How to plot a GPS location on an image being used as a map?

Question

I have images of malls that I need to use as maps for an app I am making. I have the GPS lat/long of the bottom corners of the map and I figured out the distance from the bottom GPS coordinates to what would be the top of the map image. How ever these are not straight up and down linear maps meaning I can't just plot my lat and long all nice and neat.

I've tried using various formulas and I'm so close but I can't plot the top lat and long of the top left and right of the map. So far this is what I have:

double distanceFromLeftToRightGPS = bottomLeft.distanceTo(bottomRight);
double bearingleftToRight= bottomLeft.bearingTo(bottomRight);

double distmapFromLeftToRightImg = map.getWidth();
double distmapFromTopToBottomImg = map.getHeight();

double percentageValueOfTopToBottomImg = (distmapFromTopToBottomImg * 100)
        / distmapFromLeftToRightImg;
double distanceFromTopToBottomGPS = (percentageValueOfTopToBottomImg * 0.01)
        * distanceFromLeftToRightGPS;

double bearingToTopFromBottom = -90;
double lat1 = Math.toRadians(bottomLeft.getLatitude());
double lon1 = Math.toRadians(bottomLeft.getLongitude());

double dist = (distanceFromTopToBottomGPS/1000f)/6371.0f;

double lat2 = Math.asin(Math.sin(lat1) * Math.cos(dist)
        + Math.cos(lat1) * Math.sin(dist) * Math.cos(bearingToTopFromBottom));

double a = Math.atan2(Math.sin(bearingToTopFromBottom) * Math.sin(dist)
        * Math.cos(lat1), Math.cos(dist) - Math.sin(lat1) * Math.sin(lat2));

System.out.println("a = " +  a);
double lon2 = lon1 + a;

lon2 = (lon2 + 3 * Math.PI) % (2 * Math.PI) - Math.PI;

System.out.println("Latitude = " + Math.toDegrees(lat2) + "\nLongitude = "
        + Math.toDegrees(lon2));

This gets me oh so close but the end location is off from where it really should be. I'm also not sure what bearing I should be using to look to what would be up from the bottom of the map. If anyone else has some info on how to get this to work that would be awesome.

Answer 1

You need to identify 3 points on the map with their lat/lon coordinates. Then use the Helmert Transformation.
Here on SO there are some post for "Helmert" transformation.

Answer 2

These two methods where the solution I came up with from some other posts here on SO. If you have a top left GPS coord and a bottom right GPS coord for the top left and bottom right corners of your map then using these two methods you can figure out where to draw your third GPS coord on the map. These will be as acurate as your top left and bottom right GPS coords are. I then draw the third point on the bitmap using a canvas.

public final static double OneEightyDeg = 180.0d;
public static double ImageSizeW, ImageSizeH ;

getSizesFromBitmap(ImageSizeW, ImageSizeH);


public double getCurrentPixelY(Location upperLeft, Location lowerRight, Location current) {
    double hypotenuse = upperLeft.distanceTo(current);
    double bearing = upperLeft.bearingTo(current);
    double currentDistanceY = Math.cos(bearing * Math.PI / OneEightyDeg) * hypotenuse;
    //                           "percentage to mark the position"
    double totalHypotenuse = upperLeft.distanceTo(lowerRight);
    double totalDistanceY = totalHypotenuse * Math.cos(upperLeft.bearingTo(lowerRight) * Math.PI / OneEightyDeg);
    double currentPixelY = currentDistanceY / totalDistanceY * ImageSizeH;

    return currentPixelY;
}

public double getCurrentPixelX(Location upperLeft, Location lowerRight, Location current) {
    double hypotenuse = upperLeft.distanceTo(current);
    double bearing = upperLeft.bearingTo(current);
    double currentDistanceX = Math.sin(bearing * Math.PI / OneEightyDeg) * hypotenuse;
    //                           "percentage to mark the position"
    double totalHypotenuse = upperLeft.distanceTo(lowerRight);
    double totalDistanceX = totalHypotenuse * Math.sin(upperLeft.bearingTo(lowerRight) * Math.PI / OneEightyDeg);
    double currentPixelX = currentDistanceX / totalDistanceX * ImageSizeW;

    return currentPixelX;
}