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Comment by adolph | Hacker News Reader

I think it might be more fair if the camera was above the participants.

That sounds fine for the Olympics but rather awkward for a lower profile race at which someone just wants to roll a camera out to the track.

The same problem could also be addressed by having two cameras, one on each side of the track, synchronized and recording the same plane.

One could align the cameras into the same plane by putting a vertical array of distinctive marks (e.g. rapidly blinking LEDs) on each camera, above and below the optics and in line with it, such that each camera would see the other’s marks when correctly aligned.

> a vertical array of distinctive marks (e.g. rapidly blinking LEDs)

This doesn't work, as light beams diverge. Even taking a high-quality laser beam with a divergence of 0.1 milliradian (for comparison, a typical laser pointer is about 1-2 mrad), after crossing the 11 meters width of a 9-lane athletics track, you end up with a beam diameter of 2.2 millimeters. At the 10 m/s speed of the athletes and a 40000 fps framerate, they travel 250 micrometers between each frame.

I'm not sure what the issue you're describing is. If I have two devices, each with a camera and a line of marks, if they can each see each other's marks, then they are aligned to within the horizontal spread of the camera pixels. There are no lasers involved -- the marks can be paint, stickers, blinking wide-angle LEDs, etc. -- my suggestion to use blinking LEDs is just so that's it's more obvious when one is in the field of view of the camera.

You don't just need the cameras to see each other, you need them to be perfectly parallel to each other as well, as otherwise they're photographing along a different plane, which may give conflicting results.

Suppose camera A has line L_A on the camera. A’s optics and marks are both on L_A, so A’s image plane contains L_A and camera B’s image plane also contains L_A (you know the latter because you’ve aligned the cameras so camera B sees L_A). And vice versa: camera A sees L_B. In 3D Euclidean space, two distinct lines define a plane, and both camera’s are photographing planes that contain L_A and L_B, so both cameras are photographing the same plane.

More concretely, if the cameras are photographing along different but parallel planes, then they won’t see each other.

Your solution works in a geometric world, where light propagates in a perfect straight line of infinitesimally small width. That's not true in reality, where light propagates in an ever-expanding cone.

More concretely, you can have two cameras photographing along different but parallel planes that do see each other.

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