302 lines
12 KiB
C#
302 lines
12 KiB
C#
using System;
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namespace Plane.Geography
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{
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/// <summary>
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/// 提供地理相关计算的方法。
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/// </summary>
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public static class GeographyUtils
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{
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/// <summary>
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/// 米数转换为纬度跨度时需要乘的常数。
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/// </summary>
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public const double METERS_TO_LAT_SPAN = 1 / (GLOBE_CIRCUMFERENCE / 360);
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/// <summary>
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/// 角度转换为弧度时需要乘的常数。
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/// </summary>
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private const double DEG_TO_RAD = Math.PI / 180;
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/// <summary>
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/// 地球的半径。
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/// </summary>
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private const double EARTH_RADIUS = 6371000;
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/// <summary>
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/// 当前星球的周长。
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/// </summary>
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private const double GLOBE_CIRCUMFERENCE = GLOBE_RADIUS * 2 * Math.PI;
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/// <summary>
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/// 当前星球的半径。
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/// </summary>
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private const double GLOBE_RADIUS = EARTH_RADIUS;
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/// <summary>
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/// 计算从 (lat1, lng1) 到 (lat2, lng2) 的方向，单位为弧度。
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/// </summary>
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/// <param name="lat1">第一个点的纬度。</param>
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/// <param name="lng1">第一个点的经度。</param>
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/// <param name="lat2">第二个点的纬度。</param>
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/// <param name="lng2">第二个点的经度。</param>
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/// <returns>点 1 到点 2 的方向。</returns>
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public static double CalcDirection2D(double lat1, double lng1, double lat2, double lng2)
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{
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return Math.Atan2((lng2 - lng1) / CalcMetersToLngSpan(lat1), (lat2 - lat1) / METERS_TO_LAT_SPAN).NormalizeDirectionRad();
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}
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/// <summary>
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/// 计算空间中两点间的距离，单位为米。
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/// </summary>
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/// <param name="l1">点 1。</param>
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/// <param name="l2">点 2。</param>
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/// <returns>空间中两点间的距离，单位为米。</returns>
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public static double CalcDistance(ILocation l1, ILocation l2)
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{
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return CalcDistance(l1.Latitude, l1.Longitude, l1.Altitude, l2.Latitude, l2.Longitude, l2.Altitude);
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}
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/// <summary>
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/// 计算空间中两点之间的距离，单位为米。
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/// </summary>
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/// <param name="lat1">纬度 1。</param>
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/// <param name="lng1">经度 1。</param>
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/// <param name="alt1">高度 1。</param>
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/// <param name="lat2">纬度 2。</param>
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/// <param name="lng2">经度 2。</param>
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/// <param name="alt2">高度 2。</param>
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/// <returns>空间中两点之间的距离，单位为米。</returns>
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public static double CalcDistance(double lat1, double lng1, double alt1, double lat2, double lng2, double alt2)
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{
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// generally used geo measurement function
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// var R = 6378.137; // Radius of earth in KM
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var dLat = (lat2 - lat1) * Math.PI / 180;
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var dLon = (lng2 - lng1) * Math.PI / 180;
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var a = Math.Sin(dLat / 2) * Math.Sin(dLat / 2)
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+ Math.Cos(lat1 * Math.PI / 180) * Math.Cos(lat2 * Math.PI / 180) * Math.Sin(dLon / 2) * Math.Sin(dLon / 2);
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var c = 2 * Math.Atan2(Math.Sqrt(a), Math.Sqrt(1 - a));
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var d = GLOBE_RADIUS * c;
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return Math.Sqrt(Math.Pow((alt2 - alt1), 2) + Math.Pow(d, 2));
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}
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/// <summary>
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/// 计算二维平面上两个位置之间的距离，单位为米。
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/// </summary>
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/// <param name="l1">位置 1。</param>
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/// <param name="l2">位置 2。</param>
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/// <returns>空间中两点间的距离。</returns>
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public static double CalcDistance2D(ILocation2D l1, ILocation2D l2)
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=> CalcDistance2D(l1.Latitude, l1.Longitude, l2.Latitude, l2.Longitude);
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/// <summary>
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/// 计算二维平面上两个位置之间的距离，单位为米。
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/// </summary>
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/// <param name="lat1">纬度 1。</param>
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/// <param name="lng1">经度 1。</param>
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/// <param name="lat2">纬度 2。</param>
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/// <param name="lng2">经度 2。</param>
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/// <returns>计算二维平面上两个位置之间的距离，单位为米。</returns>
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public static double CalcDistance2D(double lat1, double lng1, double lat2, double lng2)
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=> CalcDistance(lat1, lng1, 0, lat2, lng2, 0);
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/// <summary>
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/// 计算在水平面上从指定点往指定方向移动指定距离后所在的点。
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/// </summary>
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/// <param name="lat1">出发点的纬度。</param>
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/// <param name="lng1">出发点的经度。</param>
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/// <param name="directionDegrees">移动方向，单位为角度。</param>
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/// <param name="distance">移动距离。</param>
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/// <returns>从指定点往指定方向移动指定距离后所在的点。</returns>
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public static Tuple<double, double> CalcLatLngSomeMetersAway2D(double lat1, double lng1, float directionDegrees, float distance)
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{
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var direction = directionDegrees.DegToRad();
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return Tuple.Create(
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lat1 + distance * Math.Cos(direction) * METERS_TO_LAT_SPAN,
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lng1 + distance * Math.Sin(direction) * CalcMetersToLngSpan(lat1)
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);
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}
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/// <summary>
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/// 计算在水平面上从指定点往指定方向移动指定距离后所在的点。
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/// </summary>
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/// <param name="loc1">出发点。</param>
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/// <param name="directionDegrees">移动方向，单位为角度。</param>
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/// <param name="distance">移动距离。</param>
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/// <returns>从指定点往指定方向移动指定距离后所在的点。</returns>
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public static ILocation2D CalcLatLngSomeMetersAway2D(ILocation2D loc1, float directionDegrees, float distance)
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{
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var direction = directionDegrees.DegToRad();
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return new PLLocation(
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loc1.Latitude + distance * Math.Cos(direction) * METERS_TO_LAT_SPAN,
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loc1.Longitude + distance * Math.Sin(direction) * CalcMetersToLngSpan(loc1.Latitude),
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0
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);
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}
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/// <summary>
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/// 计算在指定纬度上，米数转换为经度跨度时需要乘的值。
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/// </summary>
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/// <param name="latitude">纬度。</param>
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/// <returns>在指定纬度上，米数转换为经度跨度时需要乘的值。</returns>
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public static double CalcMetersToLngSpan(double latitude)
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{
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return METERS_TO_LAT_SPAN / Math.Cos(latitude * DEG_TO_RAD);
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}
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/// <summary>
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/// 检测同一水平面上（忽略高度）的两条线段是否相交。
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/// </summary>
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/// <param name="l1">线段 A 端点 1。</param>
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/// <param name="l2">线段 A 端点 2。</param>
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/// <param name="l3">线段 B 端点 1。</param>
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/// <param name="l4">线段 B 端点 2。</param>
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/// <returns>若相交，返回 true；否则返回 false。</returns>
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public static bool CheckCrossing2D(ILocation2D l1, ILocation2D l2, ILocation2D l3, ILocation2D l4)
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=> CheckCrossing2D(l1.Latitude, l1.Longitude, l2.Latitude, l2.Longitude, l3.Latitude, l3.Longitude, l4.Latitude, l4.Longitude);
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/// <summary>
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/// 检测同一水平面上的两条线段是否相交。
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/// </summary>
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/// <param name="latA1">线段 A 端点 1 的纬度。</param>
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/// <param name="lngA1">线段 A 端点 1 的经度。</param>
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/// <param name="latA2">线段 A 端点 2 的纬度。</param>
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/// <param name="lngA2">线段 A 端点 2 的经度。</param>
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/// <param name="latB1">线段 B 端点 1 的纬度。</param>
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/// <param name="lngB1">线段 B 端点 1 的经度。</param>
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/// <param name="latB2">线段 B 端点 2 的纬度。</param>
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/// <param name="lngB2">线段 B 端点 2 的经度。</param>
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/// <returns>若相交，返回 true；否则返回 false。</returns>
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public static bool CheckCrossing2D(double latA1, double lngA1, double latA2, double lngA2,
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double latB1, double lngB1, double latB2, double lngB2)
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{
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// 线段 A(x1, y1) - B(x2, y2), 所在直线 L1 方程为 F(x, y) = 0;
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// 线段 C(x3, y3) - D(x4, y4), 所在直线 L2 方程为 G(x, y) = 0;
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// 思路:
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// (即问题的充要条件)
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// (点 A 与点 B 在直线 L2 两侧) AND (点 C 与点 D 在直线 L1 两侧);
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// 方法:
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// 如果点 P(Xp, Yp) 不在直线 a * x + b * y + c = 0 上, 则 a* Xp + b * Yp + c <> 0;
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// 如果用两个点的坐标代入同一直线方程 a * x + b * y + c 计算出的值异号, 则两点在直线两侧;
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// 解法:
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// (G(x1, y1) * G(x2, y2) < 0) AND (F(x3, y3) * F(x4, y4) < 0)
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// 斜截式 y = kx + b
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// 即 kx - y + b = 0
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var k1 = (latA2 - latA1) / (lngA2 - lngA1);
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var b1 = latA1 - k1 * lngA1;
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var k2 = (latB2 - latB1) / (lngB2 - lngB1);
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var b2 = latB1 - k2 * lngB1;
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return k2 * lngA1 - latA1 + b2 > 0 != k2 * lngA2 - latA2 + b2 > 0 &&
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k1 * lngB1 - latB1 + b1 > 0 != k1 * lngB2 - latB2 + b1 > 0;
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}
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/// <summary>
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/// 把角度转换为弧度。
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/// </summary>
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/// <param name="value">角度值。</param>
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/// <returns>弧度值。</returns>
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public static double DegToRad(this float value)
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{
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return value * DEG_TO_RAD;
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}
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/// <summary>
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/// 把角度转换为弧度。
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/// </summary>
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/// <param name="value">角度值。</param>
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/// <returns>弧度值。</returns>
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public static double DegToRad(this double value)
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{
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return value * DEG_TO_RAD;
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}
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/// <summary>
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/// 把角度转换为弧度。
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/// </summary>
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/// <param name="value">角度值。</param>
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/// <returns>弧度值。</returns>
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public static double DegToRad(this short value)
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{
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return value * DEG_TO_RAD;
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}
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/// <summary>
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/// 把指示方向的角度数限制在 [0, 360)。
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/// </summary>
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/// <param name="value">指示方向的角度数。</param>
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/// <returns>等价的在标准范围内的角度。</returns>
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public static float NormalizeDirection(this float value)
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{
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while (value < 0)
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{
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value += 360;
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}
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while (value >= 360)
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{
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value -= 360;
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}
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return value;
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}
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/// <summary>
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/// 把指示方向的角度值限制在 [0, 360)。
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/// </summary>
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/// <param name="value">指示方向的角度值。</param>
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/// <returns>等价的在标准范围内的角度。</returns>
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public static double NormalizeDirection(this double value)
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{
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while (value < 0)
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{
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value += 360;
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}
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while (value >= 360)
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{
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value -= 360;
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}
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return value;
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}
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/// <summary>
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/// 把指示方向的弧度值限制在 [0, 2PI)。
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/// </summary>
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/// <param name="value">指示方向的弧度值。</param>
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/// <returns>等价的在标准范围内的弧度。</returns>
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public static double NormalizeDirectionRad(this double value)
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{
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while (value < 0)
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{
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value += Math.PI * 2;
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}
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while (value >= Math.PI * 2)
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{
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value -= Math.PI * 2;
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}
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return value;
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}
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/// <summary>
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/// 把弧度转换为角度。
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/// </summary>
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/// <param name="value">弧度值。</param>
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/// <returns>角度值。</returns>
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public static double RadToDeg(this float value)
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{
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return value / DEG_TO_RAD;
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}
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/// <summary>
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/// 把弧度转换为角度。
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/// </summary>
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/// <param name="value">弧度值。</param>
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/// <returns>角度值。</returns>
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public static double RadToDeg(this double value)
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{
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return value / DEG_TO_RAD;
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}
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}
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}
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