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98 changes: 98 additions & 0 deletions Source/EbsdLib/Core/DirectionalStats.cpp
Original file line number Diff line number Diff line change
@@ -1,3 +1,101 @@
/* ============================================================================
* Copyright (c) 2026 BlueQuartz Software, LLC
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*
* Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* Redistributions in binary form must reproduce the above copyright notice, this
* list of conditions and the following disclaimer in the documentation and/or
* other materials provided with the distribution.
*
* Neither the name of BlueQuartz Software, the US Air Force, nor the names of its
* contributors may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
* USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */

/* ============================================================================
* THIRD-PARTY ATTRIBUTION: EMsoft
*
* This file is a C++ port of the directional statistics routines of the EMsoft
* package, module 'dictmod' (Source/EMsoftLib/dictmod.f90) together with the
* supporting Bessel function and pseudo-random number generators of
* Source/EMsoftLib/math.f90. EMsoft is written by the Marc De Graef Research
* Group at Carnegie Mellon University. The EMsoft source attributes the original
* Expectation-Maximization implementation to Yu-Hui Chen (University of Michigan)
* and Marc De Graef (Carnegie Mellon University).
*
* Routine correspondence, EbsdLib <- EMsoft:
*
* DirectionalStats::EMforDS <- dictmod::DI_EMforDD
* DirectionalStats::Estep_ <- dictmod::DD_Estep
* DirectionalStats::Mstep_ <- dictmod::DD_Mstep
* DirectionalStats::getQandL_ <- dictmod::DD_getQandL
* DirectionalStats::Density_ <- dictmod::DD_Density
* DirectionalStats::logCp_ <- dictmod::logCp
* BesselI0 / BesselI1 / BesselIn <- math::BesselI0 / BesselI1 / BesselIn
* r8_uniform_01 <- math::r8_uniform_01
* r8vec_uniform_01 <- math::r8vec_uniform_01
* r8vec_normal_01 <- math::r8vec_normal_01
*
* The 'VMF' and 'WAT' distribution selectors correspond to the EMsoft 'Dtype'
* argument. The estimator is the modified, symmetry group invariant, von
* Mises-Fisher and axial Watson distribution described in:
*
* [1] Y.H. Chen, S.U. Park, D. Wei, G. Newstadt, M.A. Jackson, J.P. Simmons,
* M. De Graef and A.O. Hero, "A Dictionary Approach to Electron Backscatter
* Diffraction Indexing", Microscopy and Microanalysis 21(3), 739-752 (2015).
* DOI: 10.1017/S1431927615000756
*
* [2] Y.H. Chen, D. Wei, G. Newstadt, M. De Graef, J.P. Simmons and A.O. Hero,
* "Parameter Estimation in Spherical Symmetry Groups", IEEE Signal Processing
* Letters 22(8), 1152-1155 (2015). DOI: 10.1109/LSP.2014.2387206
*
* EMsoft is available at https://github.com/EMsoft-org/EMsoft and is distributed
* under the BSD 3-Clause license reproduced below. That notice, the list of
* conditions and the disclaimer are retained here as the license requires.
* ----------------------------------------------------------------------------
* Copyright (c) 2014-2022, Marc De Graef Research Group/Carnegie Mellon University
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*
* - Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
* - Neither the names of Marc De Graef, Carnegie Mellon University nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
* USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */

#include "DirectionalStats.hpp"

#include "EbsdLib/Orientation/Quaternion.hpp"
Expand Down
98 changes: 98 additions & 0 deletions Source/EbsdLib/Core/DirectionalStats.hpp
Original file line number Diff line number Diff line change
@@ -1,3 +1,101 @@
/* ============================================================================
* Copyright (c) 2026 BlueQuartz Software, LLC
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*
* Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* Redistributions in binary form must reproduce the above copyright notice, this
* list of conditions and the following disclaimer in the documentation and/or
* other materials provided with the distribution.
*
* Neither the name of BlueQuartz Software, the US Air Force, nor the names of its
* contributors may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
* USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */

/* ============================================================================
* THIRD-PARTY ATTRIBUTION: EMsoft
*
* This file is a C++ port of the directional statistics routines of the EMsoft
* package, module 'dictmod' (Source/EMsoftLib/dictmod.f90) together with the
* supporting Bessel function and pseudo-random number generators of
* Source/EMsoftLib/math.f90. EMsoft is written by the Marc De Graef Research
* Group at Carnegie Mellon University. The EMsoft source attributes the original
* Expectation-Maximization implementation to Yu-Hui Chen (University of Michigan)
* and Marc De Graef (Carnegie Mellon University).
*
* Routine correspondence, EbsdLib <- EMsoft:
*
* DirectionalStats::EMforDS <- dictmod::DI_EMforDD
* DirectionalStats::Estep_ <- dictmod::DD_Estep
* DirectionalStats::Mstep_ <- dictmod::DD_Mstep
* DirectionalStats::getQandL_ <- dictmod::DD_getQandL
* DirectionalStats::Density_ <- dictmod::DD_Density
* DirectionalStats::logCp_ <- dictmod::logCp
* BesselI0 / BesselI1 / BesselIn <- math::BesselI0 / BesselI1 / BesselIn
* r8_uniform_01 <- math::r8_uniform_01
* r8vec_uniform_01 <- math::r8vec_uniform_01
* r8vec_normal_01 <- math::r8vec_normal_01
*
* The 'VMF' and 'WAT' distribution selectors correspond to the EMsoft 'Dtype'
* argument. The estimator is the modified, symmetry group invariant, von
* Mises-Fisher and axial Watson distribution described in:
*
* [1] Y.H. Chen, S.U. Park, D. Wei, G. Newstadt, M.A. Jackson, J.P. Simmons,
* M. De Graef and A.O. Hero, "A Dictionary Approach to Electron Backscatter
* Diffraction Indexing", Microscopy and Microanalysis 21(3), 739-752 (2015).
* DOI: 10.1017/S1431927615000756
*
* [2] Y.H. Chen, D. Wei, G. Newstadt, M. De Graef, J.P. Simmons and A.O. Hero,
* "Parameter Estimation in Spherical Symmetry Groups", IEEE Signal Processing
* Letters 22(8), 1152-1155 (2015). DOI: 10.1109/LSP.2014.2387206
*
* EMsoft is available at https://github.com/EMsoft-org/EMsoft and is distributed
* under the BSD 3-Clause license reproduced below. That notice, the list of
* conditions and the disclaimer are retained here as the license requires.
* ----------------------------------------------------------------------------
* Copyright (c) 2014-2022, Marc De Graef Research Group/Carnegie Mellon University
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without modification,
* are permitted provided that the following conditions are met:
*
* - Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
* - Neither the names of Marc De Graef, Carnegie Mellon University nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE
* USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */

#pragma once

#include "EbsdLib/Core/EbsdLibConstants.h"
Expand Down
7 changes: 7 additions & 0 deletions Source/EbsdLib/Core/OrientationTransformation.hpp
Original file line number Diff line number Diff line change
Expand Up @@ -1159,12 +1159,19 @@ OutputType ho2ax(const InputType& h)
InputType hn = h;
OutputValueType sqrRtHMag = static_cast<OutputValueType>(1.0 / sqrt(hmag));
ArrayHelpers<InputType, typename InputType::value_type>::scalarMultiply(hn, sqrRtHMag); // In place scalar multiply
if(hmag > static_cast<OutputValueType>(LPs::R1 * LPs::R1))
{
hmag = static_cast<OutputValueType>(LPs::R1 * LPs::R1);
hm = hmag;
}
// The tfit series is valid only for 0 <= |h|^2 <= R1^2.
OutputValueType s = static_cast<OutputValueType>(LPs::tfit[0] + LPs::tfit[1] * hmag);
for(int i = 2; i < 16; i++)
{
hm = hm * hmag;
s = static_cast<OutputValueType>(s + LPs::tfit[i] * hm);
}
s = std::clamp(s, static_cast<OutputValueType>(-1.0), static_cast<OutputValueType>(1.0));
s = static_cast<OutputValueType>(2.0 * acos(s));
res[0] = hn[0];
res[1] = hn[1];
Expand Down
12 changes: 8 additions & 4 deletions Source/EbsdLib/LaueOps/CubicLowOps.cpp
Original file line number Diff line number Diff line change
Expand Up @@ -87,8 +87,9 @@ constexpr std::array<size_t, 3> k_OdfNumBins = {36, 36, 36}; // Represents a 5De
static const std::array<double, 3> k_OdfDimInitValue = {std::pow((0.75 * (ebsdlib::constants::k_PiOver2D - std::sin(ebsdlib::constants::k_PiOver2D))), (1.0 / 3.0)),
std::pow((0.75 * (ebsdlib::constants::k_PiOver2D - std::sin(ebsdlib::constants::k_PiOver2D))), (1.0 / 3.0)),
std::pow((0.75 * (ebsdlib::constants::k_PiOver2D - std::sin(ebsdlib::constants::k_PiOver2D))), (1.0 / 3.0))};
static const std::array<double, 3> k_OdfDimStepValue = {k_OdfDimInitValue[0] / static_cast<double>(k_OdfNumBins[0]) / 2.0, k_OdfDimInitValue[1] / static_cast<double>(k_OdfNumBins[1]) / 2.0,
k_OdfDimInitValue[2] / static_cast<double>(k_OdfNumBins[2]) / 2.0};
// Dividing by half the bin count makes the inverse grid span from -init to +init, as required by the forward ODF map.
static const std::array<double, 3> k_OdfDimStepValue = {k_OdfDimInitValue[0] / static_cast<double>(k_OdfNumBins[0] / 2), k_OdfDimInitValue[1] / static_cast<double>(k_OdfNumBins[1] / 2),
k_OdfDimInitValue[2] / static_cast<double>(k_OdfNumBins[2] / 2)};

constexpr int k_SymSize0 = 6;
constexpr int k_SymSize1 = 12;
Expand Down Expand Up @@ -191,7 +192,10 @@ constexpr double k_EtaMax = 90.0;
} // namespace CubicLow

// -----------------------------------------------------------------------------
CubicLowOps::CubicLowOps() = default;
CubicLowOps::CubicLowOps()
: LaueOps(CubicLow::k_OdfDimInitValue, CubicLow::k_OdfDimStepValue)
{
}

// -----------------------------------------------------------------------------
CubicLowOps::~CubicLowOps() = default;
Expand Down Expand Up @@ -398,7 +402,7 @@ EulerDType CubicLowOps::determineEulerAngles(double random[3], int choose) const
phi[1] = static_cast<int32_t>((choose / CubicLow::k_OdfNumBins[0]) % CubicLow::k_OdfNumBins[1]);
phi[2] = static_cast<int32_t>(choose / (CubicLow::k_OdfNumBins[0] * CubicLow::k_OdfNumBins[1]));

_calcDetermineHomochoricValues(random, init, step, phi, h1, h2, h3);
_calcDetermineHomochoricValuesInBall(random, init, step, phi, h1, h2, h3);

RodriguesDType ro = HomochoricDType(h1, h2, h3).toRodrigues();
ro = getODFFZRod(ro);
Expand Down
1 change: 1 addition & 0 deletions Source/EbsdLib/LaueOps/CubicLowOps.h
Original file line number Diff line number Diff line change
Expand Up @@ -189,6 +189,7 @@ class EbsdLib_EXPORT CubicLowOps : public LaueOps
int getMisoBin(const RodriguesDType& rod) const override;
bool inUnitTriangle(double eta, double chi) const override;
EulerDType determineEulerAngles(double random[3], int choose) const override;
using LaueOps::randomizeEulerAngles; /* Required due to C++ name hiding rules. Keeps base class 2 argument version visible */
EulerDType randomizeEulerAngles(const EulerDType& synea) const override;
RodriguesDType determineRodriguesVector(double random[3], int choose) const override;
int getOdfBin(const RodriguesDType& rod) const override;
Expand Down
7 changes: 5 additions & 2 deletions Source/EbsdLib/LaueOps/CubicOps.cpp
Original file line number Diff line number Diff line change
Expand Up @@ -278,7 +278,10 @@ constexpr double k_EtaMax = 45.0;
} // namespace CubicHigh

// -----------------------------------------------------------------------------
CubicOps::CubicOps() = default;
CubicOps::CubicOps()
: LaueOps(CubicHigh::k_OdfDimInitValue, CubicHigh::k_OdfDimStepValue)
{
}

// -----------------------------------------------------------------------------
CubicOps::~CubicOps() = default;
Expand Down Expand Up @@ -770,7 +773,7 @@ EulerDType CubicOps::determineEulerAngles(double random[3], int choose) const
phi[1] = static_cast<int32_t>((choose / CubicHigh::k_OdfNumBins[0]) % CubicHigh::k_OdfNumBins[1]);
phi[2] = static_cast<int32_t>(choose / (CubicHigh::k_OdfNumBins[0] * CubicHigh::k_OdfNumBins[1]));

_calcDetermineHomochoricValues(random, init, step, phi, h1, h2, h3);
_calcDetermineHomochoricValuesInBall(random, init, step, phi, h1, h2, h3);

RodriguesDType ro = HomochoricDType(h1, h2, h3).toRodrigues();
ro = getODFFZRod(ro);
Expand Down
1 change: 1 addition & 0 deletions Source/EbsdLib/LaueOps/CubicOps.h
Original file line number Diff line number Diff line change
Expand Up @@ -188,6 +188,7 @@ class EbsdLib_EXPORT CubicOps : public LaueOps
int getMisoBin(const RodriguesDType& rod) const override;
bool inUnitTriangle(double eta, double chi) const override;
EulerDType determineEulerAngles(double random[3], int choose) const override;
using LaueOps::randomizeEulerAngles; /* Required due to C++ name hiding rules. Keeps base class 2 argument version visible */
EulerDType randomizeEulerAngles(const EulerDType& synea) const override;
RodriguesDType determineRodriguesVector(double random[3], int choose) const override;
int getOdfBin(const RodriguesDType& rod) const override;
Expand Down
7 changes: 5 additions & 2 deletions Source/EbsdLib/LaueOps/HexagonalLowOps.cpp
Original file line number Diff line number Diff line change
Expand Up @@ -241,7 +241,10 @@ static const SymOps k_SymOps_XParallelA = SymOps::build<ebsdlib::HexConvention::
} // namespace HexagonalLow

// -----------------------------------------------------------------------------
HexagonalLowOps::HexagonalLowOps() = default;
HexagonalLowOps::HexagonalLowOps()
: LaueOps(HexagonalLow::k_OdfDimInitValue, HexagonalLow::k_OdfDimStepValue)
{
}

// -----------------------------------------------------------------------------
HexagonalLowOps::~HexagonalLowOps() = default;
Expand Down Expand Up @@ -457,7 +460,7 @@ EulerDType HexagonalLowOps::determineEulerAngles(double random[3], int choose) c
phi[1] = static_cast<int32_t>((choose / HexagonalLow::k_OdfNumBins[0]) % HexagonalLow::k_OdfNumBins[1]);
phi[2] = static_cast<int32_t>(choose / (HexagonalLow::k_OdfNumBins[0] * HexagonalLow::k_OdfNumBins[1]));

_calcDetermineHomochoricValues(random, init, step, phi, h1, h2, h3);
_calcDetermineHomochoricValuesInBall(random, init, step, phi, h1, h2, h3);

RodriguesDType ro = HomochoricDType(h1, h2, h3).toRodrigues();
ro = getODFFZRod(ro);
Expand Down
1 change: 1 addition & 0 deletions Source/EbsdLib/LaueOps/HexagonalLowOps.h
Original file line number Diff line number Diff line change
Expand Up @@ -189,6 +189,7 @@ class EbsdLib_EXPORT HexagonalLowOps : public LaueOps
int getMisoBin(const RodriguesDType& rod) const override;
bool inUnitTriangle(double eta, double chi) const override;
EulerDType determineEulerAngles(double random[3], int choose) const override;
using LaueOps::randomizeEulerAngles; /* Required due to C++ name hiding rules. Keeps base class 2 argument version visible */
EulerDType randomizeEulerAngles(const EulerDType& euler) const override;
RodriguesDType determineRodriguesVector(double random[3], int choose) const override;
int getOdfBin(const RodriguesDType& rod) const override;
Expand Down
7 changes: 5 additions & 2 deletions Source/EbsdLib/LaueOps/HexagonalOps.cpp
Original file line number Diff line number Diff line change
Expand Up @@ -313,7 +313,10 @@ static const SymOps k_SymOps_XParallelA = SymOps::build<ebsdlib::HexConvention::
} // namespace HexagonalHigh

// -----------------------------------------------------------------------------
HexagonalOps::HexagonalOps() = default;
HexagonalOps::HexagonalOps()
: LaueOps(HexagonalHigh::k_OdfDimInitValue, HexagonalHigh::k_OdfDimStepValue)
{
}

// -----------------------------------------------------------------------------
HexagonalOps::~HexagonalOps() = default;
Expand Down Expand Up @@ -545,7 +548,7 @@ EulerDType HexagonalOps::determineEulerAngles(double random[3], int choose) cons
phi[1] = static_cast<int32_t>((choose / HexagonalHigh::k_OdfNumBins[0]) % HexagonalHigh::k_OdfNumBins[1]);
phi[2] = static_cast<int32_t>(choose / (HexagonalHigh::k_OdfNumBins[0] * HexagonalHigh::k_OdfNumBins[1]));

_calcDetermineHomochoricValues(random, init, step, phi, h1, h2, h3);
_calcDetermineHomochoricValuesInBall(random, init, step, phi, h1, h2, h3);

RodriguesDType ro = HomochoricDType(h1, h2, h3).toRodrigues();
ro = getODFFZRod(ro);
Expand Down
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