scholarly journals 3D-Orientation Space; Filters and Sampling

2003 ◽  
pp. 36-42 ◽  
Author(s):  
Frank G. A. Faas ◽  
Lucas J. van Vliet
Keyword(s):  
Orientation Space

scholarly journals Properties of Projection Lines in the Space of the Orientation Distribution Function

1989 ◽  
Vol 10 (3) ◽  
pp. 243-264 ◽  
Author(s):  
A. Morawiec ◽  
J. Pospiech
Keyword(s):  
Distribution Function ◽  
Pole Figure ◽  
Orientation Distribution Function ◽  
Analytical Description ◽  
Orientation Distribution ◽  
Orientation Space ◽  
The Relationship ◽  
Symmetry Operations

The relationship between the orientation distribution function (ODF) and the pole figure is based on the geometry of projection lines in the orientation space.The paper presents an analytical description of the projection lines and their transformations by symmetry operations. Using simple algebraical rules some properties of the projection lines as well as some properties of the associated projection lines (coupled due to the centrosymmetry of the pole figure) have been derived.

scholarly journals Nearly uniform sampling of crystal orientations

2018 ◽  
Vol 51 (4) ◽  
pp. 1162-1173 ◽  
Author(s):  
Romain Quey ◽  
Aurélien Villani ◽  
Claire Maurice
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Uniform Distributions ◽  
Orientation Space ◽  
Unit Quaternions ◽  
Spatial Uniformity ◽  
Unit Hypersphere ◽  
Open Source Software Package ◽  
Diffraction Patterns ◽  
Thomson Problem

A method is presented for generating nearly uniform distributions of three-dimensional orientations in the presence of symmetry. The method is based on the Thomson problem, which consists in finding the configuration of minimal energy of N electrons located on a unit sphere – a configuration of high spatial uniformity. Orientations are represented as unit quaternions, which lie on a unit hypersphere in four-dimensional space. Expressions of the electrostatic potential energy and Coulomb's forces are derived by working in the tangent space of orientation space. Using the forces, orientations are evolved in a conventional gradient-descent optimization until equilibrium. The method is highly versatile as it can generate uniform distributions for any number of orientations and any symmetry, and even allows one to prescribe some orientations. For large numbers of orientations, the forces can be computed using only the close neighbourhoods of orientations. Even uniform distributions of as many as 106 orientations, such as those required for dictionary-based indexing of diffraction patterns, can be generated in reasonable computation times. The presented algorithms are implemented and distributed in the free (open-source) software package Neper.

Spatiality and World Politics

2020 ◽  
Author(s):  
Duncan Weaver
Keyword(s):  
International Relations ◽  
World Politics ◽  
Sovereign Power ◽  
Many Worlds ◽  
Orientation Space ◽  
The Many

Space has always animated world politics, but three spatial orientations are striking. First, the Westphalian orientation deems space a sovereign power container. Second, the scalar takes recourse to the local, regional, national, and global spaces in which world politics is played out. Third, the relational deems space a (re)produced, sociohistorically contingent phenomenon that changes according to the humans occupying it and the thought, power, and resources flowing through it. Under this latter orientation, space is lived, lived in and lived through. Whilst relationality, to a degree, calls into question the received wisdoms of International Relations (IR), the fixity of sovereignty and territory remain. The orientations coexist concomitantly, reflecting the “many worlds” humankind occupies.

scholarly journals Resolving pseudosymmetry in tetragonal ZrO2 using electron backscatter diffraction with a modified dictionary indexing approach

2020 ◽  
Vol 53 (4) ◽  
pp. 1060-1072 ◽  
Author(s):  
Edward L. Pang ◽  
Peter M. Larsen ◽  
Christopher A. Schuh
Keyword(s):  
Present Method ◽  
Electron Backscatter Diffraction ◽  
Source Code ◽  
Tetragonal Zro2 ◽  
Data Set ◽  
Orientation Space ◽  
Indexing Method ◽  
Wide Range ◽  
Electron Backscatter ◽  
Backscatter Diffraction

Resolving pseudosymmetry has long presented a challenge for electron backscatter diffraction and has been notoriously challenging in the case of tetragonal ZrO2 in particular. In this work, a method is proposed to resolve pseudosymmetry by building upon the dictionary indexing method and augmenting it with the application of global optimization to fit accurate pattern centers, clustering of the Hough-indexed orientations to focus the dictionary in orientation space and interpolation to improve the accuracy of the indexed solution. The proposed method is demonstrated to resolve pseudosymmetry with 100% accuracy in simulated patterns of tetragonal ZrO2, even with high degrees of binning and noise. The method is then used to index an experimental data set, which confirms its ability to efficiently and accurately resolve pseudosymmetry in these materials. The present method can be applied to resolve pseudosymmetry in a wide range of materials, possibly even some more challenging than tetragonal ZrO2. Source code for this implementation is available online.

Relating Cognitive Development To Cartographic Education With A Model Of Orientation Space

1993 ◽  
pp. 3-8 ◽  
Author(s):  
Henry W. Castner
Keyword(s):  
Cognitive Development ◽  
Common Ground ◽  
Spatial Relationships ◽  
Orientation Space ◽  
Vast Literature

An "orientation space" is briefly described as a means of synthesizing a vast literature and of providing psychologists and cartographers with some common ground for discussing the issues of cognitive development in children as they might ap ply to elementary cartographic education. The vast literature refers to the work in many fields on the questions of how children navigate and orient themselves, how they visualize and organize space and spatial relationships, and how they express these ideas graphically.

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