Incremental and Transitive Discrete Rotations

Details Incremental and Transitive Discrete Rotations Incremental and Transitive Discrete Rotations

2005-12-16

arxiv.org/abs/cs/0512070v2

Computer Science

Discrete Mathematics

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Incremental and Transitive Discrete Rotations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Incremental and Transitive Discrete Rotations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Incremental and Transitive Discrete Rotations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-112149