问题
I'm trying to calculate distance between two points, using latitude longitude and altitude (elevation).
I was using euklides formula in order to get my distance:
D=√((Long1-Long2)²+(Lat1-Lat2)²+(Alt1-Alt2)²)
My points are geographical coordinates and ofcourse altitude is my height above the sea. I only have lat and lng, I'm using GOOGLE API Elevation to get my altitude.
I'm developing an application which calculates my traveled distance (on my skis). Every application which I have used, gets distance traveled with included altitude. Like #Endomondo or #Garmin I cannot get my distance in 2D space because true distances are going to vary from the ones I've returned.
Which formula would be the best to calculate my distance ? Ofcourse with included altitude.
I'm writing my app in Python, with PostGis.
回答1:
I used the solution provided by John Moutafis but I didn't get a right answer.The formula needs some corrections. You will get the conversion of coordinates from Polar to Cartesian (x, y, z) at http://electron9.phys.utk.edu/vectors/3dcoordinates.htm. Use the above formula to convert spherical coordinates(Polar) to Cartesian and calculate Euclidean distance.
I used the following c# in a console app. Considering following dummy lat long
double lat_1 = 18.457793 * (Math.PI / 180);
double lon_1 = 73.3951930277778 *(Math.PI/180);
double alt_1 = 270.146;
double lat_2 = 18.4581253333333 * (Math.PI / 180);
double lon_2 = 73.3963755277778 * (Math.PI / 180);
double alt_2 = 317.473;
const Double r = 6376.5 *1000;//redius of earth in meaters
double x_1 = r * Math.Sin(lon_1) * Math.Cos(lat_1);
double y_1 = r * Math.Sin(lon_1) * Math.Sin(lat_1);
double z_1 = r * Math.Cos(lon_1);
double x_2 = r * Math.Sin(lon_2) * Math.Cos(lat_2);
double y_2 = r * Math.Sin(lon_2) * Math.Sin(lat_2);
double z_2 = r * Math.Cos(lon_2);
double dist = Math.Sqrt((x_2 - x_1) * (x_2 - x_1) + (y_2 - y_1) *
(y_2 - y_1) + (z_2 - z_1) * (z_2 - z_1));
回答2:
You can get the correct calculation by translating your coordinates from Polar (long, lat, alt) to Cartesian (x, y, z):
- Let:
polar_point_1 = (long_1, lat_1, alt_1)
andpolar_point_2 = (long_2, lat_2, alt_2)
Translate each point to it's Cartesian equivalent by utilizing this formula:
x = alt * cos(lat) * sin(long) y = alt * sin(lat) z = alt * cos(lat) * cos(long)
and you will have
p_1 = (x_1, y_1, z_1)
andp_2 = (x_2, y_2, z_2)
points respectively.Finally use the Euclidean formula:
dist = sqrt((x_2-x_1)**2 + (y_2-y_1)**2 + (z_2-z_1)**2)
EDIT 2018: Since this answer, I composed a Q&A style example to answer similar questions (including this one as an example): How to calculate 3D distance (including altitude) between two points in GeoDjango
回答3:
You can calculate distance between flat coordinates in, say, meters by using geopy
package or Vincenty's formula, pasting coordinates directly. Suppose the result is d
meters. Then the total distance travelled is sqrt(d**2 + h**2)
where h
is the change in elevation in meters.
来源:https://stackoverflow.com/questions/33111529/calculating-distance-between-two-points-using-latitude-longitude-and-altitude-e