Incremental and Transitive Discrete Rotations
| dc.creator | Nouvel, Bertrand | |
| dc.creator | Remila, Eric | |
| dc.date | 2005-12-16 | |
| dc.date | 2006-01-05 | |
| dc.date.accessioned | 2026-07-07T06:53:51Z | |
| dc.date.available | 2026-07-07T06:53:51Z | |
| dc.description | A discrete rotation algorithm can be apprehended as a parametric application $f\_α$ 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. | |
| dc.identifier | https://arxiv.org/abs/cs/0512070 | |
| dc.identifier | http://arxiv.org/abs/cs/0512070 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/105736 | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Graphics | |
| dc.title | Incremental and Transitive Discrete Rotations | |
| dc.type | text |