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package org.opentripplanner.common.geometry;
import static org.apache.commons.math3.util.FastMath.abs;
import static org.apache.commons.math3.util.FastMath.atan2;
import static org.apache.commons.math3.util.FastMath.cos;
import static org.apache.commons.math3.util.FastMath.sin;
import static org.apache.commons.math3.util.FastMath.sqrt;
import static org.apache.commons.math3.util.FastMath.toDegrees;
import static org.apache.commons.math3.util.FastMath.toRadians;
import org.apache.commons.math3.util.FastMath;
import org.locationtech.jts.geom.Coordinate;
import org.locationtech.jts.geom.Envelope;
import org.locationtech.jts.geom.LineString;
import org.locationtech.jts.geom.Point;
public abstract class SphericalDistanceLibrary {
public static final double RADIUS_OF_EARTH_IN_KM = 6371.01;
public static final double RADIUS_OF_EARTH_IN_M = RADIUS_OF_EARTH_IN_KM * 1000;
// Max admissible lat/lon delta for approximated distance computation
public static final double MAX_LAT_DELTA_DEG = 4.0;
public static final double MAX_LON_DELTA_DEG = 4.0;
// 1 / Max over-estimation error of approximated distance,
// for delta lat/lon in given range
public static final double MAX_ERR_INV = 0.999462;
public static final double distance(Coordinate from, Coordinate to) {
return distance(from.y, from.x, to.y, to.x);
}
public static final double fastDistance(Coordinate from, Coordinate to) {
return fastDistance(from.y, from.x, to.y, to.x);
}
public static final double fastDistance(Coordinate from, Coordinate to, double cosLat) {
double dLat = toRadians(from.y - to.y);
double dLon = toRadians(from.x - to.x) * cosLat;
return RADIUS_OF_EARTH_IN_M * sqrt(dLat * dLat + dLon * dLon);
}
/**
* Compute an (approximated) distance between a point and a linestring expressed in standard geographical
* coordinates (lon, lat in degrees).
* @param point The coordinates of the point (longitude, latitude degrees).
* @param lineString The set of points representing the polyline, in the same coordinate system.
* @return The (approximated) distance, in meters, between the point and the linestring.
*/
public static final double fastDistance(Coordinate point, LineString lineString) {
// Transform in equirectangular projection on sphere of radius 1,
// centered at point
double lat = Math.toRadians(point.y);
double cosLat = FastMath.cos(lat);
double lon = Math.toRadians(point.x) * cosLat;
Point point2 = GeometryUtils.getGeometryFactory().createPoint(new Coordinate(lon, lat));
LineString lineString2 = equirectangularProject(lineString, cosLat);
return lineString2.distance(point2) * RADIUS_OF_EARTH_IN_M;
}
/**
* Compute the (approximated) length of a polyline
* @param lineString The polyline in (longitude, latitude degrees).
* @return The (approximated) length, in meters, of the linestring.
*/
public static final double fastLength(LineString lineString) {
// Warn: do not use LineString.getCentroid() as it is broken
// for degenerated geometry (same first/last point).
Coordinate[] coordinates = lineString.getCoordinates();
double middleY = (coordinates[0].y + coordinates[coordinates.length - 1].y) / 2.0;
double cosLat = FastMath.cos(Math.toRadians(middleY));
return equirectangularProject(lineString, cosLat).getLength() * RADIUS_OF_EARTH_IN_M;
}
/**
* Compute the (approximated) length of a polyline, with known cos(lat).
* @param lineString The polyline in (longitude, latitude degrees).
* @return The (approximated) length, in meters, of the linestring.
*/
public static final double fastLength(LineString lineString, double cosLat) {
return equirectangularProject(lineString, cosLat).getLength() * RADIUS_OF_EARTH_IN_M;
}
/**
* Equirectangular project a polyline.
* @param lineString
* @param cosLat cos(lat) of the projection center point.
* @return The projected polyline. Coordinates in radians.
*/
private static LineString equirectangularProject(LineString lineString, double cosLat) {
Coordinate[] coords = lineString.getCoordinates();
Coordinate[] coords2 = new Coordinate[coords.length];
for (int i = 0; i < coords.length; i++) {
coords2[i] = new Coordinate(Math.toRadians(coords[i].x) * cosLat,
Math.toRadians(coords[i].y));
}
return GeometryUtils.getGeometryFactory().createLineString(coords2);
}
public static final double distance(double lat1, double lon1, double lat2, double lon2) {
return distance(lat1, lon1, lat2, lon2, RADIUS_OF_EARTH_IN_M);
}
/**
* Compute an (approximated) distance between two points, with a known cos(lat).
* Be careful, this is approximated and never check for the validity of input cos(lat).
*/
public static final double fastDistance(double lat1, double lon1, double lat2, double lon2) {
return fastDistance(lat1, lon1, lat2, lon2, RADIUS_OF_EARTH_IN_M);
}
public static final double distance(double lat1, double lon1, double lat2, double lon2,
double radius) {
// http://en.wikipedia.org/wiki/Great-circle_distance
lat1 = toRadians(lat1); // Theta-s
lon1 = toRadians(lon1); // Lambda-s
lat2 = toRadians(lat2); // Theta-f
lon2 = toRadians(lon2); // Lambda-f
double deltaLon = lon2 - lon1;
double y = sqrt(p2(cos(lat2) * sin(deltaLon))
+ p2(cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(deltaLon)));
double x = sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(deltaLon);
return radius * atan2(y, x);
}
/**
* Approximated, fast and under-estimated equirectangular distance between two points.
* Works only for small delta lat/lon, fall-back on exact distance if not the case.
* See: http://www.movable-type.co.uk/scripts/latlong.html
*/
public static final double fastDistance(double lat1, double lon1, double lat2, double lon2, double radius) {
if (abs(lat1 - lat2) > MAX_LAT_DELTA_DEG || abs(lon1 - lon2) > MAX_LON_DELTA_DEG) {
return distance(lat1, lon1, lat2, lon2, radius);
}
double dLat = toRadians(lat2 - lat1);
double dLon = toRadians(lon2 - lon1) * cos(toRadians((lat1 + lat2) / 2));
return radius * sqrt(dLat * dLat + dLon * dLon) * MAX_ERR_INV;
}
private static final double p2(double a) {
return a * a;
}
/**
* @param distanceMeters Distance in meters.
* @return The number of degree for the given distance. For degrees latitude, this is nearly correct. For degrees
* longitude, this is an overestimate because meridians converge toward the poles.
*/
public static double metersToDegrees(double distanceMeters) {
return 360 * distanceMeters / (2 * Math.PI * RADIUS_OF_EARTH_IN_M);
}
/**
* @return the approximate number of meters for the given number of degrees latitude. If degrees longitude are
* supplied, this is an overestimate anywhere off the equator because meridians converge toward the poles.
*/
public static double degreesLatitudeToMeters(double degreesLatitude) {
return (2 * Math.PI * RADIUS_OF_EARTH_IN_M) * degreesLatitude / 360;
}
/**
* @param distanceMeters Distance in meters.
* @param latDeg Latitude of center point, in degree.
* @return The number of longitude degree for the given distance. This is a slight overestimate
* as the number of degree of longitude for a given distance depends on the exact
* latitude.
*/
public static double metersToLonDegrees(double distanceMeters, double latDeg) {
double dLatDeg = 360 * distanceMeters / (2 * Math.PI * RADIUS_OF_EARTH_IN_M);
/*
* The computation below ensure that minCosLat is the minimum value of cos(lat) for lat in
* the range [lat-dLat, lat+dLat].
*/
double minCosLat;
if (latDeg > 0) {
minCosLat = FastMath.cos(FastMath.toRadians(latDeg + dLatDeg));
} else {
minCosLat = FastMath.cos(FastMath.toRadians(latDeg - dLatDeg));
}
return dLatDeg / minCosLat;
}
public static final Envelope bounds(double lat, double lon, double latDistance, double lonDistance) {
double radiusOfEarth = RADIUS_OF_EARTH_IN_M;
double latRadians = toRadians(lat);
double lonRadians = toRadians(lon);
double latRadius = radiusOfEarth;
double lonRadius = cos(latRadians) * radiusOfEarth;
double latOffset = latDistance / latRadius;
double lonOffset = lonDistance / lonRadius;
double latFrom = toDegrees(latRadians - latOffset);
double latTo = toDegrees(latRadians + latOffset);
double lonFrom = toDegrees(lonRadians - lonOffset);
double lonTo = toDegrees(lonRadians + lonOffset);
return new Envelope(new Coordinate(lonFrom, latFrom), new Coordinate(lonTo, latTo));
}
}
