/** Return the distance (measured along the surface of the sphere) to the given point. */
public S1Angle getDistance(final S2LatLng o) {
// This implements the Haversine formula, which is numerically stable for
// small distances but only gets about 8 digits of precision for very large
// distances (e.g. antipodal points). Note that 8 digits is still accurate
// to within about 10cm for a sphere the size of the Earth.
//
// This could be fixed with another sin() and cos() below, but at that point
// you might as well just convert both arguments to S2Points and compute the
// distance that way (which gives about 15 digits of accuracy for all
// distances).
double lat1 = lat().radians();
double lat2 = o.lat().radians();
double lng1 = lng().radians();
double lng2 = o.lng().radians();
double dlat = Math.sin(0.5 * (lat2 - lat1));
double dlng = Math.sin(0.5 * (lng2 - lng1));
double x = dlat * dlat + dlng * dlng * Math.cos(lat1) * Math.cos(lat2);
return S1Angle.radians(2 * Math.atan2(Math.sqrt(x), Math.sqrt(Math.max(0.0, 1.0 - x))));
// Return the distance (measured along the surface of the sphere) to the
// given S2LatLng. This is mathematically equivalent to:
//
// S1Angle::FromRadians(ToPoint().Angle(o.ToPoint())
//
// but this implementation is slightly more efficient.
}
/**
* Basic constructor. The latitude and longitude must be within the ranges allowed by is_valid()
* below.
*
* <p>TODO(dbeaumont): Make this a static factory method (fromLatLng() ?).
*/
public S2LatLng(S1Angle lat, S1Angle lng) {
this(lat.radians(), lng.radians());
}
public static S1Angle longitude(S2Point p) {
// Note that atan2(0, 0) is defined to be zero.
return S1Angle.radians(Math.atan2(p.get(1), p.get(0)));
}
public static S1Angle latitude(S2Point p) {
// We use atan2 rather than asin because the input vector is not necessarily
// unit length, and atan2 is much more accurate than asin near the poles.
return S1Angle.radians(
Math.atan2(p.get(2), Math.sqrt(p.get(0) * p.get(0) + p.get(1) * p.get(1))));
}
/** Returns the longitude of this point as a new S1Angle. */
public S1Angle lng() {
return S1Angle.radians(this.lngRadians);
}
/** Returns the latitude of this point as a new S1Angle. */
public S1Angle lat() {
return S1Angle.radians(this.latRadians);
}