How to find the distance of coordinates between two points

This article shows how to find the straight line distance between two points from their latitude and longitude.

What is latitude and longitude?
Algorithm for finding a straight line distance from latitude and longitude
Finally

What is latitude and longitude?

If you have arrived here, there is no need to explain it now, but I will explain it just in case.
Latitude and longitude are a coordinate system that expresses our position on the earth. Latitude is the angle from the equator, and longitude is the angle from the meridian line passing through the site of Greenwich Observatory in England.
Some people may find it easier to understand if they remember that longitude is in the x-direction and latitude is in the y-direction.
Using these values, we can calculate the distance between two points on the earth.

Algorithm for finding a straight line distance from latitude and longitude

Several algorithms exist to determine linear distances from latitude and longitude.
These methods can be used depending on the shape of the earth and accuracy requirements.
This article describes three typical types.

Hybeny’s Distance Formula

It is obtained from the commonly used Hybeny’s distance formula.

	/**
	* ２地点間の距離(m)を求める
	* ヒュベニの公式から求めるバージョン
	*
	* @param float $lat1 緯度（始点）
	* @param float $lon1 経度（始点）
	* @param float $lat2 緯度(終点)
	* @param float $lon2 経度(終点)
	* @param boolean $mode 測地系 true:世界(default) false:日本
	* @return float 距離(m)
	*/
	function distance($lat1, $lon1, $lat2, $lon2, $mode=true)
	{
	// 緯度経度をラジアンに変換
	$radLat1 = deg2rad($lat1); // 緯度（始点）
	$radLon1 = deg2rad($lon1); // 経度（始点）
	$radLat2 = deg2rad($lat2); // 緯度(終点)
	$radLon2 = deg2rad($lon2); // 経度(終点)

	// 緯度差
	$radLatDiff = abs($radLat1 - $radLat2);

	// 経度差算(距離の短い方を採用する)
	$radLonDiff = abs($radLon1 - $radLon2);
	$radLonDiff = min($radLonDiff, 2 * pi() - $radLonDiff);

	// 平均緯度
	$radLatAve = ($radLat1 + $radLat2) / 2.0;

	// 測地系による値の違い
	$a = $mode ? 6378137.0 : 6377397.155; // 赤道半径
	$b = $mode ? 6356752.314140356 : 6356078.963; // 極半径
	//$e2 = ($a * $a - $b * $b) / ($a * $a);
	$e2 = $mode ? 0.00669438002301188 : 0.00667436061028297; // 第一離心率^2
	//$a1e2 = $a * (1 - $e2);
	$a1e2 = $mode ? 6335439.32708317 : 6334832.10663254; // 赤道上の子午線曲率半径

	$sinLat = sin($radLatAve);
	$W2 = 1.0 - $e2 * ($sinLat * $sinLat);
	$M = $a1e2 / (sqrt($W2) * $W2); // 子午線曲率半径M
	$N = $a / sqrt($W2); // 卯酉線曲率半径

	$t1 = $M * $radLatDiff;
	$t2 = $N * cos($radLatAve) * $radLonDiff;
	$dist = sqrt(($t1 * $t1) + ($t2 * $t2));

	return $dist;
	}

view raw HybenysDistanceFormula.php hosted with ❤ by GitHub

Haversine Formula

The GoogleMapAPI geometory.computeDistanceBetween uses this formula.
In reality, the earth is not an exact sphere but an ellipsoid, so there is an error, but the formula is simple and can be calculated quickly.

	/**
	* ２地点間の距離を求める
	* GoogleMapAPIのgeometory.computeDistanceBetweenのロジック
	* 浮動小数点の精度が足りないためGoogleより桁数が少ないかもしれません
	*
	* @param float $lat1 緯度(始点)
	* @param float $lon1 経度(始点)
	* @param float $lat2 緯度(終点)
	* @param float $lon2 経度(終点)
	* @return float 距離(m)
	*/
	public static function google_distance($lat1, $lon1, $lat2, $lon2) {
	// 緯度経度をラジアンに変換
	$radLat1 = deg2rad($lat1); // 緯度(始点)
	$radLon1 = deg2rad($lon1); // 経度(始点)
	$radLat2 = deg2rad($lat2); // 緯度(終点)
	$radLon2 = deg2rad($lon2); // 経度(終点)

	$r = 6378137.0; // 赤道半径

	$averageLat = ($radLat1 - $radLat2) / 2;
	$averageLon = ($radLon1 - $radLon2) / 2;
	return $r * 2 * asin(sqrt(pow(sin($averageLat), 2) + cos($radLat1) * cos($radLat2) * pow(sin($averageLon), 2)));
	}

view raw spherical_trigonometry.php hosted with ❤ by GitHub

Geodesic Navigation

	/**
	* ２地点間の距離(m)を求める
	* 測地線航海算法バージョン
	*
	* @param float $lat1 緯度（始点）
	* @param float $lon1 経度（始点）
	* @param float $lat2 緯度(終点)
	* @param float $lon2 経度(終点)
	* @return float 距離(m)
	*/
	function distance($lat1, $lon1, $lat2, $lon2)
	{
	// 緯度経度をラジアンに変換
	$radLat1 = deg2rad($lat1); // 緯度（始点）
	$radLon1 = deg2rad($lon1); // 経度（始点）
	$radLat2 = deg2rad($lat2); // 緯度(終点)
	$radLon2 = deg2rad($lon2); // 経度(終点)

	$A = 6378137.0; // 赤道半径
	$B = 6356752.314140356; // 極半径
	// $F = ($A - $B) / $A;
	$F = 0.003352858356825; // 扁平率

	$BdivA = 0.99664714164317; // $B/$A
	$P1 = atan($BdivA * tan($radLat1));
	$P2 = atan($BdivA * tan($radLat2));

	$sd = acos(sin($P1)sin($P2) + cos($P1) cos($P2) * cos($radLon1 - $radLon2));

	$cos_sd = cos($sd/2);
	$sin_sd = sin($sd/2);
	$c = (sin($sd) - $sd) * pow(sin($P1)+sin($P2),2) / $cos_sd / $cos_sd;
	$s = (sin($sd) + $sd) * pow(sin($P1)-sin($P2),2) / $sin_sd / $sin_sd;
	$delta = $F / 8.0 * ($c - $s);

	return $A * ($sd + $delta);
	}

view raw GeodesicSailing.php hosted with ❤ by GitHub

Finally

The above sources are available in Composer, so you can try them yourself for speed and performance.

composer require chiyoyo/distance

Bash