proj format it was listed as a regular omerc which is not correct even though many sites describe it that way.
>
>Anyhow, I was just wondering what the status was on the development of this projection
>
>-Max Clever
------------------------------
Message: 2
Date: Fri, 21 Jul 2006 23:19:01 -0400
From: "Clever, Max" <Maxc at spicergroup.com>
Subject: [Proj] Michigan Georef Projection Problems
To: <proj at lists.maptools.org>
Message-ID:
<B5DFCBECD06C8246A4B1279EC6487B740837CE at sag-x225-exchg0.spicergroup.com>
Content-Type: text/plain; charset="utf-8"
>From reading the previous posts on proj's support for RSO's it sounds like it is already in the works. Just to make sure though, I just want to let everyone know that the Michigan Georef Projection is not supported by proj. The only proj definition that I have seen for it is the one described under the ESRI listing that describes it as an <omerc> which is not really correct.
Michigan Georef is a Hotine Oblique Mercator. The official parameters are listed at this website http://www.michigan.gov/documents/DNR_Map_Proj_and_MI_Georef_Info_20889_7.pdf The parameters as given at this site require the computation of gamma, hopefully that helps you figure out whether to have gamma as a mandatory or optional parameter requirement.
I appreciate any help that could be given. Please see the history of emails below for reference to this problem. Thanks.
-Max
Frank,
First, to answer your question, the parameters Melita offered are not accurate enough and are not the true parameters of the Michigan Georef Projection. Also, the translation from EPSG to PROJ4 is not correct. I don't think Proj 4 supports a point azimuth method transformation for Hotine oblique Mercator (Rectified Skew Orthomorphic Projection)
Here is a link that contains the formulas for oblique mercator and Hotine Oblique Mercator (Michigan Georef is Hotine Oblique).
http://www.posc.org/Epicentre.2_2/DataModel/ExamplesofUsage/eu_cs34i.html <http://www.posc.org/Epicentre.2_2/DataModel/ExamplesofUsage/eu_cs34i.html>
please note though, that in the forward case, I believe the small "v" should be computed using Log not natural log.
Also, if you want it for reference, below is the code of a couple of VB forms that I wrote 3 years ago with help from my professor in college to perform the forward and reverse cases. It is only accurate to about 7 cm in the Northing and 3 mm in the Easting when converting a point from Michigan Georef to Geographic and back. I think there must be some lack of precision in the code that is the reason for the accuracy problem. I hope this helps.
Const a = 6378137 ' semi major axis of the GRS80 ellipsoid
Const e2 = 0.0066943800229 ' excentricity^2 of the GRS80 ellipsoid
Dim Pi As Double
Dim E As Double ' excentricity of the GRS80 ellipsoid
Public Function G2GREF(CoordIN() As Double) As Double()
Dim M1 As Double ' Paramter
Dim m2 As Double ' Paramter
Dim t1 As Double ' Paramter
Dim t2 As Double ' Paramter
Dim t0 As Double ' Paramter
Dim n As Double ' Paramter
Dim F As Double ' Paramter
Dim Eb As Double ' Paramter
Dim Nb As Double ' Paramter
Dim R As Double ' Paramter
MS_GeoRef = "Projection Oblique Mercator; Datum: NAD83; Ellipsoid: GRS80 " & vbCrLf & _
"Standard Units: Meters" & vbCrLf & _
"Origin = 86Â° 00' 00 W and 45Â° 18' 33 N" & vbCrLf & _
"Scale factor at projection's center: k= 0.9996" & vbCrLf & _
"Azimuth at center of projection: 337Â° 15' 20" & vbCrLf & _
"False Easting: 2546731.496, False Northing: -4354009.816"
Lon1 = -86# ' Longitude of projection's origin: 86Â° 00' 00" W
Lon1 = Lon1 * Pi / 180#
Lat1 = 45.30916666667 ' Latitude of projection's origin: 45Â° 18' 33" N
Lat1 = Lat1 * Pi / 180#
Az = 337.255555555556 ' Azimuth at center of projection: 337Â° 15' 20
Az = Az * Pi / 180#
SF = 0.9996 ' Scale factor at projection's center
Eb = 2546731.496 ' False Easting ( Eb = 528600.24)
Nb = -4354009.816 ' False Northing (Nb = 499839.834)
B = Sqr(1 + e2 * Cos(Lat1) ^ 4 / (1 - e2))
A1 = a * B * SF * Sqr(1 - e2) / (1 - e2 * (Sin(Lat1) ^ 2))
Temp = ((1 - E * Sin(Lat1)) / (1 + E * Sin(Lat1))) ^ (0.5 * E)
t0 = Tan(Pi / 4 - (Lat1) / 2) / Temp
D = B * Sqr(1 - e2) / (Cos(Lat1) * Sqr(1 - e2 * Sin(Lat1) ^ 2))
F = D + Lat1 / Abs(Lat1) * Sqr(D ^ 2 - 1) ' Eq. 4.110
E1 = F * t0 ^ B ' Eq. 4.111
G = 0.5 * (F - 1 / F) ' Eq. 4.112
Gamma0 = Isin(Sin(Az) / D) ' Eq. 4.113
Lon0 = Lon1 - Isin(G * Tan(Gamma0)) / B ' Lambda 0 at Eq. 4.114
U0 = (Lat1 / Abs(Lat1)) * (A1 / B) * Atn(Sqr(D ^ 2 - 1) / Cos(Az))
V0 = 0
LatIN = DMS2R(CoordIN(1))
LonIN = DMS2R(CoordIN(2))
Temp = ((1 - E * Sin(LatIN)) / (1 + E * Sin(LatIN))) ^ (0.5 * E)
t = Tan(Pi / 4 - (LatIN) / 2) / Temp ' Eq. 4.117
Q = E1 / (t ^ B)
S = 0.5 * (Q - 1 / Q)
Tc1 = 0.5 * (Q + 1 / Q)
V1 = Sin(B * (LonIN - Lon0))
U1 = (-V1 * Cos(Gamma0) + S * Sin(Gamma0)) / Tc1
vl = A1 * Log((1 - U1) / (1 + U1)) / (2 * B)
temp1 = (S * Cos(Gamma0) + V1 * Sin(Gamma0)) / Cos(B * (LonIN - Lon0))
ul = (A1 / B) * Atn(temp1)
x = vl * Cos(Az) + ul * Sin(Az) + Eb
y = ul * Cos(Az) - vl * Sin(Az) + Nb
ReDim Preserve CTemp(1 To 2) As Double
CTemp(1) = x
CTemp(2) = y
G2GREF = CTemp
End Function
Public Function GREF2G(CoordIN() As Double) As Double()
Dim M1 As Double ' Paramter
Dim m2 As Double ' Paramter
Dim t1 As Double ' Paramter
Dim t2 As Double ' Paramter
Dim t0 As Double ' Paramter
Dim n As Double ' Paramter
Dim F As Double ' Paramter
Dim Eb As Double ' Paramter
Dim Nb As Double ' Paramter
Dim PhiOut As Double ' Paramter
Dim LonOut As Double ' Paramter
MS_GeoRef = "Projection Oblique Mercator; Datum: NAD83; Ellipsoid: GRS80 " & vbCrLf & _
"Standard Units: Meters" & vbCrLf & _
"Origin = 86Â° 00' 00 W and 45Â° 18' 33 N" & vbCrLf & _
"Scale factor at projection's center: k= 0.9996" & vbCrLf & _
"Azimuth at center of projection: 337Â° 15' 20" & vbCrLf & _
"False Easting: 2546731.496, False Northing: -4354009.816"
Lon1 = -86# ' Longitude of projection's origin: 86Â° 00' 00" W
Lon1 = Lon1 * Pi / 180#
Lat1 = 45.309166666667 ' Latitude of projection's origin: 45Â° 18' 33" N
Lat1 = Lat1 * Pi / 180#
Az = 337.255555555556 ' Azimuth at center of projection: 337Â° 15' 20
Az = Az * Pi / 180#
SF = 0.9996 ' Scale factor at projection's center
Eb = 2546731.496 ' False Easting ( Eb = 528600.24)
Nb = -4354009.816 ' False Northing (Nb = 499839.834)
ttemp = e2 * (Cos(Lat1) ^ 4) / (1 - e2)
B = Sqr(1 + ttemp)
A1 = a * B * SF * Sqr(1 - e2) / (1 - e2 * (Sin(Lat1)) ^ 2)
Temp = ((1 - E * Sin(Lat1)) / (1 + E * Sin(Lat1))) ^ ( 0.5 * E)
t0 = Tan(Pi / 4 - (Lat1) / 2) / Temp
ttemp1 = Cos(Lat1) * Sqr(1 - e2 * (Sin(Lat1)) ^ 2)
D = B * Sqr(1 - e2) / ttemp1
F = D + Lat1 / Abs(Lat1) * Sqr(D ^ 2 - 1) ' Eq. 4.110
E1 = F * t0 ^ B ' Eq. 4.111
G = 0.5 * (F - 1 / F) ' Eq. 4.112
Gamma0 = Isin(Sin(Az) / D) ' Eq. 4.113
Lon0 = Lon1 - Isin(G * Tan(Gamma0)) / B ' Lambda 0 at Eq. 4.114
xIN = CoordIN(1)
yIN = CoordIN(2)
'Actual Computations for Reverse case Hotine Oblique Mercator
xr = xIN - Eb
yr = yIN - Nb
vs = xr * Cos(Az) - yr * Sin(Az)
us = yr * Cos(Az) + xr * Sin(Az)
temp1 = -B * vs / A1
Qp = (2.71828182845905) ^ temp1
Sp = 0.5 * (Qp - 1 / Qp)
Tp = 0.5 * (Qp + 1 / Qp)
Vp = Sin(B * us / A1)
Up = (Vp * Cos(Gamma0) + Sp * Sin(Gamma0)) / Tp
temp2 = (1 + Up) / (1 - Up)
t = (E1 / Sqr(temp2)) ^ (1 / B)
PhiOut = Pi / 2 - 2 * Atn(t)
'Iterative Solution for Phi Out
' For i = 1 To 30
' Temp = ((1 - E * Sin(PhiOut)) / (1 + E * Sin(PhiOut))) ^ ( 0.5 * E)
' PhiOut = Pi / 2 - 2 * Atn(t * Temp)
' Next i
'Single Line Solution for Phi Out
PhiOut = PhiOut + Sin(2 * PhiOut) * (e2 / 2 + (5 * e2 ^ 2) / 24 + (e2 ^ 4) / 12 + (13 * e2 ^ 6) / 360) + Sin(4 * PhiOut) * ((7 * e2 ^ 2) / 48 + (29 * e2 ^ 4) / 240 + (811 * e2 ^ 6) / 11520) + Sin(6 * PhiOut) * ((7 * e2 ^ 4) / 120 + (81 * e2 ^ 6) / 1120) + Sin(8 * PhiOut) * ((4279 * e2 ^ 6) / 161280)
temp3 = (Sp * Cos(Gamma0) - Vp * Sin(Gamma0)) / Cos(B * us / A1)
LonOut = Lon0 - Atn(temp3) / B
ReDim Preserve CTemp(1 To 2) As Double
CTemp(1) = r2dms(PhiOut)
CTemp(2) = r2dms(LonOut)
GREF2G = CTemp
End Function
-----Original Message-----
From: Frank Warmerdam [mailto:fwarmerdam at gmail.com <mailto:fwarmerdam at gmail.com> ] On Behalf Of Frank Warmerdam
Sent: Saturday, July 15, 2006 10:01 PM
To: Clever, Max
Subject: Re: [UMN_MAPSERVER-USERS] FW: Michigan Georef Projection Problems in Proj4
Clever, Max wrote:
> Hi,
>
>
>
> Did anyone see this the last time I sent it? It relates to Mapserver as
> well since Mapserver uses Proj4 for its projections.
Max,
I have skimmed this material, but frankly I'm not sure what action item
there is, and I find myself with limited time for work on PROJ.4.
Is the problem that the parameters Melita offered a couple years ago
aren't accurate enough? Or that the underlying translation from EPSG
to PROJ.4 wasn't fixed so the epsg file keeps getting regenerated
wrong? If it is a tranlation problem, then that is basically something
I ought to fix. But I basically need some formulation to recognise
a distinct oblique mercator case for the michigan projection from the
EPSG codes (or parameters), and what that should map to in WKT format,
and in PROJ.4 format. I'm happy to use the ESRI WKT representation if
there isn't an obvious existing form for this special case.
If you can walk me through what should be changed, I'm willing to work
on it.
Best regards,
...
> Two years ago, I ran into a problem with the Michigan Georef Projection
> and the way that proj identified it. I had sent emails back and forth
> for a while until someone sent a temporary solution of providing false
> parameters that worked.. *for the most part*. This temporary solution,
> of course, did not actually solve the problem, but instead delayed the
> fixing of the methods that proj identifies projections and translates
> them. For that I am sorry for not remaining vigilant in seeing a true
> solution being devised. But now, since I have just now installed the
> latest version of GRASS 6.1, I have come full circle and face this
> problem again. To provide a quick access to the background of what has
> already been said on this projection please note the previous emails
> below. I believe, at this time still, that the *omerc* projection and
> its parameters as used by proj cannot correctly describe or transform a
> omerc projection with a "natural origin". From what I understand,
> Hotine oblique mercator and Rectified Skew Orthomorphic are one and the
> same or depend on where the skew is corrected. Has there been a
> solution determined for this projection? If not, maybe a solution to
> this problem would be to have Proj have oblique mercators split between
> "natural origins" and cartesian center point origins. I hope, maybe,
> someone has been looking at this lately but I doubt it. Any comments or
> solutions would be very welcome. Thanks.
--
---------------------------------------+--------------------------------------
I set the clouds in motion - turn up | Frank Warmerdam, warmerdam at pobox.com
light and sound - activate the windows | http://pobox.com/~warmerdam <http://pobox.com/~warmerdam>
and watch the world go round - Rush | President OSGF, http://osgeo.org <http://osgeo.org>
------------------------------
Message: 3
Date: Sat, 22 Jul 2006 13:22:24 +0200
From: Mateusz Loskot <mateusz at loskot.net>
Subject: Re: FW: [Proj] First attempt of porting PROJ.4 to Windows CE
To: "PROJ.4 and general Projections Discussions"
<proj at lists.maptools.org>
Message-ID: <44C20A70.2020600 at loskot.net>
Content-Type: text/plain; charset=ISO-8859-1
Wynand Kruger wrote:
> Where can we find 'proj4-wince-port.zip'?
Hi Wynand,
I replied to your first e-mail in you're asking about it.
Please, take a look at:
http://lists.maptools.org/pipermail/proj/2006-July/002406.html
Best regards
--
Mateusz Loskot
http://mateusz.loskot.net
------------------------------
Message: 4
Date: Sat, 22 Jul 2006 10:01:25 -0500
From: Michael P Finn <mfinn at usgs.gov>
Subject: [Proj] Michael P Finn of the USGS/ National Geospatial
Technical Operations Center is out of the office.
To: "PROJ.4 and general Projections Discussions"
<proj at lists.maptools.org>
Message-ID:
<OFDAAE9684.8189DBFE-ON862571B3.005286F5-862571B3.005286F5 at usgs.gov>
Content-Type: text/plain; charset=US-ASCII
I will be out of the office starting 07/22/2006 and will not return until
07/31/2006.
I will be unable to check e-mail regularly while I am out. If I can't
respond to your message while I am out, then I will when I return. If you
have anything that cannot wait, please contact my colleague, Mr. Timothy
Krupinski, at tkrupinski at usgs.gov. Mike
------------------------------
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