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I am trying to take pictures of small and large rugs. I have Canon 6D with 24-70mm lens. Could you please suggest the best way for mounting the camera to the ceiling, and any other recommendations for my camera/lens setup?
The ceiling has steel supports with height around 12ft (3.6 metres).
There are about 4000 rugs, small and too large. the use case for photos is for uploading in website for customers
Mounting the rugs on a suitably sized and sloped flat board and the camera on a high floor stand would probably be easier than mounting the camera on the ceiling where it will be inaccessible and difficult to control.
Frankly though you're going to have to move, unroll, photograph, rollup, and replace each rug so exactly how you do that efficiently takes precedence in what makes things easiest.
To save you a lot of effort you might want to consider other options for the website such as displaying close up images of the rug pattern, showing them in situ in a posed scenario, or grouping similar rugs together. It all depends on the type and style of the rugs.
With a full-frame camera like the 6D, and a 24mm focal length (widest you've got there), and a maximum subject-distance of 12ft (3.6m), you'd be able to fit a rug of up to 3.6 x 5.4 metres (12ft by 18ft) in the frame.
You can adjust calculations here, if that isn't big enough (note that this will calculate the vertical field-of-view, i.e. the maximum rug-width, or you can ask it the required focal length for a given view-size and subject distance). If that is insufficient, then you could try getting a 17-40mm f/4L or 16-35mm f/2.8L for significantly wider field of view.
If you have freedom to move the rugs, the easiest solution could be to temporarily hang them from a wall and the simply photograph them straight on horizontally.
If the rugs must be photographed in place, one cheap and easy solution would be to stand on a ladder along the middle of one edge of the rug, pointing the camera downward. This will of course result in converging lines, making the rug appear like a trapezoid. This can be corrected in post processing by using the perspective correction feature of software like Lightroom, typically used to correct the converging lines of the similar geometric situation of tilting a camera upward to photograph a building. You may be able to avoid the post processing step by resting a tilt-shift lens and using it to correct the converging lines in the camera.
The Gorillapod SLR-Zoom is a tripod with flexible legs that can be securely mounted anywhere it's legs can wrap around, so if the ceiling has anything in approximately the right location that a Gorillapod could attach to, this could be a relatively inexpensive solution for mounting the camera directly above the rug. Since the camera might be quite awkward to control in this location, it may be necessary to tether it to a computer with Canon's EOS Utility software.
