/
HexagonalLowOps.cpp
1615 lines (1466 loc) · 56.9 KB
/
HexagonalLowOps.cpp
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/* ============================================================================
* Copyright (c) 2009-2016 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.
*
* The code contained herein was partially funded by the followig contracts:
* United States Air Force Prime Contract FA8650-07-D-5800
* United States Air Force Prime Contract FA8650-10-D-5210
* United States Prime Contract Navy N00173-07-C-2068
*
* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ */
#include "HexagonalLowOps.h"
#ifdef SIMPLib_USE_PARALLEL_ALGORITHMS
#include <tbb/parallel_for.h>
#include <tbb/blocked_range.h>
#include <tbb/partitioner.h>
#include <tbb/task_scheduler_init.h>
#include <tbb/task_group.h>
#include <tbb/task.h>
#endif
// Include this FIRST because there is a needed define for some compiles
// to expose some of the constants needed below
#include "SIMPLib/Math/SIMPLibMath.h"
#include "SIMPLib/Utilities/ColorTable.h"
#include "OrientationLib/OrientationMath/OrientationArray.hpp"
#include "OrientationLib/OrientationMath/OrientationTransforms.hpp"
#include "OrientationLib/Utilities/PoleFigureUtilities.h"
#include "OrientationLib/Utilities/ComputeStereographicProjection.h"
namespace Detail
{
static const float HexDim1InitValue = powf((0.75f * ((float(SIMPLib::Constants::k_Pi)) - sinf((float(SIMPLib::Constants::k_Pi))))), (1.0f / 3.0f));
static const float HexDim2InitValue = powf((0.75f * ((float(SIMPLib::Constants::k_Pi)) - sinf((float(SIMPLib::Constants::k_Pi))))), (1.0f / 3.0f));
static const float HexDim3InitValue = powf((0.75f * ((float(SIMPLib::Constants::k_Pi) / 6.0f) - sinf((float(SIMPLib::Constants::k_Pi) / 6.0f)))), (1.0f / 3.0f));
static const float HexDim1StepValue = HexDim1InitValue / 36.0f;
static const float HexDim2StepValue = HexDim2InitValue / 36.0f;
static const float HexDim3StepValue = HexDim3InitValue / 6.0f;
namespace HexagonalLow
{
static const int symSize0 = 2;
static const int symSize1 = 2;
static const int symSize2 = 2;
}
}
const int HexagonalLowOps::k_OdfSize = 62208;
const int HexagonalLowOps::k_MdfSize = 62208;
const int HexagonalLowOps::k_NumSymQuats = 6;
static const QuatF HexQuatSym[HexagonalLowOps::k_NumSymQuats] = {QuaternionMathF::New(0.000000000f, 0.000000000f, 0.000000000f, 1.000000000f),
QuaternionMathF::New(0.000000000f, 0.000000000f, 0.500000000f, 0.866025400f),
QuaternionMathF::New(0.000000000f, 0.000000000f, 0.866025400f, 0.500000000f),
QuaternionMathF::New(0.000000000f, 0.000000000f, 1.000000000f, 0.000000000f),
QuaternionMathF::New(0.000000000f, 0.000000000f, 0.866025400f, -0.50000000f),
QuaternionMathF::New(0.000000000f, 0.000000000f, 0.500000000f, -0.86602540f)
};
static const float HexRodSym[HexagonalLowOps::k_NumSymQuats][3] = {{0.0f, 0.0f, 0.0f},
{0.0f, 0.0f, 0.57735f},
{0.0f, 0.0f, 1.73205f},
{0.0f, 0.0f, 1000000000000.0f},
{0.0f, 0.0f, -1.73205f},
{0.0f, 0.0f, -0.57735f}
};
static const float HexMatSym[HexagonalLowOps::k_NumSymQuats][3][3] =
{
{ {1.0f, 0.0f, 0.0f},
{0.0f, 1.0f, 0.0f},
{0.0f, 0.0f, 1.0f}
},
{ { -0.5f, static_cast<float>(SIMPLib::Constants::k_Root3Over2), 0.0f},
{ static_cast<float>(-SIMPLib::Constants::k_Root3Over2), -0.5f, 0.0f},
{0.0f, 0.0f, 1.0f}
},
{ { -0.5f, static_cast<float>(-SIMPLib::Constants::k_Root3Over2), 0.0f},
{static_cast<float>(SIMPLib::Constants::k_Root3Over2), -0.5f, 0.0f},
{0.0f, 0.0f, 1.0f}
},
{ {0.5f, static_cast<float>(SIMPLib::Constants::k_Root3Over2), 0.0f},
{ static_cast<float>(-SIMPLib::Constants::k_Root3Over2), 0.5f, 0.0f},
{0.0f, 0.0f, 1.0f}
},
{ { -1.0f, 0.0f, 0.0f},
{0.0f, -1.0f, 0.0f},
{0.0f, 0.0f, 1.0f}
},
{ {0.5f, static_cast<float>(-SIMPLib::Constants::k_Root3Over2), 0.0f},
{static_cast<float>(SIMPLib::Constants::k_Root3Over2), 0.5f, 0.0f},
{0.0f, 0.0f, 1.0f}
}
};
using namespace Detail;
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
HexagonalLowOps::HexagonalLowOps()
{
float junk1 = Detail::HexDim1StepValue * 1.0f;
float junk2 = junk1 / Detail::HexDim2StepValue;
float junk3 = junk2 / Detail::HexDim3StepValue;
junk1 = junk3 / junk2;
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
HexagonalLowOps::~HexagonalLowOps()
{
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
bool HexagonalLowOps::getHasInversion()
{
return true;
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
int HexagonalLowOps::getODFSize()
{
return k_OdfSize;
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
int HexagonalLowOps::getMDFSize()
{
return k_MdfSize;
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
int HexagonalLowOps::getNumSymOps()
{
return k_NumSymQuats;
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
QString HexagonalLowOps::getSymmetryName()
{
return "Hexagonal 6/m";;
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
float HexagonalLowOps::_calcMisoQuat(const QuatF quatsym[12], int numsym,
QuatF& q1, QuatF& q2,
float& n1, float& n2, float& n3)
{
float wmin = 9999999.0f; //,na,nb,nc;
float w = 0;
float n1min = 0.0f;
float n2min = 0.0f;
float n3min = 0.0f;
QuatF qr;
QuatF qc;
QuatF q2inv;
QuaternionMathF::Copy(q2, q2inv);
QuaternionMathF::Conjugate(q2inv);
QuaternionMathF::Multiply(q1, q2inv, qr);
for (int i = 0; i < numsym; i++)
{
QuaternionMathF::Multiply(quatsym[i], qr, qc);
if (qc.w < -1)
{
qc.w = -1;
}
else if (qc.w > 1)
{
qc.w = 1;
}
FOrientArrayType ax(4, 0.0f);
FOrientTransformsType::qu2ax(FOrientArrayType(qc.x, qc.y, qc.z, qc.w), ax);
ax.toAxisAngle(n1, n2, n3, w);
if (w > SIMPLib::Constants::k_Pi)
{
w = SIMPLib::Constants::k_2Pi - w;
}
if (w < wmin)
{
wmin = w;
n1min = n1;
n2min = n2;
n3min = n3;
}
}
float denom = sqrt((n1min * n1min + n2min * n2min + n3min * n3min));
n1 = n1min / denom;
n2 = n2min / denom;
n3 = n3min / denom;
if(denom == 0)
{
n1 = 0.0, n2 = 0.0, n3 = 1.0;
}
if(wmin == 0)
{
n1 = 0.0, n2 = 0.0, n3 = 1.0;
}
return wmin;
}
float HexagonalLowOps::getMisoQuat(QuatF& q1, QuatF& q2, float& n1, float& n2, float& n3)
{
int numsym = 6;
return _calcMisoQuat(HexQuatSym, numsym, q1, q2, n1, n2, n3);
}
void HexagonalLowOps::getQuatSymOp(int i, QuatF& q)
{
QuaternionMathF::Copy(HexQuatSym[i], q);
}
void HexagonalLowOps::getRodSymOp(int i, float* r)
{
r[0] = HexRodSym[i][0];
r[1] = HexRodSym[i][1];
r[2] = HexRodSym[i][2];
}
void HexagonalLowOps::getMatSymOp(int i, float g[3][3])
{
g[0][0] = HexMatSym[i][0][0];
g[0][1] = HexMatSym[i][0][1];
g[0][2] = HexMatSym[i][0][2];
g[1][0] = HexMatSym[i][1][0];
g[1][1] = HexMatSym[i][1][1];
g[1][2] = HexMatSym[i][1][2];
g[2][0] = HexMatSym[i][2][0];
g[2][1] = HexMatSym[i][2][1];
g[2][2] = HexMatSym[i][2][2];
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
FOrientArrayType HexagonalLowOps::getODFFZRod(FOrientArrayType rod)
{
int numsym = 6;
return _calcRodNearestOrigin(HexRodSym, numsym, rod);
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
FOrientArrayType HexagonalLowOps::getMDFFZRod(FOrientArrayType rod)
{
float w = 0.0f, n1 = 0.0f, n2 = 0.0f, n3 = 0.0f;
float FZn1 = 0.0f, FZn2 = 0.0f, FZn3 = 0.0f, FZw = 0.0f;
float n1n2mag = 0.0f;
rod = _calcRodNearestOrigin(HexRodSym, 12, rod);
FOrientArrayType ax(4, 0.0f);
OrientationTransforms<FOrientArrayType, float>::ro2ax(rod, ax);
n1 = ax[0];
n2 = ax[1], n3 = ax[2], w = ax[3];
float denom = sqrt((n1 * n1 + n2 * n2 + n3 * n3));
n1 = n1 / denom;
n2 = n2 / denom;
n3 = n3 / denom;
if(n3 < 0)
{
n1 = -n1, n2 = -n2, n3 = -n3;
}
float angle = 180.0f * atan2(n2, n1) * SIMPLib::Constants::k_1OverPi;
if(angle < 0)
{
angle = angle + 360.0f;
}
FZn1 = n1;
FZn2 = n2;
FZn3 = n3;
if(angle > 30.0f)
{
n1n2mag = sqrt(n1 * n1 + n2 * n2);
if (int(angle / 30) % 2 == 0)
{
FZw = angle - (30.0f * int(angle / 30.0f));
FZw = FZw * SIMPLib::Constants::k_PiOver180;
FZn1 = n1n2mag * cosf(FZw);
FZn2 = n1n2mag * sinf(FZw);
}
else
{
FZw = angle - (30.0f * int(angle / 30.0f));
FZw = 30.0f - FZw;
FZw = FZw * SIMPLib::Constants::k_PiOver180;
FZn1 = n1n2mag * cosf(FZw);
FZn2 = n1n2mag * sinf(FZw);
}
}
ax.fromAxisAngle(FZn1, FZn2, FZn3, w);
OrientationTransforms<FOrientArrayType, float>::ax2ro(ax, rod);
return rod;
}
void HexagonalLowOps::getNearestQuat(QuatF& q1, QuatF& q2)
{
int numsym = 6;
_calcNearestQuat(HexQuatSym, numsym, q1, q2);
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
void HexagonalLowOps::getFZQuat(QuatF& qr)
{
int numsym = 6;
_calcQuatNearestOrigin(HexQuatSym, numsym, qr);
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
int HexagonalLowOps::getMisoBin(FOrientArrayType rod)
{
float dim[3];
float bins[3];
float step[3];
FOrientArrayType ho(3);
OrientationTransforms<FOrientArrayType, float>::ro2ho(rod, ho);
dim[0] = HexDim1InitValue;
dim[1] = HexDim2InitValue;
dim[2] = HexDim3InitValue;
step[0] = HexDim1StepValue;
step[1] = HexDim2StepValue;
step[2] = HexDim3StepValue;
bins[0] = 72.0f;
bins[1] = 72.0f;
bins[2] = 12.0f;
return _calcMisoBin(dim, bins, step, ho);
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
FOrientArrayType HexagonalLowOps::determineEulerAngles(uint64_t seed, int choose)
{
float init[3];
float step[3];
int32_t phi[3];
float h1, h2, h3;
init[0] = HexDim1InitValue;
init[1] = HexDim2InitValue;
init[2] = HexDim3InitValue;
step[0] = HexDim1StepValue;
step[1] = HexDim2StepValue;
step[2] = HexDim3StepValue;
phi[0] = static_cast<int32_t>(choose % 72);
phi[1] = static_cast<int32_t>((choose / 72) % 72);
phi[2] = static_cast<int32_t>(choose / (72 * 72));
_calcDetermineHomochoricValues(seed, init, step, phi, choose, h1, h2, h3);
FOrientArrayType ho(h1, h2, h3);
FOrientArrayType ro(4);
OrientationTransforms<FOrientArrayType, float>::ho2ro(ho, ro);
ro = getODFFZRod(ro);
FOrientArrayType eu(4);
OrientationTransforms<FOrientArrayType, float>::ro2eu(ro, eu);
return eu;
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
FOrientArrayType HexagonalLowOps::randomizeEulerAngles(FOrientArrayType synea)
{
QuatF q;
QuatF qc;
size_t symOp = getRandomSymmetryOperatorIndex(k_NumSymQuats);
FOrientArrayType quat(4, 0.0f);
OrientationTransforms<FOrientArrayType, float>::eu2qu(synea, quat);
q = quat.toQuaternion();
QuaternionMathF::Multiply(HexQuatSym[symOp], q, qc);
quat.fromQuaternion(qc);
OrientationTransforms<FOrientArrayType, float>::qu2eu(quat, synea);
return synea;
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
FOrientArrayType HexagonalLowOps::determineRodriguesVector(uint64_t seed, int choose)
{
float init[3];
float step[3];
int32_t phi[3];
float h1, h2, h3;
init[0] = HexDim1InitValue;
init[1] = HexDim2InitValue;
init[2] = HexDim3InitValue;
step[0] = HexDim1StepValue;
step[1] = HexDim2StepValue;
step[2] = HexDim3StepValue;
phi[0] = static_cast<int32_t>(choose % 72);
phi[1] = static_cast<int32_t>((choose / 72) % 72);
phi[2] = static_cast<int32_t>(choose / (72 * 72));
_calcDetermineHomochoricValues(seed, init, step, phi, choose, h1, h2, h3);
FOrientArrayType ho(h1, h2, h3);
FOrientArrayType ro(4);
OrientationTransforms<FOrientArrayType, float>::ho2ro(ho, ro);
ro = getMDFFZRod(ro);
return ro;
}
// -----------------------------------------------------------------------------
//
// -----------------------------------------------------------------------------
int HexagonalLowOps::getOdfBin(FOrientArrayType rod)
{
float dim[3];
float bins[3];
float step[3];
FOrientArrayType ho(3);
OrientationTransforms<FOrientArrayType, float>::ro2ho(rod, ho);
dim[0] = HexDim1InitValue;
dim[1] = HexDim2InitValue;
dim[2] = HexDim3InitValue;
step[0] = HexDim1StepValue;
step[1] = HexDim2StepValue;
step[2] = HexDim3StepValue;
bins[0] = 72.0f;
bins[1] = 72.0f;
bins[2] = 12.0f;
return _calcODFBin(dim, bins, step, ho);
}
void HexagonalLowOps::getSchmidFactorAndSS(float load[3], float& schmidfactor, float angleComps[2], int& slipsys)
{
float theta1, theta2, theta3, theta4, theta5, theta6, theta7, theta8, theta9;
float lambda1, lambda2, lambda3, lambda4, lambda5, lambda6, lambda7, lambda8, lambda9, lambda10;
float schmid1, schmid2, schmid3, schmid4, schmid5, schmid6;
float caratio = 1.633f;
float ph1sdx1 = 1.0f;
float ph1sdy1 = 0.0f;
float ph1sdz1 = 0.0f;
float ph1sdx2 = 0.0f;
float ph1sdy2 = 1.0f;
float ph1sdz2 = 0.0f;
float ph1sdx3 = -0.707f;
float ph1sdy3 = -0.707f;
float ph1sdz3 = 0.0f;
float ph1sdx4 = 0.0f;
float ph1sdy4 = -0.707f;
float ph1sdz4 = 0.707f;
float ph1sdx5 = -0.57735f;
float ph1sdy5 = -0.57735f;
float ph1sdz5 = 0.57735f;
float ph1sdx6 = 0.707f;
float ph1sdy6 = 0.0f;
float ph1sdz6 = 0.707f;
float ph1sdx7 = 0.57735f;
float ph1sdy7 = 0.57735f;
float ph1sdz7 = 0.57735f;
float ph1sdx8 = 0.0f;
float ph1sdy8 = 0.707f;
float ph1sdz8 = 0.707f;
float ph1sdx9 = -0.707f;
float ph1sdy9 = 0.0f;
float ph1sdz9 = 0.707f;
float ph1spnx1 = 0.0f;
float ph1spny1 = 0.0f;
float ph1spnz1 = 1.0f;
float ph1spnx2 = 0.4472f;
float ph1spny2 = 0.8944f;
float ph1spnz2 = 0.0f;
float ph1spnx3 = 0.8944f;
float ph1spny3 = 0.4472f;
float ph1spnz3 = 0.0f;
float ph1spnx4 = -0.707f;
float ph1spny4 = 0.707f;
float ph1spnz4 = 0.0f;
float ph1spnx5 = 0.4082f;
float ph1spny5 = 0.8164f;
// float ph1spnz5 = -0.4082f;
float ph1spnx6 = 0.4082f;
float ph1spny6 = 0.8164f;
// float ph1spnz6 = 0.4082f;
float ph1spnx7 = 0.8164f;
float ph1spny7 = 0.4082f;
// float ph1spnz7 = -0.4082f;
float ph1spnx8 = 0.8164f;
float ph1spny8 = 0.4082f;
// float ph1spnz8 = 0.4082f;
float ph1spnx9 = -0.57735f;
float ph1spny9 = 0.57735f;
// float ph1spnz9 = -0.57735f;
float ph1spnx10 = -0.57735f;
float ph1spny10 = 0.57735f;
// float ph1spnz10 = 0.57735f;
float loadx = load[0];
float loady = load[1];
float loadz = load[2];
float t1x = (0.866025f * ph1sdx1) + (0.0f * ph1sdy1) + (0.0f * ph1sdz1);
float t1y = (-0.5f * ph1sdx1) + (1.0f * ph1sdy1) + (0.0f * ph1sdz1);
float t1z = (0.0f * ph1sdx1) + (0.0f * ph1sdy1) + (caratio * ph1sdz1);
float denomt1 = powf((t1x * t1x + t1y * t1y + t1z * t1z), 0.5f);
t1x = t1x / denomt1;
t1y = t1y / denomt1;
t1z = t1z / denomt1;
theta1 = ((t1x * loadx) + (t1y * loady) + (t1z * loadz));
theta1 = fabs(theta1);
float t2x = (0.866025f * ph1sdx2) + (0.0f * ph1sdy2) + (0.0f * ph1sdz2);
float t2y = (-0.5f * ph1sdx2) + (1.0f * ph1sdy2) + (0.0f * ph1sdz2);
float t2z = (0.0f * ph1sdx2) + (0.0f * ph1sdy2) + (caratio * ph1sdz2);
float denomt2 = powf((t2x * t2x + t2y * t2y + t2z * t2z), 0.5f);
t2x = t2x / denomt2;
t2y = t2y / denomt2;
t2z = t2z / denomt2;
theta2 = ((t2x * loadx) + (t2y * loady) + (t2z * loadz));
theta2 = fabs(theta2);
float t3x = (0.866025f * ph1sdx3) + (0.0f * ph1sdy3) + (0.0f * ph1sdz3);
float t3y = (-0.5f * ph1sdx3) + (1.0f * ph1sdy3) + (0.0f * ph1sdz3);
float t3z = (0.0f * ph1sdx3) + (0.0f * ph1sdy3) + (caratio * ph1sdz3);
float denomt3 = powf((t3x * t3x + t3y * t3y + t3z * t3z), 0.5f);
t3x = t3x / denomt3;
t3y = t3y / denomt3;
t3z = t3z / denomt3;
theta3 = ((t3x * loadx) + (t3y * loady) + (t3z * loadz));
theta3 = fabs(theta3);
float l1nx = (0.866025f * ph1spnx1) + (0.0f * ph1spny1);
float l1ny = (-0.5f * ph1spnx1) + (1.0f * ph1spny1);
float l1nz = -caratio * ph1spnz1;
float denoml1 = powf((l1nx * l1nx + l1ny * l1ny + l1nz * l1nz), 0.5f);
l1nx = l1nx / denoml1;
l1ny = l1ny / denoml1;
l1nz = l1nz / denoml1;
lambda1 = ((l1nx * loadx) + (l1ny * loady) + (l1nz * loadz));
lambda1 = fabs(lambda1);
schmid1 = theta1 * lambda1;
schmid2 = theta2 * lambda1;
schmid3 = theta3 * lambda1;
float l2nx = (0.866025f * ph1spnx2) + (0.0f * ph1spny2);
float l2ny = (-0.5f * ph1spnx2) + (1 * ph1spny2);
float l2nz = -caratio * ph1spnz2;
float denoml2 = powf((l2nx * l2nx + l2ny * l2ny + l2nz * l2nz), 0.5f);
l2nx = l2nx / denoml2;
l2ny = l2ny / denoml2;
l2nz = l2nz / denoml2;
lambda2 = ((l2nx * loadx) + (l2ny * loady) + (l2nz * loadz));
lambda2 = fabs(lambda2);
float l3nx = (0.866025f * ph1spnx3) + (0.0f * ph1spny3);
float l3ny = (-0.5f * ph1spnx3) + (1.0f * ph1spny3);
float l3nz = -caratio * ph1spnz3;
float denoml3 = powf((l3nx * l3nx + l3ny * l3ny + l3nz * l3nz), 0.5f);
l3nx = l3nx / denoml3;
l3ny = l3ny / denoml3;
l3nz = l3nz / denoml3;
lambda3 = ((l3nx * loadx) + (l3ny * loady) + (l3nz * loadz));
lambda3 = fabs(lambda3);
float l4nx = (0.866025f * ph1spnx4) + (0.0f * ph1spny4);
float l4ny = (-0.5f * ph1spnx4) + (1 * ph1spny4);
float l4nz = -caratio * ph1spnz4;
float denoml4 = powf((l4nx * l4nx + l4ny * l4ny + l4nz * l4nz), 0.5f);
l4nx = l4nx / denoml4;
l4ny = l4ny / denoml4;
l4nz = l4nz / denoml4;
lambda4 = ((l4nx * loadx) + (l4ny * loady) + (l4nz * loadz));
lambda4 = fabs(lambda4);
schmid4 = theta1 * lambda2;
schmid5 = theta2 * lambda3;
schmid6 = theta3 * lambda4;
float l5nx = (0.866025f * ph1spnx5) + (0.0f * ph1spny5);
float l5ny = (-0.5f * ph1spnx5) + (1 * ph1spny5);
float l5nz = float((l5nx * -l5nx + l5ny * -l5ny)) / (caratio * 0.8164f);
float denoml5 = powf((l5nx * l5nx + l5ny * l5ny + l5nz * l5nz), 0.5f);
l5nx = l5nx / denoml5;
l5ny = l5ny / denoml5;
l5nz = l5nz / denoml5;
float l6nx = (0.866025f * ph1spnx6) + (0.0f * ph1spny6);
float l6ny = (-0.5f * ph1spnx6) + (1.0f * ph1spny6);
float l6nz = float(-(l6nx * -l6nx + l6ny * -l6ny)) / (caratio * 0.8164f);
float denoml6 = powf((l6nx * l6nx + l6ny * l6ny + l6nz * l6nz), 0.5f);
l6nx = l6nx / denoml6;
l6ny = l6ny / denoml6;
l6nz = l6nz / denoml6;
float l7nx = (0.866025f * ph1spnx7) + (0.0f * ph1spny7);
float l7ny = (-0.5f * ph1spnx7) + (1.0f * ph1spny7);
float l7nz = float((l7nx * -l7nx + l7ny * -l7ny)) / (caratio * 0.8164f);
float denoml7 = powf((l7nx * l7nx + l7ny * l7ny + l7nz * l7nz), 0.5f);
l7nx = l7nx / denoml7;
l7ny = l7ny / denoml7;
l7nz = l7nz / denoml7;
float l8nx = (0.866025f * ph1spnx8) + (0 * ph1spny8);
float l8ny = (-0.5f * ph1spnx8) + (1.0f * ph1spny8);
float l8nz = float(-(l8nx * -l8nx + l8ny * -l8ny)) / (caratio * 0.8164f);
float denoml8 = powf((l8nx * l8nx + l8ny * l8ny + l8nz * l8nz), 0.5f);
l8nx = l8nx / denoml8;
l8ny = l8ny / denoml8;
l8nz = l8nz / denoml8;
float l9nx = (0.866025f * ph1spnx9) + (0.0f * ph1spny9);
float l9ny = (-0.5f * ph1spnx9) + (1.0f * ph1spny9);
float l9nz = float((l9nx * -l9nx + l9ny * -l9ny)) / (caratio * 1.154f);
float denoml9 = powf((l9nx * l9nx + l9ny * l9ny + l9nz * l9nz), 0.5f);
l9nx = l9nx / denoml9;
l9ny = l9ny / denoml9;
l9nz = l9nz / denoml9;
float l10nx = (0.866025f * ph1spnx10) + (0.0f * ph1spny10);
float l10ny = (-0.5f * ph1spnx10) + (1 * ph1spny10);
float l10nz = float(-(l10nx * -l10nx + l10ny * -l10ny)) / (caratio * 1.154f);
float denoml10 = powf((l10nx * l10nx + l10ny * l10ny + l10nz * l10nz), 0.5f);
l10nx = l10nx / denoml10;
l10ny = l10ny / denoml10;
l10nz = l10nz / denoml10;
lambda5 = ((l5nx * loadx) + (l5ny * loady) + (-l5nz * loadz));
lambda5 = fabs(lambda5);
lambda6 = ((l5nx * loadx) + (l5ny * loady) + (l5nz * loadz));
lambda6 = fabs(lambda6);
lambda7 = ((l7nx * loadx) + (l7ny * loady) + (-l7nz * loadz));
lambda7 = fabs(lambda7);
lambda8 = ((l7nx * loadx) + (l7ny * loady) + (l7nz * loadz));
lambda8 = fabs(lambda8);
lambda9 = ((l9nx * loadx) + (l9ny * loady) + (-l9nz * loadz));
lambda9 = fabs(lambda9);
lambda10 = ((l9nx * loadx) + (l9ny * loady) + (l9nz * loadz));
lambda10 = fabs(lambda10);
// schmid7 = theta1 * lambda5;
// schmid8 = theta1 * lambda6;
// schmid9 = theta2 * lambda7;
// schmid10 = theta2 * lambda8;
// schmid11 = theta3 * lambda9;
// schmid12 = theta3 * lambda10;
float t4x = (0.866025f * ph1sdx4) + (0.0f * ph1sdy4) + (0.0f * ph1sdz4);
float t4y = (-0.5f * ph1sdx4) + (1.0f * ph1sdy4) + (0.0f * ph1sdz4);
float t4z = (0.0f * ph1sdx4) + (0.0f * ph1sdy4) + (caratio * ph1sdz4);
float denomt4 = powf((t4x * t4x + t4y * t4y + t4z * t4z), 0.5f);
t4x = t4x / denomt4;
t4y = t4y / denomt4;
t4z = t4z / denomt4;
theta4 = ((t4x * loadx) + (t4y * loady) + (t4z * loadz));
theta4 = fabs(theta4);
float t5x = (0.866025f * ph1sdx5) + (0.0f * ph1sdy5) + (0.0f * ph1sdz5);
float t5y = (-0.5f * ph1sdx5) + (1.0f * ph1sdy5) + (0.0f * ph1sdz5);
float t5z = (0.0f * ph1sdx5) + (0.0f * ph1sdy5) + (caratio * ph1sdz5);
float denomt5 = powf((t5x * t5x + t5y * t5y + t5z * t5z), 0.5f);
t5x = t5x / denomt5;
t5y = t5y / denomt5;
t5z = t5z / denomt5;
theta5 = ((t5x * loadx) + (t5y * loady) + (t5z * loadz));
theta5 = fabs(theta5);
float t6x = (0.866025f * ph1sdx6) + (0.0f * ph1sdy6) + (0.0f * ph1sdz6);
float t6y = (-0.5f * ph1sdx6) + (1.0f * ph1sdy6) + (0.0f * ph1sdz6);
float t6z = (0.0f * ph1sdx6) + (0.0f * ph1sdy6) + (caratio * ph1sdz6);
float denomt6 = powf((t6x * t6x + t6y * t6y + t6z * t6z), 0.5f);
t6x = t6x / denomt6;
t6y = t6y / denomt6;
t6z = t6z / denomt6;
theta6 = ((t6x * loadx) + (t6y * loady) + (t6z * loadz));
theta6 = fabs(theta6);
float t7x = (0.866025f * ph1sdx7) + (0.0f * ph1sdy7) + (0.0f * ph1sdz7);
float t7y = (-0.5f * ph1sdx7) + (1.0f * ph1sdy7) + (0.0f * ph1sdz7);
float t7z = (0.0f * ph1sdx7) + (0.0f * ph1sdy7) + (caratio * ph1sdz7);
float denomt7 = powf((t7x * t7x + t7y * t7y + t7z * t7z), 0.5f);
t7x = t7x / denomt7;
t7y = t7y / denomt7;
t7z = t7z / denomt7;
theta7 = ((t7x * loadx) + (t7y * loady) + (t7z * loadz));
theta7 = fabs(theta7);
float t8x = (0.866025f * ph1sdx8) + (0.0f * ph1sdy8) + (0.0f * ph1sdz8);
float t8y = (-0.5f * ph1sdx8) + (1.0f * ph1sdy8) + (0.0f * ph1sdz8);
float t8z = (0.0f * ph1sdx8) + (0.0f * ph1sdy8) + (caratio * ph1sdz8);
float denomt8 = powf((t8x * t8x + t8y * t8y + t8z * t8z), 0.5f);
t8x = t8x / denomt8;
t8y = t8y / denomt8;
t8z = t8z / denomt8;
theta8 = ((t8x * loadx) + (t8y * loady) + (t8z * loadz));
theta8 = fabs(theta8);
float t9x = (0.866025f * ph1sdx9) + (0.0f * ph1sdy9) + (0.0f * ph1sdz9);
float t9y = (-0.5f * ph1sdx9) + (1 * ph1sdy9) + (0 * ph1sdz9);
float t9z = (0.0f * ph1sdx9) + (0.0f * ph1sdy9) + (caratio * ph1sdz9);
float denomt9 = powf((t9x * t9x + t9y * t9y + t9z * t9z), 0.5f);
t9x = t9x / denomt9;
t9y = t9y / denomt9;
t9z = t9z / denomt9;
theta9 = ((t9x * loadx) + (t9y * loady) + (t9z * loadz));
theta9 = fabs(theta9);
// schmid13 = theta7 * lambda6;
// schmid14 = theta8 * lambda6;
// schmid15 = theta6 * lambda9;
// schmid16 = theta4 * lambda9;
// schmid17 = theta6 * lambda8;
// schmid18 = theta7 * lambda8;
// schmid19 = theta4 * lambda5;
// schmid20 = theta5 * lambda5;
// schmid21 = theta8 * lambda10;
// schmid22 = theta9 * lambda10;
// schmid23 = theta9 * lambda7;
// schmid24 = theta5 * lambda7;
if(schmid1 > schmidfactor)
{
schmidfactor = schmid1, slipsys = 1, angleComps[0] = theta1, angleComps[1] = lambda1;
}
if(schmid2 > schmidfactor)
{
schmidfactor = schmid2, slipsys = 2, angleComps[0] = theta2, angleComps[1] = lambda1;
}
if(schmid3 > schmidfactor)
{
schmidfactor = schmid3, slipsys = 3, angleComps[0] = theta3, angleComps[1] = lambda1;
}
if(schmid4 > schmidfactor)
{
schmidfactor = schmid4, slipsys = 4, angleComps[0] = theta1, angleComps[1] = lambda2;
}
if(schmid5 > schmidfactor)
{
schmidfactor = schmid5, slipsys = 5, angleComps[0] = theta2, angleComps[1] = lambda3;
}
if(schmid6 > schmidfactor)
{
schmidfactor = schmid6, slipsys = 6, angleComps[0] = theta3, angleComps[1] = lambda4;
}
//if(schmid7 > schmidfactor) { schmidfactor = schmid7, slipsys = 7; }
//if(schmid8 > schmidfactor) { schmidfactor = schmid8, slipsys = 8; }
//if(schmid9 > schmidfactor) { schmidfactor = schmid9, slipsys = 9; }
//if(schmid10 > schmidfactor) { schmidfactor = schmid10, slipsys = 10; }
//if(schmid11 > schmidfactor) { schmidfactor = schmid11, slipsys = 11; }
//if(schmid12 > schmidfactor) { schmidfactor = schmid12, slipsys = 12; }
//if(schmid13 > schmidfactor) { schmidfactor = schmid13, slipsys = 13; }
//if(schmid14 > schmidfactor) { schmidfactor = schmid14, slipsys = 14; }
//if(schmid15 > schmidfactor) { schmidfactor = schmid15, slipsys = 15; }
//if(schmid16 > schmidfactor) { schmidfactor = schmid16, slipsys = 16; }
//if(schmid17 > schmidfactor) { schmidfactor = schmid17, slipsys = 17; }
//if(schmid18 > schmidfactor) { schmidfactor = schmid18, slipsys = 18; }
//if(schmid19 > schmidfactor) { schmidfactor = schmid19, slipsys = 19; }
//if(schmid20 > schmidfactor) { schmidfactor = schmid20, slipsys = 20; }
//if(schmid21 > schmidfactor) { schmidfactor = schmid21, slipsys = 21; }
//if(schmid22 > schmidfactor) { schmidfactor = schmid22, slipsys = 22; }
//if(schmid23 > schmidfactor) { schmidfactor = schmid23, slipsys = 23; }
//if(schmid24 > schmidfactor) { schmidfactor = schmid24, slipsys = 24; }
}
void HexagonalLowOps::getSchmidFactorAndSS(float load[3], float plane[3], float direction[3], float& schmidfactor, float angleComps[2], int& slipsys)
{
schmidfactor = 0;
slipsys = 0;
angleComps[0] = 0;
angleComps[1] = 0;
//compute mags
float loadMag = sqrt( load[0] * load[0] + load[1] * load[1] + load[2] * load[2] );
float planeMag = sqrt( plane[0] * plane[0] + plane[1] * plane[1] + plane[2] * plane[2] );
float directionMag = sqrt( direction[0] * direction[0] + direction[1] * direction[1] + direction[2] * direction[2] );
planeMag *= loadMag;
directionMag *= loadMag;
//loop over symmetry operators finding highest schmid factor
for(int i = 0; i < k_NumSymQuats; i++)
{
//compute slip system
float slipPlane[3] = {0};
slipPlane[2] = HexMatSym[i][2][0] * plane[0] + HexMatSym[i][2][1] * plane[1] + HexMatSym[i][2][2] * plane[2];
//dont consider negative z planes (to avoid duplicates)
if( slipPlane[2] >= 0)
{
slipPlane[0] = HexMatSym[i][0][0] * plane[0] + HexMatSym[i][0][1] * plane[1] + HexMatSym[i][0][2] * plane[2];
slipPlane[1] = HexMatSym[i][1][0] * plane[0] + HexMatSym[i][1][1] * plane[1] + HexMatSym[i][1][2] * plane[2];
float slipDirection[3] = {0};
slipDirection[0] = HexMatSym[i][0][0] * direction[0] + HexMatSym[i][0][1] * direction[1] + HexMatSym[i][0][2] * direction[2];
slipDirection[1] = HexMatSym[i][1][0] * direction[0] + HexMatSym[i][1][1] * direction[1] + HexMatSym[i][1][2] * direction[2];
slipDirection[2] = HexMatSym[i][2][0] * direction[0] + HexMatSym[i][2][1] * direction[1] + HexMatSym[i][2][2] * direction[2];
float cosPhi = fabs( load[0] * slipPlane[0] + load[1] * slipPlane[1] + load[2] * slipPlane[2] ) / planeMag;
float cosLambda = fabs( load[0] * slipDirection[0] + load[1] * slipDirection[1] + load[2] * slipDirection[2] ) / directionMag;
float schmid = cosPhi * cosLambda;
if(schmid > schmidfactor)
{
schmidfactor = schmid;
slipsys = i;
angleComps[0] = acos(cosPhi);
angleComps[1] = acos(cosLambda);
}
}
}
}
void HexagonalLowOps::getmPrime(QuatF& q1, QuatF& q2, float LD[3], float& mPrime)
{
Q_ASSERT(false);
#if 0
/* I am asserting here because this code will simply give junk results and if someone uses it
* they could unknowningly get really bad results
*/
float g1[3][3];
float g2[3][3];
float h1, k1, l1, u1, v1, w1;
float h2, k2, l2, u2, v2, w2;
float denomhkl1, denomhkl2, denomuvw1, denomuvw2;
float planemisalignment, directionmisalignment;
QuattoMat(q1, g1);
QuattoMat(q2, g2);
// Note the order of multiplication is such that I am actually multiplying by the inverse of g1 and g2
/* h1 = CubicSlipSystems[ss1][0]*g1[0][0]+CubicSlipSystems[ss1][1]*g1[1][0]+CubicSlipSystems[ss1][2]*g1[2][0];
k1 = CubicSlipSystems[ss1][0]*g1[0][1]+CubicSlipSystems[ss1][1]*g1[1][1]+CubicSlipSystems[ss1][2]*g1[2][1];
l1 = CubicSlipSystems[ss1][0]*g1[0][2]+CubicSlipSystems[ss1][1]*g1[1][2]+CubicSlipSystems[ss1][2]*g1[2][2];
u1 = CubicSlipSystems[ss1][3]*g1[0][0]+CubicSlipSystems[ss1][4]*g1[1][0]+CubicSlipSystems[ss1][5]*g1[2][0];
v1 = CubicSlipSystems[ss1][3]*g1[0][1]+CubicSlipSystems[ss1][4]*g1[1][1]+CubicSlipSystems[ss1][5]*g1[2][1];
w1 = CubicSlipSystems[ss1][3]*g1[0][2]+CubicSlipSystems[ss1][4]*g1[1][2]+CubicSlipSystems[ss1][5]*g1[2][2];
denomhkl1 = sqrtf((h1*h1+k1*k1+l1*l1));
denomuvw1 = sqrtf((u1*u1+v1*v1+w1*w1));
h2 = CubicSlipSystems[ss2][0]*g2[0][0]+CubicSlipSystems[ss2][1]*g2[1][0]+CubicSlipSystems[ss2][2]*g2[2][0];
k2 = CubicSlipSystems[ss2][0]*g2[0][1]+CubicSlipSystems[ss2][1]*g2[1][1]+CubicSlipSystems[ss2][2]*g2[2][1];
l2 = CubicSlipSystems[ss2][0]*g2[0][2]+CubicSlipSystems[ss2][1]*g2[1][2]+CubicSlipSystems[ss2][2]*g2[2][2];
u2 = CubicSlipSystems[ss2][3]*g2[0][0]+CubicSlipSystems[ss2][4]*g2[1][0]+CubicSlipSystems[ss2][5]*g2[2][0];
v2 = CubicSlipSystems[ss2][3]*g2[0][1]+CubicSlipSystems[ss2][4]*g2[1][1]+CubicSlipSystems[ss2][5]*g2[2][1];
w2 = CubicSlipSystems[ss2][3]*g2[0][2]+CubicSlipSystems[ss2][4]*g2[1][2]+CubicSlipSystems[ss2][5]*g2[2][2];
*/
denomhkl2 = sqrtf((h2 * h2 + k2 * k2 + l2 * l2));
denomuvw2 = sqrtf((u2 * u2 + v2 * v2 + w2 * w2));
planemisalignment = fabs((h1 * h2 + k1 * k2 + l1 * l2) / (denomhkl1 * denomhkl2));
directionmisalignment = fabs((u1 * u2 + v1 * v2 + w1 * w2) / (denomuvw1 * denomuvw2));
mPrime = planemisalignment * directionmisalignment;
#endif
}
void HexagonalLowOps::getF1(QuatF& q1, QuatF& q2, float LD[3], bool maxSF, float& F1)
{
Q_ASSERT(false);
#if 0
/* I am asserting here because this code will simply give junk results and if someone uses it
* they could unknowningly get really bad results
*/
float g1[3][3];
float g2[3][3];
// float hkl1[3], uvw1[3];
// float hkl2[3], uvw2[3];
// float slipDirection[3], slipPlane[3];
// float denomhkl1=0, denomhkl2=0, denomuvw1=0, denomuvw2=0;
// float directionMisalignment=0, totalDirectionMisalignment=0;
// float schmidFactor1=0, schmidFactor2=0;
float maxSchmidFactor = 0;
// float directionComponent1=0, planeComponent1=0;
// float directionComponent2=0, planeComponent2=0;
// float maxF1=0;
QuattoMat(q1, g1);
QuattoMat(q2, g2);
MatrixMath::Normalize3x1(LD);
// Note the order of multiplication is such that I am actually multiplying by the inverse of g1 and g2
if(maxSF == true)
{
maxSchmidFactor = 0;
}
/* for(int i=0;i<12;i++)
{
slipDirection[0] = CubicSlipDirections[i][0];
slipDirection[1] = CubicSlipDirections[i][1];
slipDirection[2] = CubicSlipDirections[i][2];
slipPlane[0] = CubicSlipPlanes[i][0];
slipPlane[1] = CubicSlipPlanes[i][1];
slipPlane[2] = CubicSlipPlanes[i][2];
MatrixMath::Multiply3x3with3x1(g1,slipDirection,hkl1);
MatrixMath::Multiply3x3with3x1(g1,slipPlane,uvw1);
MatrixMath::Normalize3x1(hkl1);
MatrixMath::Normalize3x1(uvw1);
directionComponent1 = MatrixMath::DotProduct(LD,uvw1);
planeComponent1 = MatrixMath::DotProduct(LD,hkl1);
schmidFactor1 = directionComponent1*planeComponent1;
if(schmidFactor1 > maxSchmidFactor || maxSF == false)
{
totalDirectionMisalignment = 0;
if(maxSF == true) maxSchmidFactor = schmidFactor1;
for(int j=0;j<12;j++)
{
slipDirection[0] = CubicSlipDirections[i][0];
slipDirection[1] = CubicSlipDirections[i][1];
slipDirection[2] = CubicSlipDirections[i][2];
slipPlane[0] = CubicSlipPlanes[i][0];
slipPlane[1] = CubicSlipPlanes[i][1];
slipPlane[2] = CubicSlipPlanes[i][2];
MatrixMath::Multiply3x3with3x1(g2,slipDirection,hkl2);
MatrixMath::Multiply3x3with3x1(g2,slipPlane,uvw2);
MatrixMath::Normalize3x1(hkl2);
MatrixMath::Normalize3x1(uvw2);
directionComponent2 = MatrixMath::DotProduct(LD,uvw2);
planeComponent2 = MatrixMath::DotProduct(LD,hkl2);
schmidFactor2 = directionComponent2*planeComponent2;
totalDirectionMisalignment = totalDirectionMisalignment + directionMisalignment;
}
F1 = schmidFactor1*directionComponent1*totalDirectionMisalignment;
if(maxSF == false)
{
if(F1 < maxF1) F1 = maxF1;
else maxF1 = F1;
}
}
}
*/
#endif
}
void HexagonalLowOps::getF1spt(QuatF& q1, QuatF& q2, float LD[3], bool maxSF, float& F1spt)
{
Q_ASSERT(false);
#if 0
float g1[3][3];
float g2[3][3];
// float hkl1[3], uvw1[3];
// float hkl2[3], uvw2[3];
// float slipDirection[3], slipPlane[3];
// float directionMisalignment=0, totalDirectionMisalignment=0;
// float planeMisalignment=0, totalPlaneMisalignment=0;
// float schmidFactor1=0, schmidFactor2=0;
float maxSchmidFactor = 0;
// float directionComponent1=0, planeComponent1=0;
// float directionComponent2=0, planeComponent2=0;
// float maxF1spt=0;
QuattoMat(q1, g1);
QuattoMat(q2, g2);
MatrixMath::Normalize3x1(LD);
// Note the order of multiplication is such that I am actually multiplying by the inverse of g1 and g2
if(maxSF == true)
{
maxSchmidFactor = 0;
}
/* for(int i=0;i<12;i++)
{
slipDirection[0] = CubicSlipDirections[i][0];
slipDirection[1] = CubicSlipDirections[i][1];
slipDirection[2] = CubicSlipDirections[i][2];
slipPlane[0] = CubicSlipPlanes[i][0];
slipPlane[1] = CubicSlipPlanes[i][1];
slipPlane[2] = CubicSlipPlanes[i][2];
MatrixMath::Multiply3x3with3x1(g1,slipDirection,hkl1);
MatrixMath::Multiply3x3with3x1(g1,slipPlane,uvw1);
MatrixMath::Normalize3x1(hkl1);
MatrixMath::Normalize3x1(uvw1);
directionComponent1 = MatrixMath::DotProduct(LD,uvw1);