Polar Coordinate Systems - 3D Math Primer for Graphics and Game Development - page 205

Step 3. Rotate your arm downward by the angle φ. Your arm now points
in the direction specified by the polar angles θ and φ.
Step 4. Displace from the origin along this direction by the distance r.
You've arrived at the point described by the spherical coordinates
(r,θ,φ).
Figure 7.6 shows how this works.
Figure 7.6
Spherical coordinates used
by math people
Other people use different notation. The convention in which the symbols θ
and φ are reversed is frequently used, especially in physics. Other authors,
perhaps intent on replacing all Roman letters with Greek, use ρ instead of
r as the name of the radial distance. We present some conventions that are
a bit more practical for video game purposes in Section 7.3.3.
The horizontal angle θ is known as the azimuth, and φ is the zenith.
Other terms that you've probably heard are longitude and latitude. Lon-
gitude is basically the same as θ, and latitude is the angle of inclination,
90 o −φ. So, you see, the latitude/longitude system for describing locations
on planet Earth is actually a type of spherical coordinate system. We're
often interested only in describing points on the planet's surface, and so
the radial distance r, which would measure the distance to the center of
the Earth, isn't necessary. We can think of r as being roughly equivalent to