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We construct a bijection from R2 to R2, which maps, for each αÎ (0, ¥), rectangles of arbitrary edges 2aL1, 2aL2 onto ellipses with semi-axes aa, ab, with a, b satisfying 4L1L2 = pab. This bijection preserves area and thus allows us to construct uniform and refinable grids on elliptic domains starting from uniform and refinable grids on rectangles.

Mathematics Subject Classification (2010): 65M50, 65N50.

Keywords: Uniform grid, refinable grid, hierarchical grid, equal area projection, ellipse.