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### 3D discrete rotations using hinge angles

Yohan Thibault, Akihiro Sugimoto, Yukiko Kenmochi
2011 Theoretical Computer Science
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.  ...  Then, we give a method to sort all 3D hinge angles with integer computations.  ...  Acknowledgment We would like to thank Laurent Fuchs and Éric Andrès at University of Poitier, France, and Bertrand Nouvel at the National Institute of Informatics, Japan, for the useful discussions.  ...

### Hinge Angles for 3D Discrete Rotations [chapter]

Yohan Thibault, Akihiro Sugimoto, Yukiko Kenmochi
2009 Lecture Notes in Computer Science
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.  ...  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.  ...  Hinge angles on rotation planes also allow us to design a 3D incremental discrete rotation.  ...

### Computing upper and lower bounds of rotation angles from digital images

Yohan Thibault, Yukiko Kenmochi, Akihiro Sugimoto
2009 Pattern Recognition
For such a set of admissible rotation angles, there exist two angles that achieve the lower and the upper bounds. To find those lower and upper bounds, we use hinge angles as used in [7] .  ...  In the discrete plane, there are many angles giving the rotation from A to B, which we called admissible rotation angles from A to B.  ...  Because in 3D hinge angles are not yet defined in 3D, the first direction we should take is to design 3D hinge angles and develop a 3D discrete rotation algorithm based on 3D hinge angles.  ...

### (2+1) Regge Calculus: Discrete Curvatures, Bianchi Identity, and Gauss-Codazzi Equation [article]

Seramika Ariwahjoedi, Freddy P. Zen
2017 arXiv   pre-print
deficit angles, and their clear geometrical interpretations in the first order discrete geometry.  ...  It turns out that the discrete Bianchi identity and Gauss-Codazzi equation, at least in 3-dimension, could be derived from the dihedral angle formula of a tetrahedron, while the dihedral angle relation  ...  be rotated by the deficit angle δφ in the direction of the plane of rotation, which in turns, is perpendicular to the hinge [56] .  ...

### Curvatures and discrete Gauss–Codazzi equation in (2 + 1)-dimensional loop quantum gravity

Seramika Ariwahjoedi, Jusak Sali Kosasih, Carlo Rovelli, Freddy P. Zen
2015 International Journal of Geometric Methods in Modern Physics (IJGMMP)
We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles  ...  This allows us to write operators acting on spin network states in (2+1)-dimensional loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional intrinsic, and 2-dimensional extrinsic  ...  In discrete geometry, this rotation angle is the same as the deficit angle on the hinges. 2D intrinsic curvature (SO(2)) Using FIG. 4 as the simplest case, we take loop γ circling point p on the surface  ...

### FlexM: Designing a Physical Construction Kit for 3d Modeling

Markus Eng, Ken Camarata, Ellen Yi-Luen Do, Mark D Gross
2006 International Journal of Architectural Computing
Using the FlexM hub and strut components, designers can build and explore 3D geometry with the ease of a toy and the power of a computer.  ...  FlexM is a prototype in progress of a flexible physical interface for manipulating and building 3D geometry.  ...  The sockets will be attached to two hinges as shown in Figure 15 . The hinges will have rotational potentiometers to serve as the mechanical hinge and measure the angle of the hinge.  ...

### How far can you reach? [chapter]

Ciprian Borcea, Ileana Streinu
2010 Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms
The problem of computing the maximum reach configurations of a 3D revolute-jointed manipulator is a longstanding open problem in robotics.  ...  The algorithms rely on our recent theoretical results characterizing combinatorially the maximum of panel-and-hinge chains.  ...  After that, in linear time we compute the angles by which the panels will be rotated at the fold points.  ...

### Algorithmic design of self-folding polyhedra

S. Pandey, M. Ewing, A. Kunas, N. Nguyen, D. H. Gracias, G. Menon
2011 Proceedings of the National Academy of Sciences of the United States of America
We also find that shortest paths between 2D nets and the 3D polyhedron in a discrete model of the configuration space of foldings are a useful idealization of experimentally observed folding pathways.  ...  Our focus in this work is on the role of discrete geometry in self-assembly.  ...  Folding hinges melt and cause panels to rotate. Locking hinges meet and fuse when panels linked at the vertex connection have rotated through approximately the dihedral angle about a folding hinge.  ...

### Inversion of geological knowledge for fold geometry

Lachlan Grose, Laurent Ailleres, Gautier Laurent, Robin Armit, Mark Jessell
2019 Journal of Structural Geology
Existing geological knowledge is usually indirectly incorporated into 3D models using the geologist's non-unique interpretation as form lines, cross sections and level maps.  ...  The process of building three-dimensional (3D) geological models can be framed as an inverse problem where a model describing the 3D distribution of rock units is non-uniquely derived from geological observations  ...  Jupyter notebooks for the synthetic examples can be obtained from www.github.com/lachlangrose/inverting_knowledge_JSG. 3D examples and software can be obtained by contacting the corresponding author.  ...

### Wrist and Finger Torque Sensor for the quantification of upper limb motor impairments following brain injury

A. H. A. Stienen, T. S. Moulton, L. C. Miller, J. P. A. Dewald
2011 2011 IEEE International Conference on Rehabilitation Robotics
The WFTS can be used in combination with rehabilitation robots such as the ACT-3D, with isometric measurement stations, or as a stand-alone device.  ...  involve the hand in isolation, the WFTS is designed to investigate abnormal joint torque coupling at the paretic wrist and fingers in individuals with adult-onset stroke or childhood hemiplegia during 3D  ...  The finger and wrist flexion/extension angle can be set at discrete angles via bolted connections respectively between the dark-blue angle adjuster and the orange slider, and the dark-red angle adjuster  ...

### Implicit modeling of folds and overprinting deformation

Gautier Laurent, Laurent Ailleres, Lachlan Grose, Guillaume Caumon, Mark Jessell, Robin Armit
2016 Earth and Planetary Science Letters
However, existing approaches are still limited by the type of structural data they are able to use and by their lack of structural meaning.  ...  A fold coordinate system is used to support the numerical description of fold geometry and to modify the behavior of classical structural interpolators.  ...  Data and tools used in this this paper are available upon request to the corresponding author.  ...

### Experimental and computational studies of the aerodynamic performance of a flapping and passively rotating insect wing

Yufeng Chen, Nick Gravish, Alexis Lussier Desbiens, Ronit Malka, Robert J. Wood
2016 Journal of Fluid Mechanics
Here, we investigate the fluid mechanics of flapping wings that possess a single flexible hinge allowing passive wing pitch rotation under load.  ...  Our dual approach of running at-scale experiments and numerical simulations gives useful guidelines for choosing wing hinge stiffnesses that lead to efficient flapping.  ...  Wood Stroke angle Hinge angle Downstroke Upstroke r 2L Pitch rotation Pitch rotation Stroke acceleration Stroke deceleration 40 20 0 -20 -40 Angle (deg.)  ...

### Preface

Valentin E. Brimkov, Reneta P. Barneva, Petra Wiederhold
2011 Theoretical Computer Science
In the paper "Two Discrete Versions of the Inscribed Square Conjecture and Some Related Problems", the authors Feliú Sagols and Raúl Marín consider a discrete version of the long-standing Inscribed Square  ...  In the paper ''3D Discrete Rotations Using Hinge Angles'', the authors Yohan Thibault, Akihiro Sugimoto, and Yukiko Kenmochi study 3D rotations on grid points computed by using only integer arithmetic.  ...  They define 3D ''hinge angles'' which determine a transition of a grid point from a voxel to its adjacent voxel during the rotation.  ...

### Nanoscale Origami for 3D Optics

Jeong-Hyun Cho, Michael D. Keung, Niels Verellen, Liesbet Lagae, Victor V. Moshchalkov, Pol Van Dorpe, David H. Gracias
2011 Small
We have observed that yields are greatly enhanced by the use of both folding and locking hinges; the self-folding hinges rotate the panels to their approximate 3D position and the locking hinges self-align  ...  [ 15 ] Here, another control parameter, namely manipulation of the etch time was found to result in structures with panels rotated by 45 ° or 90 ° angles; the extent of rotation could be correlated  ...

### Contracted Bianchi Identity and Angle Relation on n-dimensional Simplicial Complex of Regge Calculus [article]

Seramika Ariwahjoedi, Freddy P. Zen
2018 arXiv   pre-print
Here, we found that: (1) in 4-dimensional Euclidean Regge Gravity, all the holonomy circling a single hinge are simple rotations, and (2) the dihedral angle relation represents the 'contracted' Bianchi  ...  An interesting fact we found is the trace relation of SU(2) gives the spherical law of cosine which in turns is a dihedral angle relation, a constraint that must be satisfied by closed Euclidean simplices  ...  Similar with the angle relation, this is automatically satisfied in 3D but not in larger dimension.  ...
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