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<?php namespace GeometryLibrary;
/*
* Copyright 2013 Google Inc.
* https://github.com/googlemaps/android-maps-utils/blob/master/library/src/com/google/maps/android/SphericalUtil.java
*
* 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.
*/
use GeometryLibrary\MathUtil;
class 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 function computeHeading($from, $to) {
// http://williams.best.vwh.net/avform.htm#Crs
$fromLat = deg2rad($from['lat']);
$fromLng = deg2rad($from['lng']);
$toLat = deg2rad($to['lat']);
$toLng = deg2rad($to['lng']);
$dLng = $toLng - $fromLng;
$heading = atan2(
sin($dLng) * cos($toLat),
cos($fromLat) * sin($toLat) - sin($fromLat) * cos($toLat) * cos($dLng));
return MathUtil::wrap(rad2deg($heading), -180, 180);
}
/**
* Returns the LatLng resulting from moving a distance from an origin
* in the specified heading (expressed in degrees clockwise from north).
* @param from The LatLng from which to start.
* @param distance The distance to travel.
* @param heading The heading in degrees clockwise from north.
*/
public static function computeOffset($from, $distance, $heading) {
$distance /= MathUtil::$earth_radius;
$heading = deg2rad($heading);
// http://williams.best.vwh.net/avform.htm#LL
$fromLat = deg2rad($from['lat']);
$fromLng = deg2rad($from['lng']);
$cosDistance = cos($distance);
$sinDistance = sin($distance);
$sinFromLat = sin($fromLat);
$cosFromLat = cos($fromLat);
$sinLat = $cosDistance * $sinFromLat + $sinDistance * $cosFromLat * cos($heading);
$dLng = atan2(
$sinDistance * $cosFromLat * sin($heading),
$cosDistance - $sinFromLat * $sinLat);
return ['lat' => rad2deg(asin($sinLat)), 'lng' =>rad2deg($fromLng + $dLng)];
}
/**
* Returns the location of origin when provided with a LatLng destination,
* meters travelled and original heading. Headings are expressed in degrees
* clockwise from North. This function returns null when no solution is
* available.
* @param to The destination LatLng.
* @param distance The distance travelled, in meters.
* @param heading The heading in degrees clockwise from north.
*/
public static function computeOffsetOrigin($to, $distance, $heading) {
$heading = deg2rad($heading);
$distance /= MathUtil::$earth_radius;
// http://lists.maptools.org/pipermail/proj/2008-October/003939.html
$n1 = cos($distance);
$n2 = sin($distance) * cos($heading);
$n3 = sin($distance) * sin($heading);
$n4 = sin(rad2deg($to['lat']));
// 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.
$n12 = $n1 * $n1;
$discriminant = $n2 * $n2 * $n12 + $n12 * $n12 - $n12 * $n4 * $n4;
if ($discriminant < 0) {
// No real solution which would make sense in LatLng-space.
return null;
}
$b = $n2 * $n4 + sqrt($discriminant);
$b /= $n1 * $n1 + $n2 * $n2;
$a = ($n4 - $n2 * $b) / $n1;
$fromLatRadians = atan2($a, $b);
if ($fromLatRadians < -M_PI / 2 || $fromLatRadians > M_PI / 2) {
$b = $n2 * $n4 - sqrt($discriminant);
$b /= $n1 * $n1 + $n2 * $n2;
$fromLatRadians = atan2($a, $b);
}
if ($fromLatRadians < -M_PI / 2 || $fromLatRadians > M_PI / 2) {
// No solution which would make sense in LatLng-space.
return null;
}
$fromLngRadians = rad2deg($to['lng']) -
atan2($n3, $n1 * cos($fromLatRadians) - $n2 * sin($fromLatRadians));
return ['lat' => rad2deg($fromLatRadians), 'lng' => rad2deg($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 function interpolate($from, $to, $fraction) {
// http://en.wikipedia.org/wiki/Slerp
$fromLat = deg2rad($from['lat']);
$fromLng = deg2rad($from['lng']);
$toLat = deg2rad($to['lat']);
$toLng = deg2rad($to['lng']);
$cosFromLat = cos($fromLat);
$cosToLat = cos($toLat);
// Computes Spherical interpolation coefficients.
$angle = self::computeAngleBetween($from, $to);
$sinAngle = sin($angle);
if ($sinAngle < 1E-6) {
return [
'lat' => $from['lat'] + $fraction * ($to['lat'] - $from['lat']),
'lng' => $from['lng'] + $fraction * ($to['lng'] - $from['lng'])
];
}
$a = sin((1 - $fraction) * $angle) / $sinAngle;
$b = sin($fraction * $angle) / $sinAngle;
// Converts from polar to vector and interpolate.
$x = $a * $cosFromLat * cos($fromLng) + $b * $cosToLat * cos($toLng);
$y = $a * $cosFromLat * sin($fromLng) + $b * $cosToLat * sin($toLng);
$z = $a * sin($fromLat) + $b * sin($toLat);
// Converts interpolated vector back to polar.
$lat = atan2($z, sqrt($x * $x + $y * $y));
$lng = atan2($y, $x);
return [ 'lat' => rad2deg($lat), 'lng' => rad2deg($lng)];
}
/**
* Returns distance on the unit sphere; the arguments are in radians.
*/
private static function distanceRadians( $lat1, $lng1, $lat2, $lng2) {
return MathUtil::arcHav(MathUtil::havDistance($lat1, $lat2, $lng1 - $lng2));
}
/**
* Returns the angle between two LatLngs, in radians. This is the same as the distance
* on the unit sphere.
*/
private static function computeAngleBetween($from, $to) {
return self::distanceRadians(deg2rad($from['lat']), deg2rad($from['lng']),
deg2rad($to['lat']), deg2rad($to['lng']));
}
/**
* Returns the distance between two LatLngs, in meters.
*/
public static function computeDistanceBetween( $from, $to) {
return self::computeAngleBetween($from, $to) * MathUtil::$earth_radius;
}
/**
* Returns the length of the given path, in meters, on Earth.
*/
public static function computeLength($path) {
if (count($path) < 2) {
return 0;
}
$length = 0;
$prev = $path[0];
$prevLat = deg2rad($prev['lat']);
$prevLng = deg2rad($prev['lng']);
foreach($path as $point) {
$lat = deg2rad($point['lat']);
$lng = deg2rad($point['lng']);
$length += self::distanceRadians($prevLat, $prevLng, $lat, $lng);
$prevLat = $lat;
$prevLng = $lng;
}
return $length * MathUtil::$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 function computeArea($path) {
return abs(self::computeSignedArea($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 function computeSignedArea($path) {
return self::computeSignedAreaP($path, MathUtil::$earth_radius);
}
/**
* Returns the signed area of a closed path on a sphere of given radius.
* The computed area uses the same units as the radius squared.
* Used by SphericalUtilTest.
*/
private static function computeSignedAreaP($path, $radius) {
$size = count($path);
if ($size < 3) { return 0; }
$total = 0;
$prev = $path[$size - 1];
$prevTanLat = tan((M_PI / 2 - deg2rad($prev['lat'])) / 2);
$prevLng = deg2rad($prev['lng']);
// For each edge, accumulate the signed area of the triangle formed by the North Pole
// and that edge ("polar triangle").
foreach($path as $point) {
$tanLat = tan((M_PI / 2 - deg2rad($point['lat'])) / 2);
$lng = deg2rad($point['lng']);
$total += self::polarTriangleArea($tanLat, $lng, $prevTanLat, $prevLng);
$prevTanLat = $tanLat;
$prevLng = $lng;
}
return $total * ($radius * $radius);
}
/**
* Returns the signed area of a triangle which has North Pole as a vertex.
* Formula derived from "Area of a spherical triangle given two edges and the included angle"
* as per "Spherical Trigonometry" by Todhunter, page 71, section 103, point 2.
* See http://books.google.com/books?id=3uBHAAAAIAAJ&pg=PA71
* The arguments named "tan" are tan((pi/2 - latitude)/2).
*/
private static function polarTriangleArea($tan1, $lng1, $tan2, $lng2) {
$deltaLng = $lng1 - $lng2;
$t = $tan1 * $tan2;
return 2 * atan2($t * sin($deltaLng), 1 + $t * cos($deltaLng));
}
}
?>