Characterization of Bijective Discretized Rotations
نویسندگان
چکیده
A discretized rotation is the composition of an Euclidean rotation with the rounding operation. For 0 < α < π/4, we prove that the discretized rotation [rα] is bijective if and only if there exists a positive integer k such as {cosα, sinα} = { 2k + 1 2k2 + 2k + 1 , 2k + 2k 2k2 + 2k + 1 } The proof uses a particular subgroup of the torus (R/Z).
منابع مشابه
Characterization of bijective discretized rotations by Gaussian integers
Une rotation discrète est la composition d'une rotation euclidienne et d'une opération d'arrondi. Bien sûr, toutes les rotations discrètes ne sont pas bijectives : par exemple, deux points distincts peuvent avoir la même image pour une rotation discrète donnée. Néanmoins, pour un certain ensemble d'angles, les rotations discrètes sont bijectives. Dans la grille carrée régulière, les rotations d...
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