Wikipedia claims that a PS3 Eye zoomed to “blue” has a field of view of 75 degrees. This is presumably the horizontal field of view while I need both angular measures, so I decided to check both out myself.
Put PS3 Eye sensor at 4.25″ above flat surface
Reinforce 8.5″x11″ sheet of paper with tongue depressors
Holding the paper vertically in Landscape, with one edge flush against, and exactly perpendicular to, the table, adjust angle of camera (it pivots about one axis on its base) and distance from paper until the top and bottom edges are at the very top and bottom of the camera view. The camera sensor should now be entirely parallel to the sheet of paper, in all axes. The edges of the paper should disappear and reappear together if you move the paper a little closer or a little further.
Mark the distance from paper to camera
Now shift the paper side to side, at this same distance, to observe where the side edges leave the frame. Mark the edges of the frame on the paper once the paper entirely fills the frame.
The field of view is then 2*atan((paper_measurement/2)/distance_to_camera), where paper_measurement is either 8.5″ or the distance between the horizontal extremes of the sheet that you marked.
This test resulted in a horizontal field of view of 60.32 degrees (not that I actually have that many sigdigs) and a vertical of 49.35 degrees.
It is important to note that points on a plane perpendicular to the camera can have their angles linearly interpolated from pixel distance against this maximum reference. The image resolution is 620×480 in normal video rate, so the horizontal angle between two points with deltaX=310 pixels, is 30.16 degrees. This should jive, as the image doesn’t appear overly warped. Horizontal distance is relatively the same anywhere on the sensor.
If the angle of the plane is not known, it is ambiguous whether a long object appearing short on the camera feed is doing so because of being at a sharp angle to the camera or because it is far away. The distance to one point must be known. However, perhaps a 3rd point, out of plane and thus defining a cube (like one of the back corners of my rectangularly prismatic fishtank) will provide the needed scaling factor. Should be cautious of accuracy here, if those point are at highly oblique angles.
Follow along with my next steps at locating the camera at http://ryan.fish/blog/triangulating-camera-position-from-known-points/