This pull-request features the methods of approximating an ODF explained in
Schaeben, H., Bachmann, F. & Fundenberger, JJ. Construction of weighted crystallographic orientations capturing a given orientation density function. J Mater Sci 52, 2077–2090 (2017). https://doi.org/10.1007/s10853-016-0496-1
with some options to specify the way the kernel density should be approximated. Only the normalized case vol(SO3F)=1 is considered, the case vol(SO3F)!=1 has not been considered nor tested.
The function
SO3F = SO3FunRBF.quadrature(SO3Fun)
is technically not a quadrature, but was added to have an equivalent to SO3FunHarmonic.quadrature(SO3Fun).
The function SO3Fun.interpolate has been moved to SOFunRBF.interpolate in order to use the system matrix. Also, the only difference between approximation and interpolation appears to be that the approximation constraints the least squares to sum(weights)=1,weights>0 when operating in the spatial domain.
For the harmonic method, the WignerD function has been updated to follow the revised definition of the Wigner-D functions, which is firstly the change in alpha/beta/gamma convention (used in mtex-3.5.0) and secondly the change in the L2 normalization of the coefficients (since mtex-5.9). There might be a smarter and more efficient way using NSOFT or the new wignerTrafo/Adjoint to omit the very large system matrix.
This pull-request features the methods of approximating an ODF explained in
It introduces the function
with some options to specify the way the kernel density should be approximated. Only the normalized case vol(SO3F)=1 is considered, the case vol(SO3F)!=1 has not been considered nor tested.
The function
is technically not a quadrature, but was added to have an equivalent to
SO3FunHarmonic.quadrature(SO3Fun).The function
SO3Fun.interpolatehas been moved toSOFunRBF.interpolatein order to use the system matrix. Also, the only difference between approximation and interpolation appears to be that the approximation constraints the least squares to sum(weights)=1,weights>0 when operating in the spatial domain.For the harmonic method, the
WignerDfunction has been updated to follow the revised definition of the Wigner-D functions, which is firstly the change in alpha/beta/gamma convention (used in mtex-3.5.0) and secondly the change in the L2 normalization of the coefficients (since mtex-5.9). There might be a smarter and more efficient way using NSOFT or the new wignerTrafo/Adjoint to omit the very large system matrix.