The Riemann map from a simply connected domain to the unit disc can be approximated by circle packings thanks to a theorem of Rodin and Sullivan. (That is, take smaller and smaller triangulations and circle packings associated to them. There is an `easy-to-compute' map each time which gets closer and closer to the Riemann map.)

Are there effective estimates on convergence ? In other words, if I have to get within 5% of the Riemann map, can I estimate how small a mesh I need to take (and other such parameters)? I mean, can this be used to produce an algorithm for computing Riemann maps ?