The filament came out during a print and I don't know what layer it came out at. I've spent a lot of filament on this print, so is there any way to continue it?
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Measuring with the printer is an excellent idea. When in jog mode, mine displays the nozzle coordinates right on the screen.
I was considering that a truly dedicated nut could figure out which layer the print failed at (possibly approximately) and hand edit the gcode for the print to just replace all the layers up until the failed one with Z axis move up to that height. I think that would be problematic, though, because on my machine at least the model still being on the bed would definitely be in the way of the print head homing at the beginning of the print, and I don't know if there's any way to force it to skip that part of the procedure. Failure seems likely, and the penalty for failure is high.
Just printing the remaining half of the model and supergluing the parts together seems like a better idea.