/*
* Copyright 2013 Google Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.google.maps.android;
import com.google.android.gms.maps.model.LatLng;
import java.util.List;
import static com.google.maps.android.MathUtil.*;
import static java.lang.Math.*;
public class SphericalUtil {
private SphericalUtil() {
}
/**
* Returns the heading from one LatLng to another LatLng. Headings are
* expressed in degrees clockwise from North within the range [-180,180).
*
* @return The heading in degrees clockwise from north.
*/
public static double computeHeading(LatLng from, LatLng to) {
// http://williams.best.vwh.net/avform.htm#Crs
double fromLat = toRadians(from.latitude);
double fromLng = toRadians(from.longitude);
double toLat = toRadians(to.latitude);
double toLng = toRadians(to.longitude);
double dLng = toLng - fromLng;
double heading = atan2(
sin(dLng) * cos(toLat),
cos(fromLat) * sin(toLat) - sin(fromLat) * cos(toLat) * cos(dLng));
return wrap(toDegrees(heading), -180, 180);
}
/**
* Returns the LatLng resulting from moving a distance from an origin
* in the specified heading (expressed in degrees clockwise from north).
*
* @param from The LatLng from which to start.
* @param distance The distance to travel.
* @param heading The heading in degrees clockwise from north.
*/
public static LatLng computeOffset(LatLng from, double distance, double heading) {
distance /= EARTH_RADIUS;
heading = toRadians(heading);
// http://williams.best.vwh.net/avform.htm#LL
double fromLat = toRadians(from.latitude);
double fromLng = toRadians(from.longitude);
double cosDistance = cos(distance);
double sinDistance = sin(distance);
double sinFromLat = sin(fromLat);
double cosFromLat = cos(fromLat);
double sinLat = cosDistance * sinFromLat + sinDistance * cosFromLat * cos(heading);
double dLng = atan2(
sinDistance * cosFromLat * sin(heading),
cosDistance - sinFromLat * sinLat);
return new LatLng(toDegrees(asin(sinLat)), toDegrees(fromLng + dLng));
}
/**
* Returns the location of origin when provided with a LatLng destination,
* meters travelled and original heading. Headings are expressed in degrees
* clockwise from North. This function returns null when no solution is
* available.
*
* @param to The destination LatLng.
* @param distance The distance travelled, in meters.
* @param heading The heading in degrees clockwise from north.
*/
public static LatLng computeOffsetOrigin(LatLng to, double distance, double heading) {
heading = toRadians(heading);
distance /= EARTH_RADIUS;
// http://lists.maptools.org/pipermail/proj/2008-October/003939.html
double n1 = cos(distance);
double n2 = sin(distance) * cos(heading);
double n3 = sin(distance) * sin(heading);
double n4 = sin(toRadians(to.latitude));
// There are two solutions for b. b = n2 * n4 +/- sqrt(), one solution results
// in the latitude outside the [-90, 90] range. We first try one solution and
// back off to the other if we are outside that range.
double n12 = n1 * n1;
double discriminant = n2 * n2 * n12 + n12 * n12 - n12 * n4 * n4;
if (discriminant < 0) {
// No real solution which would make sense in LatLng-space.
return null;
}
double b = n2 * n4 + sqrt(discriminant);
b /= n1 * n1 + n2 * n2;
double a = (n4 - n2 * b) / n1;
double fromLatRadians = atan2(a, b);
if (fromLatRadians < -PI / 2 || fromLatRadians > PI / 2) {
b = n2 * n4 - sqrt(discriminant);
b /= n1 * n1 + n2 * n2;
fromLatRadians = atan2(a, b);
}
if (fromLatRadians < -PI / 2 || fromLatRadians > PI / 2) {
// No solution which would make sense in LatLng-space.
return null;
}
double fromLngRadians = toRadians(to.longitude) -
atan2(n3, n1 * cos(fromLatRadians) - n2 * sin(fromLatRadians));
return new LatLng(toDegrees(fromLatRadians), toDegrees(fromLngRadians));
}
/**
* Returns the LatLng which lies the given fraction of the way between the
* origin LatLng and the destination LatLng.
*
* @param from The LatLng from which to start.
* @param to The LatLng toward which to travel.
* @param fraction A fraction of the distance to travel.
* @return The interpolated LatLng.
*/
public static LatLng interpolate(LatLng from, LatLng to, double fraction) {
// http://en.wikipedia.org/wiki/Slerp
double fromLat = toRadians(from.latitude);
double fromLng = toRadians(from.longitude);
double toLat = toRadians(to.latitude);
double toLng = toRadians(to.longitude);
double cosFromLat = cos(fromLat);
double cosToLat = cos(toLat);
// Computes Spherical interpolation coefficients.
double angle = computeAngleBetween(from, to);
double sinAngle = sin(angle);
if (sinAngle < 1E-6) {
return new LatLng(
from.latitude + fraction * (to.latitude - from.latitude),
from.longitude + fraction * (to.longitude - from.longitude));
}
double a = sin((1 - fraction) * angle) / sinAngle;
double b = sin(fraction * angle) / sinAngle;
// Converts from polar to vector and interpolate.
double x = a * cosFromLat * cos(fromLng) + b * cosToLat * cos(toLng);
double y = a * cosFromLat * sin(fromLng) + b * cosToLat * sin(toLng);
double z = a * sin(fromLat) + b * sin(toLat);
// Converts interpolated vector back to polar.
double lat = atan2(z, sqrt(x * x + y * y));
double lng = atan2(y, x);
return new LatLng(toDegrees(lat), toDegrees(lng));
}
/**
* Returns distance on the unit sphere; the arguments are in radians.
*/
private static double distanceRadians(double lat1, double lng1, double lat2, double lng2) {
return arcHav(havDistance(lat1, lat2, lng1 - lng2));
}
/**
* Returns the angle between two LatLngs, in radians. This is the same as the distance
* on the unit sphere.
*/
static double computeAngleBetween(LatLng from, LatLng to) {
return distanceRadians(toRadians(from.latitude), toRadians(from.longitude),
toRadians(to.latitude), toRadians(to.longitude));
}
/**
* Returns the distance between two LatLngs, in meters.
*/
public static double computeDistanceBetween(LatLng from, LatLng to) {
return computeAngleBetween(from, to) * EARTH_RADIUS;
}
/**
* Returns the length of the given path, in meters, on Earth.
*/
public static double computeLength(List<LatLng> path) {
if (path.size() < 2) {
return 0;
}
double length = 0;
LatLng prev = path.get(0);
double prevLat = toRadians(prev.latitude);
double prevLng = toRadians(prev.longitude);
for (LatLng point : path) {
double lat = toRadians(point.latitude);
double lng = toRadians(point.longitude);
length += distanceRadians(prevLat, prevLng, lat, lng);
prevLat = lat;
prevLng = lng;
}
return length * EARTH_RADIUS;
}
/**
* Returns the area of a closed path on Earth.
*
* @param path A closed path.
* @return The path's area in square meters.
*/
public static double computeArea(List<LatLng> path) {
return abs(computeSignedArea(path));
}
/**
* Returns the signed area of a closed path on Earth. The sign of the area may be used to
* determine the orientation of the path.
* "inside" is the surface that does not contain the South Pole.
*
* @param path A closed path.
* @return The loop's area in square meters.
*/
public static double computeSignedArea(List<LatLng> path) {
return computeSignedArea(path, EARTH_RADIUS);
}
/**
* Returns the signed area of a closed path on a sphere of given radius.
* The computed area uses the same units as the radius squared.
* Used by SphericalUtilTest.
*/
static double computeSignedArea(List<LatLng> path, double radius) {
int size = path.size();
if (size < 3) {
return 0;
}
double total = 0;
LatLng prev = path.get(size - 1);
double prevTanLat = tan((PI / 2 - toRadians(prev.latitude)) / 2);
double prevLng = toRadians(prev.longitude);
// For each edge, accumulate the signed area of the triangle formed by the North Pole
// and that edge ("polar triangle").
for (LatLng point : path) {
double tanLat = tan((PI / 2 - toRadians(point.latitude)) / 2);
double lng = toRadians(point.longitude);
total += polarTriangleArea(tanLat, lng, prevTanLat, prevLng);
prevTanLat = tanLat;
prevLng = lng;
}
return total * (radius * radius);
}
/**
* Returns the signed area of a triangle which has North Pole as a vertex.
* Formula derived from "Area of a spherical triangle given two edges and the included angle"
* as per "Spherical Trigonometry" by Todhunter, page 71, section 103, point 2.
* See http://books.google.com/books?id=3uBHAAAAIAAJ&pg=PA71
* The arguments named "tan" are tan((pi/2 - latitude)/2).
*/
private static double polarTriangleArea(double tan1, double lng1, double tan2, double lng2) {
double deltaLng = lng1 - lng2;
double t = tan1 * tan2;
return 2 * atan2(t * sin(deltaLng), 1 + t * cos(deltaLng));
}
}
