Geographical coordinates on the sphere

Greetings,

I have to write the script that calculate the closest distance between two points on the sphere.

Radius is given, and points are set by the user (one give's latitude and longitude).

For example: You want to know a distance between two cities, so you enter their geographical cords and as a result you get distance bewtween them in km's.

I'm totally new. The deadline is tomorrow and I have no clue how to do that.

I wish You can help me :)!

[John DeBriere]

It's pretty strait forward:

Try the Haversine formula:

delta_latitude = lat2 - lat1;
delta_longitude = long2 - long1;
a = sin(delta_latitude /2.0) * sin(delta_latitude /2.0) + cos(lat1) * cos(lat2) * sin(delta_longitude /2.0) * sin(delta_longitude /2.0);
c = atan( sqrt(a), sqrt(1.0 - a));
d = R * c;

where R is the Earths Radius = 6371 km

Remember all angles are in radians so you need a conversion of Latitude and Longitude to radians. But first you normally also have to do the conversion from degrees, minutes, seconds to a decimal the convert that to a radian angle.

degree_to_radian = angle * Pi / 180;

radian_to_degree = radian * 180 / Pi;

You might also want to look into the "Lambert Conformal Conic to Geographic Transform". I believe that the New Zealand (.gov web sites) present this information well and you can also find formulas to calculate Bearings, Mid points and related Geo-Spatial info.

Good Luck, and hope this helped!

John D

[John DeBriere]

Sorry I was unaware of how the editor would format my message.

I hope this is better:

It's pretty strait forward:

Try the Haversine formula:

function distance = GeographcDistance(lat1, lat2, long1, long2)
   delta_latitude = lat2 - lat1; 
   delta_longitude = long2 - long1; 
   a = sin(delta_latitude /2.0) * sin(delta_latitude /2.0) + cos  (lat1) * cos(lat2) * sin(delta_longitude /2.0) * sin(delta_longitude /2.0);
   c = atan( sqrt(a), sqrt(1.0 - a)); 
   distance = R * c;
end

where R is the Earths Radius = 6371 km

Remember all angles are in radians so you need a conversion of Latitude and Longitude to radians.

But first you normally also have to do the conversion from degrees, minutes, seconds to a decimal the convert that to a radian angle.

degree_to_radian = angle * Pi / 180;

radian_to_degree = radian * 180 / Pi;

You might also want to look into the "Lambert Conformal Conic to Geographic Transform".

I believe that the New Zealand (.gov web sites) present this information well and you can also find formulas to calculate Bearings, Mid points and related Geo-Spatial info.

Good Luck, and hope this helped!

John D

Answer 1

[Niels]

i guess your classmate asked this question some days before:

Distance between two points on the sphere.

[Mateusz Talarski]

I have seen this, that's totally different story. I need to enter geo cords and somehow convert them into distance ;O!

[Niels]

if you had read the answers you would have seen that its the same, using geographical coordinates and then calculating the distance

[Mateusz Talarski]

But how am I supposed to enter geographical cords and transfer them into cardesian cords/spherical?

[Niels]

create a function with the coordinates as input arguments, or use the -"input" function inside your function to get the coordinates from the user, then adapt the code given in the second answer.

how to create a function

[Giora Enden]

1. Is the formula valid when delta_latitude is larger than 90 deg?
2. Is it valid when the two geographical sites are on oposite hemisphers?