# XYZ Coordinate on Sphere. Known Info: Radius, latitude, longitude

• Aug 13th 2012, 06:26 PM
celestesArtiste
XYZ Coordinate on Sphere. Known Info: Radius, latitude, longitude
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.

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.