Michigan Georef Projection Problems

Previous Topic Next Topic
 
classic Classic list List threaded Threaded
1 message Options
Reply | Threaded
Open this post in threaded view
|

Michigan Georef Projection Problems

Clever, Max
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-----
From: [hidden email] on behalf of [hidden email]
Sent: Sat 7/22/2006 12:00 PM
To: [hidden email]
Cc:
Subject: Proj Digest, Vol 26, Issue 13



        Send Proj mailing list submissions to
                [hidden email]
       
        To subscribe or unsubscribe via the World Wide Web, visit
                http://lists.maptools.org/mailman/listinfo/proj
        or, via email, send a message with subject or body 'help' to
                [hidden email]
       
        You can reach the person managing the list at
                [hidden email]
       
        When replying, please edit your Subject line so it is more specific
        than "Re: Contents of Proj digest..."
       
       
        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 <[hidden email]>
        Subject: [Proj] Re: Michigan GeoRef
        To: [hidden email]
        Message-ID:
                <[hidden email]>
               
        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
        [hidden email] (but posting from [hidden email])
       
        -----Original Message-----
        >Date: Thu, 20 Jul 2006 10:23:22 -0400
        >From: "Clever, Max" <[hidden email]>
        >Subject: [Proj] Michigan Georef projection support?
        >To: <[hidden email]>
        >
        >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" <[hidden email]>
        Subject: [Proj] Michigan Georef Projection Problems
        To: <[hidden email]>
        Message-ID:
                <[hidden email]>
               
        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 = 86° 00' 00 W and 45° 18' 33 N" & vbCrLf & _
                "Scale factor at projection's center: k= 0.9996" & vbCrLf & _
                "Azimuth at center of projection: 337° 15' 20" & vbCrLf & _
                "False Easting: 2546731.496, False Northing: -4354009.816"
             
            Lon1 = -86#                 ' Longitude of projection's origin: 86° 00' 00" W
            Lon1 = Lon1 * Pi / 180#
            Lat1 = 45.30916666667       ' Latitude of projection's origin: 45° 18' 33" N
            Lat1 = Lat1 * Pi / 180#
            Az = 337.255555555556       ' Azimuth at center of projection: 337° 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 = 86° 00' 00 W and 45° 18' 33 N" & vbCrLf & _
                "Scale factor at projection's center: k= 0.9996" & vbCrLf & _
                "Azimuth at center of projection: 337° 15' 20" & vbCrLf & _
                "False Easting: 2546731.496, False Northing: -4354009.816"
             
            Lon1 = -86#                 ' Longitude of projection's origin: 86° 00' 00" W
            Lon1 = Lon1 * Pi / 180#
            Lat1 = 45.309166666667       ' Latitude of projection's origin: 45° 18' 33" N
            Lat1 = Lat1 * Pi / 180#
            Az = 337.255555555556       ' Azimuth at center of projection: 337° 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:[hidden email] <mailto:[hidden email]> ] 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, [hidden email]
        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 <[hidden email]>
        Subject: Re: FW: [Proj] First attempt of porting PROJ.4 to Windows CE
        To: "PROJ.4 and general Projections Discussions"
                <[hidden email]>
        Message-ID: <[hidden email]>
        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 <[hidden email]>
        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"
                <[hidden email]>
        Message-ID:
                <[hidden email]>
        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 [hidden email].     Mike
       
       
       
        ------------------------------
       
        _______________________________________________
        Proj mailing list
        [hidden email]
        http://lists.maptools.org/mailman/listinfo/proj
       
        End of Proj Digest, Vol 26, Issue 13
        ************************************
       
       


_______________________________________________
Proj mailing list
[hidden email]
http://lists.maptools.org/mailman/listinfo/proj

winmail.dat (34K) Download Attachment