I am working on a programming problem where I want to display a cone of light from a point $p=(x,y,z)$ lying in space to some direction.
For example, if $p=(0,0,1)$, and the light is facing straight down with angle of 90 degrees, the intersection at $xy$-plane would be a circle with radius $r = 1$ (circular cone).
The equation(s) that I am looking for should be parametrized in such way that I can input $x, y, z$ and the two angles (altitude, azimuth), and get the intersection as output.
Please, no straight answers, I want to work this out by myself ;-)