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We present an extension of the anisotropic polygonal remeshing technique developed byAlliez et al. Our algorithm does not rely on a global parameterization of the mesh and therefore is applicable to arbitrary genus surfaces. We show how to exploit the structure of the original mesh in order to perform efficiently the proximity queries required in the line integration phase, thus improving dramatically the scalability and the performance of the original algorithm. Finally, we propose a novel technique for producing conforming quad-dominant meshes in isotropic regions as well by propagating directional information from the anisotropic regions.