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Constrained isometric planar parameterizations are central to a broad spectrum of applications. In this work, we present a non linear solver developed on OpenCL that is efficiently parallelizable on modern massively parallel architectures. We establish how parameterization relates to mesh smoothing and show how to ciently and robustly solve the planar mesh parameterization problem with constraints. Furthermore, we demonstrate the applicability of our approach to real-time cut-and-paste editing and interactive mesh deformation.