Title says it all. I need to find the x,y,z coordinate on the surface of a sphere where the origin is 0,0,0 at the center of the sphere. The known information is the radius, latitude, and longitude.
I'm not sure where to start with this.
Title says it all. I need to find the x,y,z coordinate on the surface of a sphere where the origin is 0,0,0 at the center of the sphere. The known information is the radius, latitude, and longitude.
I'm not sure where to start with this.
If $\displaystyle \theta$ is the longitude and $\displaystyle \phi$ is the latitude, the coordinate transformations are similar to if you were using spherical polar coordinate convention.
$\displaystyle x = R \cos{\theta} \cos{\phi} $
$\displaystyle y = R \cos{\theta} \sin{\phi} $
$\displaystyle z = R \sin{\theta} $
The difference between geographic convention (G) and spherical polar convention (SP) is in the definition of $\displaystyle \theta$. In G, this angle takes on the value 0 at the equator, 90 at the north pole and -90 at the south pole. In SP theta has 0 at the north pole and increases to 180 at the south pole. The difference in the transformations is that $\displaystyle \sin{\theta}$ and $\displaystyle \cos{\theta}$ are switched between conventions.