  An algorithm for the computation of global discrete conformal
parametrizations with prescribed global holonomy signatures for triangle meshes
was recently described in [Campen and Zorin 2017]. In this paper we provide a
detailed analysis of convergence and correctness of this algorithm. We
generalize and extend ideas of [Springborn et al. 2008] to show a connection of
the algorithm to Newton's algorithm applied to solving the system of
constraints on angles in the parametric domain, and demonstrate that this
system can be obtained as a gradient of a convex energy.
