Incremental and Transitive Discrete Rotations
<|reference_start|>Incremental and Transitive Discrete Rotations: A discrete rotation algorithm can be apprehended as a parametric application $f\_\alpha$ from $\ZZ[i]$ to $\ZZ[i]$, whose resulting permutation ``looks like'' the map induced by an Euclidean rotation. For this kind of algorithm, to be incremental means to compute successively all the intermediate rotate d copies of an image for angles in-between 0 and a destination angle. The di scretized rotation consists in the composition of an Euclidean rotation with a discretization; the aim of this article is to describe an algorithm whic h computes incrementally a discretized rotation. The suggested method uses o nly integer arithmetic and does not compute any sine nor any cosine. More pr ecisely, its design relies on the analysis of the discretized rotation as a step function: the precise description of the discontinuities turns to be th e key ingredient that will make the resulting procedure optimally fast and e xact. A complete description of the incremental rotation process is provided, also this result may be useful in the specification of a consistent set of defin itions for discrete geometry.<|reference_end|>
@article{nouvel2005incremental,
    title={Incremental and Transitive Discrete Rotations},
    author={Bertrand Nouvel (LIP), Eric Remila (LIP)},
    journal={arXiv preprint arXiv:cs/0512070},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0512070},
    primaryClass={cs.DM cs.GR}
}