In many usecases one is interested in grid of orientations that somehow uniformely cover the orientation space. The simplest way of generating equispaced orientations with given resolution is by the command
% define a crystal symmetry
cs = crystalSymmetry ( '432' )
% define a grid of orientations
ori = equispacedSO3Grid ( cs , 'resolution' , 5 * degree )
cs = crystalSymmetry
symmetry: 432
elements: 24
a, b, c : 1, 1, 1
ori = SO3Grid (432 → xyz)
grid: 4958 orientations, resolution: 5°
Lets visualize them
plot ( ori , 'axisAngle' )
plot 2000 random orientations out of 4958 given orientations
Check for equidistribution
odf = unimodalODF ( ori )
plotPDF ( odf , Miller ({ 1 , 0 , 0 },{ 1 , 1 , 0 },{ 1 , 1 , 1 }, cs ))
mtexColorbar
odf = SO3FunRBF (432 → xyz)
multimodal components
kernel: de la Vallee Poussin, halfwidth 10°
center: 4958 orientations, resolution: 5°
weight: 1
ori = regularSO3Grid ( cs , 'resolution' , 5 * degree )
ori = orientation (432 → xyz)
size: 72 x 19 x 18
plot ( ori , 'axisAngle' )
plot 2000 random orientations out of 24624 given orientations
odf = unimodalODF ( ori )
plotPDF ( odf , Miller ({ 1 , 0 , 0 },{ 1 , 1 , 0 },{ 1 , 1 , 1 }, cs ))
mtexColorbar
odf = SO3FunRBF (432 → xyz)
multimodal components
kernel: de la Vallee Poussin, halfwidth 10°
center: 24624 orientations