I have a camera in 3-space which I want to spin around the y-axis. The distance remains the same, but the x- and z-positions change.
The above is the direction I need to rotate. It's a top-down view (looking at xz-plane). The y-position never changes, but the x- and z-positions do. The distance between the camera and origin should also not change.
Say the initial point (as seen in the image) is $(0,0,-10)$, a half-rotation will leave me at $(0,0,10)$, a quarter at $(10,0,0)$, and so on. My problem is finding the inbetween points as I don't know of any formula.
Say I rotate only $15°$, what would the co-ordinates of the camera be?
The path of your camera can be parametrised by $$ [10\cos t, 0, 10\sin t] $$ where $t$ represents the angle. To set the initial point, just offset $t$.