Convert long/lat to pixel x/y on a given picture

Question

I have a city map of Moscow. We modified a Google Maps image with some artistic elements, but the relation between GPS coordinates and pixels remains the same.

Problem: How do I convert GPS coordinates from various data points we have into pixel coordinates in the image?

Ideally I can do this in Javascript, but PHP would be OK.

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I know that on small scales (for example on city scales) it to make simply enough (it is necessary to learn what geographic coordinates has one of picture corners, then to learn "price" of one pixel in geographic coordinates on a picture on axes OX and OY separately).

But on the big scales (country scale) "price" of one pixel will be not a constant, and will vary strongly enough and the method described above cannot be applied.

How to solve a problem on country scales?

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Update:

I do not use API Google Maps, I have only: geographic coordinates of the object (they are from google maps), I still have at my site a simple picture *. gif, in which I must draw a point corresponding geographic coordinates.

Answer 1

The key to all of this is understanding map projections. As others have pointed out, the cause of the distortion is the fact that the spherical (or more accurately ellipsoidal) earth is projected onto a plane.

In order to achieve your goal, you first must know two things about your data:

1. The projection your maps are in. If they are purely derived from Google Maps, then chances are they are using a spherical Mercator projection.
2. The geographic coordinate system your latitude/longitude coordinates are using. This can vary, because there are different ways of locating lat/longs on the globe. The most common GCS, used in most web-mapping applications and for GPS's, is WGS84.

I'm assuming your data is in these coordinate systems.

The spherical Mercator projection defines a coordinate pair in meters, for the surface of the earth. This means, for every lat/long coordinate there is a matching meter/meter coordinate. This enables you to do the conversion using the following procedure:

1. Find the WGS84 lat/long of the corners of the image.
2. Convert the WGS lat/longs to the spherical Mercator projection. There conversion tools out there, my favorite is to use the cs2cs tool that is part of the PROJ4 project.
3. You can safely do a simple linear transform to convert between points on the image, and points on the earth in the spherical Mercator projection, and back again.

In order to go from a WGS84 point to a pixel on the image, the procedure is now:

1. Project lat/lon to spherical Mercator. This can be done using the proj4js library.
2. Transform spherical Mercator coordinate into image pixel coordinate using the linear relationship discovered above.

You can use the proj4js library like this:

// include the library
<script src="lib/proj4js-combined.js"></script>  //adjust the path for your server
                                                 //or else use the compressed version
// creating source and destination Proj4js objects
// once initialized, these may be re-used as often as needed
var source = new Proj4js.Proj('EPSG:4326');    //source coordinates will be in Longitude/Latitude, WGS84
var dest = new Proj4js.Proj('EPSG:3785');     //destination coordinates in meters, global spherical mercators projection, see http://spatialreference.org/ref/epsg/3785/


// transforming point coordinates
var p = new Proj4js.Point(-76.0,45.0);   //any object will do as long as it has 'x' and 'y' properties
Proj4js.transform(source, dest, p);      //do the transformation.  x and y are modified in place

//p.x and p.y are now EPSG:3785 in meters