We propose a new method for anisotropic polygonal surface remeshing. Our algorithm takes as input a surface triangle mesh. An anisotropic rectangular metric, de ned at each triangle facet of the input mesh, is derived from both a user-speci ed normal-based tolerance error and the requirement to favor rectangle-shaped polygons. Our algorithm uses a greedy optimization procedure that adds, deletes and relocates generators so as to match two criteria related to partitioning and conformity.