计算坐标给出一个轴承和一个距离 [英] Calculating coordinates given a bearing and a distance

问题描述

我有实施这里这里描述的功能的问题。

I am having problems implementing the function described here here.

这是我的Java实现：

This is my Java implementation:

private static double[] pointRadialDistance(double lat1, double lon1, 
		double radianBearing, double radialDistance) {
	 double lat = Math.asin(Math.sin(lat1)*Math.cos(radialDistance)+Math.cos(lat1)
			 *Math.sin(radialDistance)*Math.cos(radianBearing));
	 double lon;
     if(Math.cos(lat) == 0) {  // Endpoint a pole
        lon=lon1;      
     }
     else {
        lon = ((lon1-Math.asin(Math.sin(radianBearing)*Math.sin(radialDistance)/Math.cos(lat))
        		+Math.PI) % (2*Math.PI)) - Math.PI;
     }
	return (new double[]{lat, lon});
}

我转换的程度轴承弧度和转换调用函数之前的距离（公里）成弧度的距离 - 。所以这不是问题。

I convert the degree bearing to radians and convert the distance (km) into a radians distance before calling the function - so that's not the problem.

然而，当我输入坐标，如： 纬度= 49.25705; LON = -123.140259; 与225（西南）轴承和1公里的距离

However, when I input coordinates such as: lat = 49.25705; lon = -123.140259; with a bearing of 225 (south-west) and a distance of 1km

我得到这个返回： 纬度：-1.0085434360125864 LON：-3.7595299668539504

I get this returned: lat: -1.0085434360125864 lon: -3.7595299668539504

它显然不是正确的，任何人都可以看到我在做什么错了？

Its obviously not correct, can anyone see what I am doing wrong?

感谢

推荐答案

好像这些都是在code中的问题：

It seems like these are the issues in your code:

1. 您需要 LAT1 和 lon1 转换为弧度调用你的函数之前。
2. 您可缩放 radialDistance 不正确。
3. 在测试一个浮点数是否相等是很危险的。两个数字是准确的运算后等于可能不是浮点运算后完全相等。因此， ABS（X-Y）＆LT;门槛较安全的 X ==是用于测试两个浮点数 X 和是平等。
4. 我想你想转换经纬度和 LON 从弧度度。

1. You need to convert lat1 and lon1 to radians before calling your function.
2. You may be scaling radialDistance incorrectly.
3. Testing a floating-point number for equality is dangerous. Two numbers that are equal after exact arithmetic might not be exactly equal after floating-point arithmetic. Thus abs(x-y) < threshold is safer than x == y for testing two floating-point numbers x and y for equality.
4. I think you want to convert lat and lon from radians to degrees.

下面是我实现的Python中的code：

Here is my implementation of your code in Python:

#!/usr/bin/env python

from math import asin,cos,pi,sin

rEarth = 6371.01 # Earth's average radius in km
epsilon = 0.000001 # threshold for floating-point equality


def deg2rad(angle):
    return angle*pi/180


def rad2deg(angle):
    return angle*180/pi


def pointRadialDistance(lat1, lon1, bearing, distance):
    """
    Return final coordinates (lat2,lon2) [in degrees] given initial coordinates
    (lat1,lon1) [in degrees] and a bearing [in degrees] and distance [in km]
    """
    rlat1 = deg2rad(lat1)
    rlon1 = deg2rad(lon1)
    rbearing = deg2rad(bearing)
    rdistance = distance / rEarth # normalize linear distance to radian angle

    rlat = asin( sin(rlat1) * cos(rdistance) + cos(rlat1) * sin(rdistance) * cos(rbearing) )

    if cos(rlat) == 0 or abs(cos(rlat)) < epsilon: # Endpoint a pole
    	rlon=rlon1
    else:
    	rlon = ( (rlon1 - asin( sin(rbearing)* sin(rdistance) / cos(rlat) ) + pi ) % (2*pi) ) - pi

    lat = rad2deg(rlat)
    lon = rad2deg(rlon)
    return (lat, lon)


def main():
    print "lat1 \t lon1 \t\t bear \t dist \t\t lat2 \t\t lon2"
    testcases = []
    testcases.append((0,0,0,1))
    testcases.append((0,0,90,1))
    testcases.append((0,0,0,100))
    testcases.append((0,0,90,100))
    testcases.append((49.25705,-123.140259,225,1))
    testcases.append((49.25705,-123.140259,225,100))
    testcases.append((49.25705,-123.140259,225,1000))
    for lat1, lon1, bear, dist in testcases:
    	(lat,lon) = pointRadialDistance(lat1,lon1,bear,dist)
    	print "%6.2f \t %6.2f \t %4.1f \t %6.1f \t %6.2f \t %6.2f" % (lat1,lon1,bear,dist,lat,lon)


if __name__ == "__main__":
    main()

下面是输出：

lat1     lon1 		 bear 	 dist 		 lat2 		 lon2
  0.00     0.00 	  0.0 	    1.0 	   0.01 	   0.00
  0.00     0.00 	 90.0 	    1.0 	   0.00 	  -0.01
  0.00     0.00 	  0.0 	  100.0 	   0.90 	   0.00
  0.00     0.00 	 90.0 	  100.0 	   0.00 	  -0.90
 49.26   -123.14 	 225.0 	    1.0 	  49.25 	 -123.13
 49.26   -123.14 	 225.0 	  100.0 	  48.62 	 -122.18
 49.26   -123.14 	 225.0 	 1000.0 	  42.55 	 -114.51

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