Transformation from spherical to cylindrical coordinates

Question

I have a coordinate on the surface of a sphere i.e latitude and longitude(two dimensions). I need to transform into a 2-D cylindrical coordinate frame i.e. r and the azimuth angle theta. Is there a transformation matrix between the two without converting to Cartesian in between ?

Answer 1

The point $(r, \theta, \phi)$ in spherical coordinates, can be represented as $(\rho, \varphi, z) = (r\cos\theta, \phi, r\sin\theta)$ in cylindrical coordinates. In this convention $\theta$ represents the latitude, and $\phi$ the longitude