[GIS] How to calculate latitude and longitude of a point in a static map

javalatitude longitudemapsopenstreetmap

Background: I have generated a static map (map.png) of a particular city using mapnik and osm data of the highest zoom level. I am able to zoom in and zoom out successfully using my Java program. It is an offline desktop application.

Question: I want to represent a point at a particular latitude and longitude on this map. How do I do it?

I went through the following references:
http://wiki.openstreetmap.org/wiki/Zoom_levels
http://wiki.openstreetmap.org/wiki/Slippy_map_tilenames#Resolution_and_Scale
How to plot a point on a static Google map [png]?

I'm still not able to understand how to plot it on a static map by calculating a specific latitude and longitude at a particular zoom level with the image having a specific pixel width and height.

Best Answer

from what I understand, you have a single ungeoreferenced image, and you want to find the extent.

This can be done in QGIS

QGIS - Using Capture Coordinate

If this is an urban map with details in the corners, you can manually match up the corners using the Capture coordinate plugin.

start with an empty project
Install the OpenLayers plugin (this goes in the Web menu), and use this to show OSM for the region around your city
Install the "Capture coordinate" capture plugin, and bring up the Capture coordinate panel using the Vector > Coordinate Capture. You might want to set the sampling to EPSG:4326 to get traditional latitude, longitude coordinates
For two corner points on your png (diagonally opposite), look at the corner of your png and find its position in OSM, panning and zooming as required.
click on 'start capture', then click on the point corresponding to the corner of your image
once you have two diagonally opposite corners' coordinates, it's now simple maths to interpolate a pixel position to/from lat, lon

QGIS - Using georeferencing

This is a little more advanced, but will give you results if it's not possible to exactly pick out where the corners are (for example, if it's empty ground or in the sea)

start with empty project
use OpenLayers plugin to display OSM as before
install the Georeferencer plugin
start it up with Raster > Georeferencer
load in your png raster (first icon)
find some landmark on your png as close as possible to one corner- a building, for example, or a road junction
click on add point, and in the dialog check 'from map canvas'. If you have a mouse wheel you can pan with that. Click on the corresponding place in the OSM map.
repeat for the other 3 corners
see the GCP table? Those are your coordinates ('ground control points')
click on Transformation settings, and set up where you want to save the raster. You might want to change the crs to EPSG:4326 if you want lat,lon.
click on the Run icon (green arrow)
you'll now have a georeferenced tiff.

There's quite a good step-by-step guide here, although it's a bit out of date.

Now if you open this geotiff (add as a raster layer) you go into properties and you'll see your extent.

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[GIS] How to “calculate” distance-to-ground of all 18 OSM zoom levels

Some ideas that can help you:

Web tile has a certain resolution (PPI, pixels per inch). You probably want to avoid displaying the tile as a texture that looses a lot of PPI. So a tile that is 256x256 probably wouldn't look too good shown as a 1024x1024 texture.
Each OSM zoom level has its own (approximate) map scale.
Since you say you'll show a flat Earth, you can still calculate the current map scale based on the distance of the observer from the Earth, the latitude the observer is on and the size of the screen.

Once you have the current map scale, you can calculate the zoom level (code taken from my project Maperitive):

public static float MapScaleToOsmZoomLevel(float mapScale, float latitude, float ppi)
{
    const float MetersPerInch = 2.54f / 100;

    const double EarthCircumference = EarthRadius * Math.PI * 2;
    double realLengthInMeters = EarthCircumference * Math.Cos (Deg2Rad (latitude));

    double zoomLevelExp = (realLengthInMeters*ppi) / (256*MetersPerInch*mapScale);

    return (float) Math.Log(zoomLevelExp, 2);
}

Now you have a zoom level as a real value and you can calculate the actual zoom level based on a "quality" setting - for example if you want a higher quality, you can use something like Math.Ceiling(zoom).

[GIS] locating latitude-longitude point in a piste-map with matrix transforms

If the image is in the least realistic--and it appears to be--then it represents a projection from a portion of Euclidean three-space onto a portion of two-space. We cannot expect this projection to have a nice mathematical formula, because it is likely the artist has introduced irrregular small distortions, but we can expect its formula to somewhat approximate formulas for such projections. These formulas tend to be linear or projective and they also tend to be simpler when Cartesian coordinates are used.

Therefore, what you should consider doing at the outset is this:

Convert all (lat, lon, elevation) values to geocentric (x, y, z) values.
Associated with each (x, y, z) value is a pair of image coordinates (u, v). We probably lose little by estimating u and v independently of each other, which reduces the problem to one of interpolating samples of a scalar function. The previous considerations suggest that you seek interpolating functions that locally are of the form
```
u = a x + b y + c z + d
```
(linear) or even
```
u = (a x + b y + c z + d) / (a' x + b' y + c' z + 1)
```
(projective) and similarly for v. This reduces the problem to one of performing an interpolation in three dimensions, which is sufficiently routine to give you access to a large body of methods and software.

Alternatively, you might consider triangulating the (x,y,z) points and interpolating their associated (u,v) values separately across the triangles; even a linear interpolation across each triangular face could do a pretty good job. This is a 3D analog of what ESRI's 3D Analyst does in two dimensions with TINs.

Please note, though, that unless you have the elevation of a given location, you cannot hope to plot it accurately on this map: changing the elevation will create a nearly vertical line on the map, whence your location could be plotted practically anywhere along this line. With considerable work you could solve this problem for points on the ground by first digitizing the evident discontinuities in the inverse projection--that is, representing the outlines of mountain ridges as polylines--and constructing a local inverse interpolator (respecting these breaklines) that associates to each (u,v) on the image a location (x,y,z) in the world. You could exploit this to identify which point along any vertical line has a (lat,lon) close to the one you started with.

Best Answer

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[GIS] How to “calculate” distance-to-ground of all 18 OSM zoom levels

[GIS] locating latitude-longitude point in a piste-map with matrix transforms

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