Hinge Angles for 3D Discrete Rotations

Thibault, Yohan; Sugimoto, Akihiro; Kenmochi, Yukiko

doi:10.1007/978-3-642-10210-3_10

Cited by 2 publications

(3 citation statements)

References 10 publications

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“…From (11) we see that p ′ z must be a rational number, so that there exists a pair of integers λ 1 , λ 2 such that p ′ z = λ1 λ2 and gcd(λ 1 , λ 2 ) = 1. From (12) we see that p ′2 z + 1 2 must be an integer.…”

Section: Proof the Equation Of The Rotation Planementioning

confidence: 99%

“…In particular, to our best knowledge, this is the first work on 3D discrete rotations using integer computations without digitization errors. This paper is an extended version of our previous paper [11]. Sections 3 and 4 about multi-grids and hinge angles are re-organized as more properties of multi-grids are added in this paper (see section 3.4 for the properties).…”

Section: Introductionmentioning

confidence: 99%

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3D discrete rotations using hinge angles

Thibault¹,

Sugimoto²,

Kenmochi³

2011

Theoretical Computer Science

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International audienceIn this paper, we study 3D rotations on grid points computed by using only integers. For that purpose, we investigate the intersection between the 3D half-grid and the rotation plane. From this intersection, we define 3D hinge angles which determine a transit of a grid point from a voxel to its adjacent voxel during the rotation. Then, we give a method to sort all 3D hinge angles with integer computations. The study of 3D hinge angles allows us to design a 3D discrete rotation and to estimate the rotation between a pair of digital images in correspondence

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Section: Proof the Equation Of The Rotation Planementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

3D discrete rotations using hinge angles

Thibault¹,

Sugimoto²,

Kenmochi³

2011

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…As a result, by using a fully 3-D discrete network, they were able to reach more in terms of accuracy to complete this medical part. Other related papers on 3-D space can also be found in (Hofmann et al, 2017;Samaniego, Sanchis, García-Nieto & Simarro, 2017;Thibault, 2010). Some of the methodology discussed in the results and discussion may be referred to (Dawkins, n.d.).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Rotations on a 3-Dimensional Lattice

Saleh,

Wan Rozali,

Zakaria

2023

RAS

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The study of resonances of Hamiltonian systems with a divided phase space is a well-established area of research which attracted the interests of many researchers over the years. We study such resonances over a discrete space focusing on the rotational motion of some orbits in the 3-Dimensional lattice, ?3. In this study, we construct the discrete standard map from 2-Dimensional to 3-Dimensional lattices. Then, we identify and categorize any transformation that could give periodicity for the 3-Dimensional lattice on a specific map. The study aims to determine the points that give the periodicity and at the same time investigate the behavior of the points for the nonlinear stable orbits over a discrete space. For some choice of parameters ???? ?, our findings showed that the orbit of the 3-Dimensional map is periodic depending on the initial conditions. Some arbitrary initial conditions may be periodic in a 3-Dimensional lattice.Keywords: Hamiltonian systems, nonlinear rotations, space discretization, arithmetic dynamics

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Hinge Angles for 3D Discrete Rotations

Cited by 2 publications

References 10 publications

3D discrete rotations using hinge angles

3D discrete rotations using hinge angles

Nonlinear Rotations on a 3-Dimensional Lattice

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