Основываясь на математике в ответ Криса Broadfoot в выше и some other code on Stack Overflow for the Mercator Projection, я получил эту
public class MercatorProjection implements Projection {
private static final double DEFAULT_PROJECTION_WIDTH = 256;
private static final double DEFAULT_PROJECTION_HEIGHT = 256;
private double centerLatitude;
private double centerLongitude;
private int areaWidthPx;
private int areaHeightPx;
// the scale that we would need for the a projection to fit the given area into a world view (1 = global, expect it to be > 1)
private double areaScale;
private double projectionWidth;
private double projectionHeight;
private double pixelsPerLonDegree;
private double pixelsPerLonRadian;
private double projectionCenterPx;
private double projectionCenterPy;
public MercatorProjection(
double centerLatitude,
double centerLongitude,
int areaWidthPx,
int areaHeightPx,
double areaScale
) {
this.centerLatitude = centerLatitude;
this.centerLongitude = centerLongitude;
this.areaWidthPx = areaWidthPx;
this.areaHeightPx = areaHeightPx;
this.areaScale = areaScale;
// TODO stretch the projection to match to deformity at the center lat/lon?
this.projectionWidth = DEFAULT_PROJECTION_WIDTH;
this.projectionHeight = DEFAULT_PROJECTION_HEIGHT;
this.pixelsPerLonDegree = this.projectionWidth/360;
this.pixelsPerLonRadian = this.projectionWidth/(2 * Math.PI);
Point centerPoint = projectLocation(this.centerLatitude, this.centerLongitude);
this.projectionCenterPx = centerPoint.x * this.areaScale;
this.projectionCenterPy = centerPoint.y * this.areaScale;
}
@Override
public Location getLocation(int px, int py) {
double x = this.projectionCenterPx + (px - this.areaWidthPx/2);
double y = this.projectionCenterPy + (py - this.areaHeightPx/2);
return projectPx(x/this.areaScale, y/this.areaScale);
}
@Override
public Point getPoint(double latitude, double longitude) {
Point point = projectLocation(latitude, longitude);
double x = (point.x * this.areaScale - this.projectionCenterPx) + this.areaWidthPx/2;
double y = (point.y * this.areaScale - this.projectionCenterPy) + this.areaHeightPx/2;
return new Point(x, y);
}
// from https://stackoverflow.com/questions/12507274/how-to-get-bounds-of-a-google-static-map
Location projectPx(double px, double py) {
final double longitude = (px - this.projectionWidth/2)/this.pixelsPerLonDegree;
final double latitudeRadians = (py - this.projectionHeight/2)/-this.pixelsPerLonRadian;
final double latitude = rad2deg(2 * Math.atan(Math.exp(latitudeRadians)) - Math.PI/2);
return new Location() {
@Override
public double getLatitude() {
return latitude;
}
@Override
public double getLongitude() {
return longitude;
}
};
}
Point projectLocation(double latitude, double longitude) {
double px = this.projectionWidth/2 + longitude * this.pixelsPerLonDegree;
double siny = Math.sin(deg2rad(latitude));
double py = this.projectionHeight/2 + 0.5 * Math.log((1 + siny)/(1 - siny)) * -this.pixelsPerLonRadian;
Point result = new org.opencv.core.Point(px, py);
return result;
}
private double rad2deg(double rad) {
return (rad * 180)/Math.PI;
}
private double deg2rad(double deg) {
return (deg * Math.PI)/180;
}
}
Вот тестовый модуль для оригинального ответа
public class MercatorProjectionTest {
@Test
public void testExample() {
// tests against values in https://stackoverflow.com/questions/10442066/getting-lon-lat-from-pixel-coords-in-google-static-map
double centerLatitude = 47;
double centerLongitude = 1.5;
int areaWidth = 480;
int areaHeight = 480;
// google (static) maps zoom level
int zoom = 5;
MercatorProjection projection = new MercatorProjection(
centerLatitude,
centerLongitude,
areaWidth,
areaHeight,
Math.pow(2, zoom)
);
Point centerPoint = projection.projectLocation(centerLatitude, centerLongitude);
Assert.assertEquals(129.06666666666666, centerPoint.x, 0.001);
Assert.assertEquals(90.04191318303863, centerPoint.y, 0.001);
Location topLeftByProjection = projection.projectPx(127.1875, 82.53125);
Assert.assertEquals(53.72271667491848, topLeftByProjection.getLatitude(), 0.001);
Assert.assertEquals(-1.142578125, topLeftByProjection.getLongitude(), 0.001);
// NOTE sample has some pretty serious rounding errors
Location topLeftByPixel = projection.getLocation(0, 0);
Assert.assertEquals(53.72271667491848, topLeftByPixel.getLatitude(), 0.05);
// the math for this is wrong in the sample (see comments)
Assert.assertEquals(-9, topLeftByPixel.getLongitude(), 0.05);
Point reverseTopLeftBase = projection.projectLocation(topLeftByPixel.getLatitude(), topLeftByPixel.getLongitude());
Assert.assertEquals(121.5625, reverseTopLeftBase.x, 0.1);
Assert.assertEquals(82.53125, reverseTopLeftBase.y, 0.1);
Point reverseTopLeft = projection.getPoint(topLeftByPixel.getLatitude(), topLeftByPixel.getLongitude());
Assert.assertEquals(0, reverseTopLeft.x, 0.001);
Assert.assertEquals(0, reverseTopLeft.y, 0.001);
Location bottomRightLocation = projection.getLocation(areaWidth, areaHeight);
Point bottomRight = projection.getPoint(bottomRightLocation.getLatitude(), bottomRightLocation.getLongitude());
Assert.assertEquals(areaWidth, bottomRight.x, 0.001);
Assert.assertEquals(areaHeight, bottomRight.y, 0.001);
}
}
Если вы (скажем,), работая с аэрофотосъемкой, я чувствую, что алгоритм не учитывает растягивающий эффект проекции меркатора, поэтому он может потерять точность, если ваша область интереса не является относительно близкой к экватору uator. Думаю, вы могли бы приблизить его, умножив ваши координаты x на cos (широта) центра?
У вас есть ссылка на страницу, где вы узнали о проспекте Меркатора? –