International audienceWe introduce a new method to compute conformal parame-terizations using a recent definition of discrete conformity, and establish a discrete version of the Riemann mapping theorem. Our algorithm can parameterize triangular, quadrangular and digital meshes. It can also be adapted to preserve metric properties. To demonstrate the efficiency of our method, many examples are shown in the experiment section

a b s t r a c tWe present a derivative estimator for discrete curves and discretized functions which uses convolutions with integer-only binomial masks. The convergence results work for C 2 functions, and as a consequence we obtain a complete uniform convergence result for parameterized C 2 curves for derivatives of any order.

We describe a method to compute conformal parameterizations with a natural boundary based on a simple differentiable expression measuring angles between edges by using complex numbers. The method can be adapted to preserve metric properties or map textures with constrained positions. Some illustrations are shown to assess the efficiency of the algorithms.