earth.inc in Location 7.3

Trigonometry for calculating geographical distances. All function arguments and return values measure distances in metres and angles in degrees. The ellipsoid model is from the WGS-84 datum. Ka-Ping Yee, 2003-08-11

File

earth.inc

<?php

/**
 * @file
 * Trigonometry for calculating geographical distances.
 * All function arguments and return values measure distances in metres
 * and angles in degrees.  The ellipsoid model is from the WGS-84 datum.
 * Ka-Ping Yee, 2003-08-11
 */

/**
 * License clarification:
 *
 * On Feb 13, 2005, in message <[e-mail]>,
 * the creator of these routines, Ka-Ping Yee, authorized these routines to be
 * distributed under the GPL.
 */

// @codingStandardsIgnoreStart
// @todo cleanup.

//$earth_radius_semimajor = 6378137.0;

//$earth_flattening = 1/298.257223563;

//$earth_radius_semiminor = $earth_radius_semimajor * (1 - $earth_flattening);

//$earth_eccentricity_sq = 2*$earth_flattening - pow($earth_flattening, 2);

// I don't know what's up: PHP is hating on my global variables (commented out above),
// so I have to write functions that return them! (-Ankur)
// Commenting out the global variables above and replacing them with functions that
// return the same values is the only thing I changed since, for some reason, my
// PHP wasn't acknowledging these global variables.
// This library is an original implementation of UCB CS graduate student, Ka-Ping Yee (http://www.zesty.ca).
// @codingStandardsIgnoreEnd

/**
 * Earth redius semimajor.
 */
function earth_radius_semimajor() {
  return 6378137.0;
}

/**
 * Earth flattening.
 */
function earth_flattening() {
  return 1 / 298.257223563;
}

/**
 * Earth radius semiminor.
 */
function earth_radius_semiminor() {
  return earth_radius_semimajor() * (1 - earth_flattening());
}

/**
 * Earth ccentricity sq.
 */
function earth_eccentricity_sq() {
  return 2 * earth_flattening() - pow(earth_flattening(), 2);
}

/**
 * Earth redius.
 *
 * Latitudes in all of U. S.: from -7.2 (American Samoa) to 70.5 (Alaska).
 * Latitudes in continental U. S.: from 24.6 (Florida) to 49.0 (Washington).
 * Average latitude of all U. S. zipcodes: 37.9.
 */
function earth_radius($latitude = 37.9) {

  // Estimate the Earth's radius at a given latitude.
  // Default to an approximate average radius for the United States.
  $lat = deg2rad($latitude);
  $x = cos($lat) / earth_radius_semimajor();
  $y = sin($lat) / earth_radius_semiminor();
  return 1 / sqrt($x * $x + $y * $y);
}

/**
 * Earth xyz.
 */
function earth_xyz($longitude, $latitude, $height = 0) {

  // Convert longitude and latitude to earth-centered earth-fixed coordinates.
  // X axis is 0 long, 0 lat; Y axis is 90 deg E; Z axis is north pole.
  $long = deg2rad($longitude);
  $lat = deg2rad($latitude);
  $coslong = cos($long);
  $coslat = cos($lat);
  $sinlong = sin($long);
  $sinlat = sin($lat);
  $radius = earth_radius_semimajor() / sqrt(1 - earth_eccentricity_sq() * $sinlat * $sinlat);
  $x = ($radius + $height) * $coslat * $coslong;
  $y = ($radius + $height) * $coslat * $sinlong;
  $z = ($radius * (1 - earth_eccentricity_sq()) + $height) * $sinlat;
  return array(
    $x,
    $y,
    $z,
  );
}

/**
 * Earth arclength.
 */
function earth_arclength($angle, $latitude = 37.9) {

  // Convert a given angle to earth-surface distance.
  return deg2rad($angle) * earth_radius($latitude);
}

/**
 * Earth distance.
 */
function earth_distance($longitude1, $latitude1, $longitude2, $latitude2) {

  // Estimate the earth-surface distance between two locations.
  $long1 = deg2rad($longitude1);
  $lat1 = deg2rad($latitude1);
  $long2 = deg2rad($longitude2);
  $lat2 = deg2rad($latitude2);
  $radius = earth_radius(($latitude1 + $latitude2) / 2);
  $cosangle = cos($lat1) * cos($lat2) * (cos($long1) * cos($long2) + sin($long1) * sin($long2)) + sin($lat1) * sin($lat2);
  return acos($cosangle) * $radius;
}

/**
 * Returns the SQL fragment needed to add a column called 'distance' to a query that includes the location table.
 *
 * @param float $longitude
 *   The measurement point.
 *
 * @param float $latitude
 *   The measurement point.
 *
 * @param string $tbl_alias
 *   If necessary, the alias name of the location table to work from.  Only required when working with named {location} tables.
 *
 * @return string
 *   SQL fragment.
 */
function earth_distance_sql($longitude, $latitude, $tbl_alias = '') {

  // Make a SQL expression that estimates the distance to the given location.
  $long = deg2rad($longitude);
  $lat = deg2rad($latitude);
  $radius = earth_radius($latitude);

  // If the table alias is specified, add on the separator.
  $tbl_alias = empty($tbl_alias) ? $tbl_alias : $tbl_alias . '.';
  $coslong = cos($long);
  $coslat = cos($lat);
  $sinlong = sin($long);
  $sinlat = sin($lat);
  return "(COALESCE(ACOS({$coslat}*COS(RADIANS({$tbl_alias}latitude))*({$coslong}*COS(RADIANS({$tbl_alias}longitude)) + {$sinlong}*SIN(RADIANS({$tbl_alias}longitude))) + {$sinlat}*SIN(RADIANS({$tbl_alias}latitude))), 0.00000)*{$radius})";
}

/**
 * Earth longitude range.
 *
 * @todo This function uses earth_asin_safe so is not accurate for all possible
 * parameter combinations. This means this function doesn't work properly
 * for high distance values. This function needs to be re-written to work properly for
 * larger distance values.
 *
 * @see http://drupal.org/node/821628
 */
function earth_longitude_range($longitude, $latitude, $distance) {

  // Estimate the min and max longitudes within $distance of a given location.
  $long = deg2rad($longitude);
  $lat = deg2rad($latitude);
  $radius = earth_radius($latitude) * cos($lat);
  if ($radius > 0) {
    $angle = abs($distance / $radius);
    $angle = min($angle, pi());
  }
  else {
    $angle = pi();
  }
  $minlong = $long - $angle;
  $maxlong = $long + $angle;
  if ($minlong < -pi()) {
    $minlong = $minlong + pi() * 2;
  }
  if ($maxlong > pi()) {
    $maxlong = $maxlong - pi() * 2;
  }
  return array(
    rad2deg($minlong),
    rad2deg($maxlong),
  );
}

/**
 * Earth latitude range.
 */
function earth_latitude_range($longitude, $latitude, $distance) {

  // Estimate the min and max latitudes within $distance of a given location.
  $long = deg2rad($longitude);
  $lat = deg2rad($latitude);
  $radius = earth_radius($latitude);
  $angle = $distance / $radius;
  $minlat = $lat - $angle;
  $maxlat = $lat + $angle;
  $rightangle = pi() / 2;

  // Wrapped around the south pole.
  if ($minlat < -$rightangle) {
    $overshoot = -$minlat - $rightangle;
    $minlat = -$rightangle + $overshoot;
    if ($minlat > $maxlat) {
      $maxlat = $minlat;
    }
    $minlat = -$rightangle;
  }

  // Wrapped around the north pole.
  if ($maxlat > $rightangle) {
    $overshoot = $maxlat - $rightangle;
    $maxlat = $rightangle - $overshoot;
    if ($maxlat < $minlat) {
      $minlat = $maxlat;
    }
    $maxlat = $rightangle;
  }
  return array(
    rad2deg($minlat),
    rad2deg($maxlat),
  );
}

/**
 * This is a helper function to avoid errors when using the asin() PHP function.
 *
 * asin is only real for values between -1 and 1.
 * If a value outside that range is given it returns NAN (not a number), which
 * we don't want to happen.
 * So this just rounds values outside this range to -1 or 1 first.
 *
 * This means that calculations done using this function with $x outside the range
 * will not be accurate.  The alternative though is getting NAN, which is an error
 * and won't give accurate results anyway.
 */
function earth_asin_safe($x) {
  return asin(max(-1, min($x, 1)));
}

Functions

Name	Description
earth_arclength	Earth arclength.
earth_asin_safe	This is a helper function to avoid errors when using the asin() PHP function.
earth_distance	Earth distance.
earth_distance_sql	Returns the SQL fragment needed to add a column called 'distance' to a query that includes the location table.
earth_eccentricity_sq	Earth ccentricity sq.
earth_flattening	Earth flattening.
earth_latitude_range	Earth latitude range.
earth_longitude_range	Earth longitude range.
earth_radius	Earth redius.
earth_radius_semimajor	Earth redius semimajor.
earth_radius_semiminor	Earth radius semiminor.
earth_xyz	Earth xyz.