Find 2 points on a 3d object and get their distance

Question

Hey,

Ok. So I guess thing would to be envision new york city and beijing highlighted on google earth...

I'm trying to figure out how to map points onto a 3d primitive object (a sphere), get their distance via any direction by the circumference, and their distance by diameter. The points are going to be latitude and longitude coordinates.

Right now, this is what i'm trying to use to map the coordinates (a code agnostic version):

  x1 =  radius * cos(long1) * cos(lat1);
  y1 =  radius * sin(long1) * cos(lat1);
  z1 =  radius * sin(lat1);

but i'm almost sure its wrong. How could I get each points position and calculate their distances straight across the sphere's diameter and also their distance going around the circumference of the sphere?

Thanks.

Answer 1

You're actually pretty close. To get the straight line distance, you simply need to do:

sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)

For the distance around the great circle, remember that it is pi*diam*angle. The dot product of the vectors from the center of the earth to the two points is the cosine of the angle. So, you get:

pi*diam*acos((x1*x2 + y1*y2 + z1*z1)/diam^2)

of course there's a 2nd distance if you go the other way around the earth, but for that you just need 2*pi - acos(...).