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Characterization of bijective discretized rotations by Gaussian integers

Tristan Roussillon 1 David Coeurjolly 1
1 M2DisCo - Geometry Processing and Constrained Optimization
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
Abstract : A discretized rotation is the composition of an Euclidean rotation with a rounding operation. It is well known that not all discretized rotations are bijective: e.g. two distinct points may have the same image by a given discretized rotation. Nevertheless, for a certain subset of rotation angles, the discretized rotations are bijective. In the regular square grid, the bijective discretized rotations have been fully characterized by Nouvel and Rémila (IWCIA'2005). We provide a simple proof that uses the arithmetical properties of Gaussian integers.
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https://hal.archives-ouvertes.fr/hal-01259826
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Submitted on : Thursday, January 21, 2016 - 10:01:59 AM
Last modification on : Wednesday, November 20, 2019 - 3:06:55 AM
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  • HAL Id : hal-01259826, version 1

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Tristan Roussillon, David Coeurjolly. Characterization of bijective discretized rotations by Gaussian integers. [Research Report] LIRIS UMR CNRS 5205. 2016. ⟨hal-01259826⟩

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