Unless the curvature is very large, you don't need to cut the negative.
All you need is a good point light source, and there happens to be one conveniently located in the sky.
Use clingfilm to hold the negative in place as close to the surface as possible, you might need to play around with it a bit before you find the best fit. Then clingfilm it in place (no more than one layer, or you will get interference and wrinkles), put the whole thing in a dark bag and take it outside. Then expose the thingy without turning the bowl (unless you can rotate it slowly at a rate of one turn per 24 hours, of course). Put it back in the dark bag, and take it inside for processing.