From Longitude/Latitude to Cartesian Coordinates (cont.)
- Derivation of the Conversion:
- \(\cos \phi = d / R \Rightarrow d = R \cos \phi\)
- \(\cos \lambda = p_{z}/d \Rightarrow p_{z} = d \cos \lambda
= R\cos \phi \cos \lambda\)
- \(\sin \lambda = p_{x}/d \Rightarrow p_{x} = d \sin \lambda
= R \cos \phi \sin \lambda\)
- \(p_{y} = R \sin \phi\)
- Note:
- This is very similar to the conversion of spherical coordinates
to Cartesian coordinates (but it uses the latitude
not the colatitude)