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I need help opening a shp file which has no projection info in ArcGIS 10.2

I have .shp , .shx , dbf and .xml file. The .xml file details are below .

QUESTION : can i make .proj from below information and how ??

{?xml version="1.0" encoding="UTF-8"?}

{data}

    {coordinateSystem}
        {name}Lambert Conformal Conic{/name}
        {datum}World Geodetic 1984 (WGS84){/datum}
        {system}Lambert Conformal Conic{/system}
        {unit}Meter{/unit}
        {majorAxis}6.378137000000000000000000e+006{/majorAxis}
        {eccentricity}8.181919084262148600000000e-002{/eccentricity}
        {centerX}0.000000000000000000000000e+000{/centerX}
        {centerY}0.000000000000000000000000e+000{/centerY}
        {centerZ}0.000000000000000000000000e+000{/centerZ}
        {rotationX}0.000000000000000000000000e+000{/rotationX}
        {rotationY}0.000000000000000000000000e+000{/rotationY}
        {rotationZ}0.000000000000000000000000e+000{/rotationZ}
        {scaleAdjustment}0.000000000000000000000000e+000{/scaleAdjustment}
        {scaleX}1.000000000000000000000000e+000{/scaleX}
        {localScaleX}1.000000000000000000000000e+000{/localScaleX}
        {scaleY}1.000000000000000000000000e+000{/scaleY}
        {localScaleY}1.000000000000000000000000e+000{/localScaleY}
        {falseEasting}2.743196426299999900000000e+006{/falseEasting}
        {localOffsetX}5.684341886080801500000000e-014{/localOffsetX}
        {falseNorthing}9.143982643000000400000000e+005{/falseNorthing}
        {localOffsetY}2.062779985549144300000000e+001{/localOffsetY}
        {centerLat}2.600000000000000000000000e+001{/centerLat}
        {centerLon}9.000000000000000000000000e+001{/centerLon}
        {firstStdLat}2.317500000000000100000000e+001{/firstStdLat}
        {secondStdLat}2.882499999999999900000000e+001{/secondStdLat}
    {/coordinateSystem}
{/data}
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There are some interesting irregularities here. I'll try to generalize the answer, particularly by discussing the parameters that are zeroes in this definition but might not be in another XML-based coordinate reference system (CRS) definition.

A colleague pointed out that usually XML has uses angle brackets for the attribute/value pairs.

The geographic CRS is given by name and defined. The "majorAxis" is actually the semi-major axis. The "eccentricity" is correct. Other CRS definitions

The map projection is listed by name, Lambert conformal conic, as is the linear unit. We have to assume that any attributes that use linear units are also in meters. No unit is given for the angular parameters, nor for the scale parameters.

The next 7 parameters--centerX/Y/Z, rotationX/Y/Z, and scaleAdjustment--look like a 7 parameter geographic/datum transformation method like Position Vector or Coordinate Frame (also sometimes called Bursa-Wolf), but we don't know which one. The signs of the rotations are opposite in the two methods. In ArcGIS software, they would be defined separately as a custom geographic transformation, or you could try to look up the transformation using the values to see if it already exists.

I don't know what the scaleX/Y and localScaleX/Y parameters could be. They would not be directly definable in ArcGIS software.

These parameters are needed by Lambert conformal conic (in ArcGIS software and others):

falseEasting
falseNorthing 
centerLat     -- latitude of center or origin
centerLon     -- central meridian / longitude of origin or center
firstStdLat   -- first standard parallel
secondStdLat  -- second standard parallel

The parameter values looked familiar to me. They turn out to be close to EPSG::24380, Kalianpur 1975 / India zone IIb. The false easting and northing values are off at the first decimal value, and the EPSG definition uses Lambert with a single standard parallel plus a scale factor. The two standard parallels given here look reasonable, but I haven't checked to see if the match using a scale factor of 0.99878641.

I don't know what the localOffsetX and localOffsetY parameters are. One is suspiciously close to the chain/meter conversion value, but other being 0.5684E-14 is practically zero.

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