Abstract.
We study the problem of approximating a rotation of the plane, α :R 2 \( \rightarrow \) R 2 , α (x,y)=(x cos θ + y sin θ , y cos θ - x sin θ ), by a bijection β :Z 2 \(\rightarrow\) Z 2 . We show by an explicit construction that β may be chosen so that \( {\rm sup}_{z \in Z^2} |\alpha (z)-\beta (z)| \leq ({1}/{\sqrt{2}}) (({1+r})/{\sqrt{1+r^2}}) \) , where r= tan ( θ /2). The scheme is based on those invented and patented by the second author in 1994.
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Received November 21, 1996, and in revised form February 20, 1997.
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Sterling, I., Sterling, T. Approximating Planar Rotations. Discrete Comput Geom 21, 45–56 (1999). https://doi.org/10.1007/PL00009409
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DOI: https://doi.org/10.1007/PL00009409