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We prove that for any discrete curvature satisfying Gauss-Bonnet formula,there exist a unique up to scaling inversive distance circle packing in thediscrete conformal equivalent class, whose polyhedral metric meets the targetcurvature. We prove it by constructing diffeomorphism between fiber bundleswith cell decomposition based on Teichm\"uller spaces, and each discreteconformal equivalent class is a fiber passing through finite cell with respectto triangulations, which means we can do surgery on the discrete Ricci flow byedge flipping using a generalized Ptolemy equation to ensure it converge andnever blow up.

The existence of inversive distance circle packing on polyhedral surface