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# Five Degree-of-Freedom Grain Boundary Interpolation
[![View Five Degree-of-Freedom Grain Boundary Interpolation on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/105940-five-degree-of-freedom-grain-boundary-interpolation) ![Lines of code](https://img.shields.io/tokei/lines/github/sgbaird-5DOF/interp) ![GitHub all releases](https://img.shields.io/github/downloads/sgbaird-5DOF/interp/total)

[![GitHub release (latest by date)](https://img.shields.io/github/v/release/sgbaird-5DOF/interp) ![GitHub Release Date](https://img.shields.io/github/release-date/sgbaird-5DOF/interp)](https://github.com/sgbaird-5DOF/interp/releases/latest) ![GitHub commits since latest release (by date)](https://img.shields.io/github/commits-since/sgbaird-5DOF/interp/latest)
[![View Five Degree-of-Freedom Grain Boundary Interpolation on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://www.mathworks.com/matlabcentral/fileexchange/105940-five-degree-of-freedom-grain-boundary-interpolation) ![Lines of code](https://img.shields.io/tokei/lines/github/sgbaird-5DOF/interp) ![GitHub all releases](https://img.shields.io/github/downloads/sgbaird-5DOF/interp/total) [![GitHub release (latest by date)](https://img.shields.io/github/v/release/sgbaird-5DOF/interp) ![GitHub Release Date](https://img.shields.io/github/release-date/sgbaird-5DOF/interp)](https://github.com/sgbaird-5DOF/interp/releases/latest) ![GitHub commits since latest release (by date)](https://img.shields.io/github/commits-since/sgbaird-5DOF/interp/latest)

Code related to meshing and interpolation of grain boundaries by representing 5DOF of grain boundaries as grain boundary octonions and mapping them into a Voronoi Fundamental Zone. ([https://github.com/sgbaird-5DOF/interp](https://github.com/sgbaird-5DOF/interp))

<img src=https://user-images.githubusercontent.com/45469701/152445635-f5f2f066-5a5d-4a59-9e01-6a1c3c7d7426.png width=400>
<sup> See table of contents figure from DOI: [10.1016/j.commatsci.2021.110756](https://doi.org/10.1016/j.commatsci.2021.110756) (top) grain boundary energy (GBE) values plotted continuously between two arbitrary octonions. (bottom-left) 2D analogy of a Grain Boundary Octonion Voronoi Fundamental Zone (GBO-VFZ). Dark blue points are mapped into the VFZ. (bottom-right) Parity plot of GPR predictions.
<img src=https://user-images.githubusercontent.com/45469701/152452613-2cab0239-1412-4a6c-8fb7-7af9f810be33.png width=750>
<sup> Figure adapted based on table of contents from DOI: 10.1016/j.commatsci.2021.110756 (a) grain boundary energy (GBE) values plotted continuously between two arbitrary grain boundary octonions (i.e. changes in all 5DOF). (b) 2D analogy of a Grain Boundary Octonion Voronoi Fundamental Zone (GBO-VFZ). Dark blue points are mapped into the VFZ. (c) Hexagonally binned parity plot of GPR predictions colored by number of points per bin. </sup>

## Citing
> 1. Baird, S. G.; Homer, E. R.; Fullwood, D. T.; Johnson, O. K. Five Degree-of-Freedom Property Interpolation of Arbitrary Grain Boundaries via Voronoi Fundamental Zone Framework. Computational Materials Science 2021, 200, 110756. https://doi.org/10.1016/j.commatsci.2021.110756.
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