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# minvtran

Unproject features from map to geographic coordinates

## Syntax

[lat,lon] = minvtran(x,y)
[lat,lon,alt] = minvtran(x,y,z)
[...] = minvtran(mstruct,...)

## Description

[lat,lon] = minvtran(x,y) applies the inverse transformation defined by the map projection in the current map axes. Using minvtran, you can convert point locations and line and polygon vertices in a planar, projected map coordinate system to latitudes and longitudes.

[lat,lon,alt] = minvtran(x,y,z) applies the inverse projection to 3-D input, resulting in 3-D output. If the input Z is empty or omitted, then Z = 0 is assumed.

[...] = minvtran(mstruct,...) takes a valid map projection structure as the first argument. In this case, no map axes is needed.

## Examples

Before using any transformation functions, it is necessary to create a map projection structure. You can do this with axesm or the defaultm function:

```mstruct = defaultm('mercator');
mstruct.origin = [38.89 -77.04 0];
mstruct = defaultm(mstruct);```

The following latitude and longitude data for the District of Columbia is obtained from the usastatelo shapefile:

```dc = shaperead('usastatelo', 'UseGeoCoords', true,...
'Selector',{@(name) strcmpi(name,'District of Columbia'),...
'Name'});
lat = [dc.Lat]';
lon = [dc.Lon]';
[lat lon]

ans =
38.9000  -77.0700
38.9500  -77.1200
39.0000  -77.0300
38.9000  -76.9000
38.7800  -77.0300
38.8000  -77.0200
38.8700  -77.0200
38.9000  -77.0700
38.9000  -77.0500
38.9000  -77.0700
NaN       NaN```

This data can be projected into Cartesian coordinates of the Mercator projection using the mfwdtran function:

```[x,y] = mfwdtran(mstruct,lat,lon);
[x y]

ans =
-0.0004    0.0002
-0.0011    0.0010
0.0001    0.0019
0.0019    0.0002
0.0001   -0.0019
0.0003   -0.0016
0.0003   -0.0003
-0.0004    0.0002
-0.0001    0.0002
-0.0004    0.0002
NaN       NaN```

To transform the projected x-y data back into the unprojected geographic system, use the minvtran function:

```[lat2,lon2] = minvtran(mstruct,x,y);
[lat2 lon2]

ans =
38.9000  -77.0700
38.9500  -77.1200
39.0000  -77.0300
38.9000  -76.9000
38.7800  -77.0300
38.8000  -77.0200
38.8700  -77.0200
38.9000  -77.0700
38.9000  -77.0500
38.9000  -77.0700
NaN       NaN```