Abstract: A geometry image offers a simple and compact way of encoding the geometry of a surface and its implicit connectivity in an image-like data structure. It has been shown to be useful in multiple applications because of its suitability for efficient hardware rendering, level of detail, filtering, etc. Most existing algorithms generate geometry images by parameterizing the surface onto a domain, and by performing a regular resampling in this domain. Unfortunately, this regular resampling fails to capture sharp features present on the surface. In this paper, we propose to slightly alter the grid to align sample positions with corners and sharp edges in the geometric model. While doing so, our goal is to maintain the resulting geometry images simple to interpret, while producing higher quality reconstructions. We demonstrate an implementation in the planar domain and show results on a range of common geometrical models.