  In this paper, we introduce a definition of discrete conformality for
triangulated surfaces with flat cone metrics and describe an algorithm for
solving the problem of prescribing curvature, that is to deform the metric
discrete conformally so that the curvature of the resulting metric coincides
with the prescribed curvature. We explicitly construct a discrete conformal map
between the input triangulated surface and the deformed triangulated surface.
Our algorithm can handle the surface with any topology with or without
boundary, and can find a deformed metric for any prescribed curvature
satisfying the Gauss-Bonnet formula. In addition, we present the numerical
examples to show the convergence of our discrete conformality and to
demonstrate the efficiency and the robustness of our algorithm.
