projinv

Unproject x-y map coordinates to latitude-longitude coordinates

Syntax

[lat,lon] = projinv(proj,x,y)

Description

[lat,lon] = projinv(proj,x,y) transforms the map coordinates specified by x and y in the projected coordinate reference system specified by proj to the latitude-longitude coordinates lat and lon. Specify proj using a projcrs object (since R2020b), a map projection structure, or a GeoTIFF information structure.

Examples

Unproject x-y Coordinates to Latitude-Longitude

Unproject x-y coordinates to latitude-longitude coordinates by specifying the projected CRS of the x-y coordinates. Then, display the latitude-longitude coordinates on geographic axes.

To do this, first import a shapefile containing the x- and y-coordinates of roads in Concord, MA. Get information about the shapefile as a structure. Find the projected CRS for the coordinates by accessing the CoordinateReferenceSystem field of the structure.

roads = shaperead('concord_roads.shp');
x = [roads.X];
y = [roads.Y];
info = shapeinfo('concord_roads.shp');
proj = info.CoordinateReferenceSystem;

Unproject the x-y coordinates to latitude-longitude coordinates.

[lat,lon] = projinv(proj,x,y);

Display the coordinates on geographic axes.

figure
geoplot(lat,lon)
hold on
geobasemap('streets')

The geographic CRS of the x-y coordinates used in this example is NAD83. You can find the geographic CRS that underlies a projected CRS by querying the GeographicCRS property.

proj.GeographicCRS.Name

ans = 
"NAD83"

The geographic CRS underlying the 'streets' basemap is WGS84. NAD83 and WGS84 are similar, but not identical. Therefore, at high zoom levels the coordinates and basemap may appear misaligned.

Input Arguments

proj — Map projection

projcrs object | scalar map projection structure | scalar GeoTIFF information structure

Map projection, specified as a projcrs object (since R2020b), a scalar map projection structure (mstruct), or a GeoTIFF information structure. For more information about map projection structures, see defaultm. For more information about GeoTIFF information structures, see geotiffinfo.

Data Types: struct

x — Projected x-coordinates

scalar value | vector | matrix | N-D array

Projected x-coordinates, specified as a scalar value, vector, matrix, or N-D array. The size of x and y must match.

Data Types: single | double

y — Projected y-coordinates

scalar value | vector | matrix | N-D array

Projected y-coordinates, specified as a scalar value, vector, matrix, or N-D array. The size of x and y must match.

Data Types: single | double

Output Arguments

lat — Geodetic latitudes

scalar value | vector | matrix | N-D array

Geodetic latitudes, returned as a scalar value, vector, matrix, or N-D array, in units of degrees.

The geographic CRS of lat matches the geographic CRS of proj. If proj is a projcrs object, then you can find its geographic CRS by querying its GeographicCRS property. For example, this code shows how to create a projcrs object from EPSG code 32610 and find the associated geographic CRS.

proj = projcrs(32610);
proj.GeographicCRS.Name

ans = 

    "WGS 84"

lon — Geodetic longitudes

scalar value | vector | matrix | N-D array

Geodetic longitudes, returned as a scalar value, vector, matrix, or N-D array, in units of degrees.

The geographic CRS of lat matches the geographic CRS of proj. If proj is a projcrs object, then you can find its geographic CRS by querying its GeographicCRS property. For example, this code shows how to create a projcrs object from EPSG code 32610 and find the associated geographic CRS.

proj = projcrs(32610);
proj.GeographicCRS.Name

ans = 

    "WGS 84"

Version History

Introduced before R2006a

R2022b: projinv shows improved performance on Windows with repeated use of projection

The projinv and projfwd functions show improved performance on Windows^® when used multiple times in the same MATLAB^® session with the same projcrs object or map projection structure as input.

For example, this code is about 1.67 times faster than in the previous release. The code:

• Gets the grid coordinates for a DTED file

• Projects and unprojects the coordinates using a projcrs object

• Gets the grid coordinates for a different DTED file

• Measures the time required to project and unproject the coordinates using the same projcrs object

function timingTest
    info1 = georasterinfo("n39_w106_3arc_v2.dt1");
    R1 = info1.RasterReference;
    [latGrid1,lonGrid1] = geographicGrid(R1);

    p = projcrs(4088);
    [xfwd1,yfwd1] = projfwd(p,latGrid1,lonGrid1);
    [latinv1,loninv1] = projinv(p,xfwd1,yfwd1);

    info2 = georasterinfo("n40_w106_3arc_v2.dt1");
    R2 = info2.RasterReference;
    [latGrid2,lonGrid2] = geographicGrid(R2);

    tic
    [xfwd2,yfwd2] = projfwd(p,latGrid2,lonGrid2);
    [latinv2,loninv2] = projinv(p,xfwd2,yfwd2);
    toc
end

The approximate execution times are:

• R2022a: 0.70 s

• R2022b: 0.42 s

This code was timed on a Windows 10 Intel^® Xeon^® CPU W-2133 @ 3.6 GHz test system, by calling the function timingTest.

R2020b: Unproject coordinates using projcrs objects and additional map projection structures

Unproject coordinates by specifying a projcrs object. A projcrs object enables you to transform coordinates using projection methods not available in earlier releases, such as Hotine Oblique Mercator.

Additionally, you can unproject coordinates by specifying a map projection structure with any valid mapprojection field. For a list of mapprojection field options, use the maplist or maps function.