Viewing Direction as 3D Cartesian Unit Vector

Question

I am reading a paper, where they represent a "2D viewing direction ($\theta$, $\phi$) as a 3D Cartesian unit vector d". Unfortunately, no further explanation is given and I am not familiar with this concept. My first intention was that they applied a rotation matrix on the standard Cartesian unit vectors, but I don't see how this fits in three dimensions. Can anyone elaborate on that please or link me to a useful source?

Answer 1

My guess is that $(\theta, \phi)$ represent spherical coordinates. The third spherical coordinate, $r$ can be assumed to be $1$, since we’re dealing with a unit vector. Unfortunately, there are (at least) two conventions for spherical coordinates, so it’s hard to say exactly what $\theta$ and $\phi$ mean. More here.

Answer 2

The direction is specified using two angles, so I'd read that as a direction in space. A 3d coordinate vector of unit length makes sense for that, as does a spherical coordinate system using two angles. The fact that the paper speaks about "2d" in my opinion does not reflect that this is a direction in a plane, but instead that the direction is essentially equivalent to a point on a (unit) sphere. That sphere itself is a two-dimensional surface, albeit a curved one not a flat plane.