Validation_codes/Twin_reorientation_check.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e2ae546c-570b-4245-99fa-60519f448e1e",
   "metadata": {},
   "source": [
    "# Code to verify and visualize reorientation caused twinning in the deformation gradient.\n",
    "## Using the correspondence matrix method.\n",
    "By Satyapriya Gupta, Achal H P\n",
    "\n",
    "Reference Niewczas, Acta Materialia, 2010"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8faa8558-2109-45ed-b795-94150b3c998d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import scipy.linalg\n",
    "from numpy.linalg import inv\n",
    "import damask"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc185fbf-e55d-445e-b8aa-f17abdd93b9a",
   "metadata": {},
   "source": [
    "### Test Case: Extension Twinning $( \\bar{1} 0 1 2) [1 0 \\bar{1} 1] $\n",
    "\n",
    "Conversion to Miller indices: $ (\\bar{1} 0 2) [2 1 1] $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fee7fbb5-3a4b-421c-bbe7-636c3fd412e9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.3743159014756228\n",
      "1.6881920256873888\n",
      "[0.63176092 0.36474734 0.68398649]\n",
      "[-0.59234968 -0.34199325  0.72949468]\n"
     ]
    }
   ],
   "source": [
    "# Twin direction:\n",
    "m = np.array([2, 1, 1])\n",
    "# Habit plane normal\n",
    "n = np.array([-1, 0, 2])\n",
    "# Mapping from Miller indes to cartesian coordinate system\n",
    "matA=np.array([[1, -0.5, 0],[0, 0.5*np.sqrt(3), 0],[0, 0, 1.624]])\n",
    "#norm of twin direction\n",
    "norm_mcart=np.linalg.norm(np.matmul(matA,m))\n",
    "# norm of twin plane\n",
    "norm_ncart=np.linalg.norm(np.matmul(n,inv(matA)))\n",
    "# normalized unit vectors:\n",
    "unit_mcart = np.matmul(matA,m)/norm_mcart\n",
    "unit_ncart = np.matmul(n, inv(matA))/norm_ncart\n",
    "# Characteristic shear for Extension twin of Mg\n",
    "s = 0.128917\n",
    "print(norm_mcart)\n",
    "print(norm_ncart)\n",
    "print(unit_mcart)\n",
    "print(unit_ncart)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "716495ad-76ca-4790-b1f4-a2f249e452db",
   "metadata": {},
   "source": [
    "### Please provide Euler Angles Here:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "eaa69469-71ca-42fc-a4ed-afa0fb84a230",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.9400045  -0.29372535  0.1735424 ]\n",
      " [-0.17610919 -0.01790229 -0.98420783]\n",
      " [ 0.2921936  -0.9557222  -0.0348995 ]]\n"
     ]
    }
   ],
   "source": [
    "phi_1 = 17\n",
    "phi_ = 92\n",
    "phi_2 = 170\n",
    "\n",
    "init = (damask.Orientation.from_Euler_angles(\n",
    "         phi=[phi_1,phi_,phi_2],\n",
    "         degrees=True,\n",
    "         family='hexagonal',\n",
    "         lattice='hP',\n",
    "         a=1.0,b=1.0,c=1.6235).as_matrix())\n",
    "print(init)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1262386a-1d9c-4bb0-a147-c409f45ec751",
   "metadata": {},
   "source": [
    "### Initial Undeformed Condition, $ F = Identity matrix $"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "689c6399-fd48-4456-be57-a8f7f7e16276",
   "metadata": {},
   "outputs": [],
   "source": [
    "F = np.identity(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64b46853-7012-432f-93c1-4acb1fe4dc9a",
   "metadata": {},
   "source": [
    "### If $F = I$, then inverse of $F$ gives $F_e$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3c3bfb00-2af0-4754-8d4e-89ee10d62519",
   "metadata": {},
   "outputs": [],
   "source": [
    "Fp=init\n",
    "Fe=inv(Fp)\n",
    "Rinv = inv(init)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6786e80d-c9b2-41de-9fc1-40e8d3fc5acd",
   "metadata": {},
   "source": [
    "### Shape change by twinning in the reference configuration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "83c683bf-e3b8-4ec3-9e59-d0a25a55ca0e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "deformation gradient of shape change= \n",
      " [[ 0.95095672  0.03054648 -0.01230733]\n",
      " [-0.09052208  1.05638144 -0.02271637]\n",
      " [-0.02924172  0.01821313  0.99266184]]\n"
     ]
    }
   ],
   "source": [
    "S_ref= (s * np.einsum('i,j',np.matmul(Rinv,unit_mcart),np.matmul(Rinv,unit_ncart)) \n",
    "        + np.identity(3))\n",
    "print(\"deformation gradient of shape change= \\n\", S_ref)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb708c6b-38ea-4f4a-ac59-91e31b55df95",
   "metadata": {},
   "source": [
    "### After twinning, $ F_1 =  Fe_1 * {F_p}_1 $ , where $ {F_p}_1 = C * {F_p}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b1ad7d3a-fcf2-4116-9339-0451961ece5d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "with determinant of  1.000000166095149\n"
     ]
    }
   ],
   "source": [
    "F1=S_ref\n",
    "C=np.array([[-0.25,0.433013,-0.923645],[0.433013,-0.75,-0.533267],[-0.812, -0.468808, 0]])\n",
    "Fe1=np.matmul(F1,inv(np.matmul(C,Fp)))\n",
    "print (\"with determinant of \",np.linalg.det(Fe1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d21c31d5-72b1-43ed-91e4-2b194cd4eaaf",
   "metadata": {},
   "source": [
    "### Right polar decomposition of $F_e$, $ F_e = R U $ gives the rotation of deformed voxel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "9e5edf14-8645-4816-86ee-89d0fb02335e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[206.53799212  70.1926324   77.64540521]\n"
     ]
    }
   ],
   "source": [
    "(R_,U_) = scipy.linalg.polar(Fe1,'right')\n",
    "check = (damask.Orientation.from_matrix(R=R_,\n",
    "                                        family='hexagonal',lattice='hP',\n",
    "                                        a=1.0,b=1.0,c=1.6235)\n",
    "         .as_Euler_angles(degrees=True))\n",
    "print(check)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "749c4997-c181-41c7-8359-f0fd37ee1a38",
   "metadata": {},
   "source": [
    "### Get the orientation details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e6e8b162-7e0b-45dc-a37f-bee3071ce353",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[102.35459479  70.1926324  333.46200788]\n"
     ]
    }
   ],
   "source": [
    "new_ori = (damask.Orientation.from_matrix(R=np.linalg.inv(R_),\n",
    "                                          family='hexagonal',\n",
    "                                          lattice='hP',a=1.0,b=1.0,c=1.6235))\n",
    "(print(damask.Orientation.from_matrix(R=np.linalg.inv(R_),\n",
    "                                      family='hexagonal',lattice='hP',\n",
    "                                      a=1.0,b=1.0,c=1.6235).as_Euler_angles(degrees=True)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "80ac2638-3ebd-47c6-8e80-243a1c69fce1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Crystal family: hexagonal\n",
      "Bravais lattice: hP\n",
      "a=1 m, b=1 m, c=1.6235 m\n",
      "α=90°, β=90°, γ=120°\n",
      "Quaternion [ 0.04240788 -0.16792654  0.69946438 -0.69336269]\n"
     ]
    }
   ],
   "source": [
    "old_ori = (damask.Orientation.from_Euler_angles(phi=[phi_1,phi_,phi_2],\n",
    "                                                degrees=True,family='hexagonal',\n",
    "                                                lattice='hP',a=1.0,b=1.0,c=1.6235))\n",
    "print(old_ori)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "cc1b231c-16e6-4d7d-bda2-8d0a4799839f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Crystal family: hexagonal\n",
      "Bravais lattice: hP\n",
      "a=1 m, b=1 m, c=1.6235 m\n",
      "α=90°, β=90°, γ=120°\n",
      "Quaternion [7.29494643e-01 6.83986524e-01 3.14974755e-08 1.07984812e-07]\n",
      "[ 0.         86.31191012  0.        ]\n"
     ]
    }
   ],
   "source": [
    "dis = old_ori.disorientation(new_ori)\n",
    "print(dis)\n",
    "print(dis.as_Euler_angles(degrees=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3efee0a1-5ebe-42bd-bb05-61721097458d",
   "metadata": {},
   "source": [
    "## Result: Print the disorientation between undeformed and deformed voxel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "10b562ea-c067-4ec0-8b26-59dd8722305a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "disorientation = 86.31191011698508 degrees\n"
     ]
    }
   ],
   "source": [
    "print('disorientation =',dis.as_axis_angle(degrees=True,pair=True)[1],'degrees')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10bdf007-9926-4e38-9195-dd3fd349f634",
   "metadata": {},
   "source": [
    "# Code to visualization of lattice reorientation caused by twinning.\n",
    "\n",
    "First cell below gives HCP unit cell with euler angles 0,0,0.\n",
    "\n",
    "Second cell below rotates unit cell by provided euler angles.\n",
    "\n",
    "Third cell below shows reorientation done after twinning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "37f8aa5b-a6df-45be-861f-46bdd218154a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from math import cos, sin, radians\n",
    "\n",
    "# Define the line\n",
    "x = np.linspace(0, 1.2, 100)\n",
    "y = np.zeros_like(x)\n",
    "z = np.zeros_like(x)\n",
    "\n",
    "x1 = np.zeros_like(x)\n",
    "y1 = np.zeros_like(x)\n",
    "z1 = np.linspace(0, 1.2, 100)\n",
    "\n",
    "x2 = np.zeros_like(x)\n",
    "y2 = np.linspace(0, 1.2, 100)\n",
    "z2 = np.zeros_like(x)\n",
    "\n",
    "h11 = np.linspace(1,0.5,100)\n",
    "h12 = h11*np.sqrt(3) - np.sqrt(3)\n",
    "h13 = np.zeros_like(h11)\n",
    "\n",
    "h21 = np.linspace(-0.5, 0.5, 100)\n",
    "h22 = np.ones_like(h21) * np.sqrt(3) / 2\n",
    "h23 = np.zeros_like(h21)\n",
    "\n",
    "h31 = np.linspace(-0.5, 0.5, 100)\n",
    "h32 = - np.ones_like(h31) * np.sqrt(3) / 2\n",
    "h33 = np.zeros_like(h31)\n",
    "\n",
    "h41 = np.linspace(1,0.5,100)\n",
    "h42 = - h41*np.sqrt(3) + np.sqrt(3)\n",
    "h43 = np.zeros_like(h41)\n",
    "\n",
    "h51 = np.linspace(-1,-0.5,100)\n",
    "h52 = - h51*np.sqrt(3) - np.sqrt(3)\n",
    "h53 = np.zeros_like(h51)\n",
    "\n",
    "h61 = np.linspace(-1,-0.5,100)\n",
    "h62 = h61*np.sqrt(3) + np.sqrt(3)\n",
    "h63 = np.zeros_like(h61)\n",
    "\n",
    "k11 = np.linspace(1,0.5,100)\n",
    "k12 = k11*np.sqrt(3) - np.sqrt(3)\n",
    "k13 = np.ones_like(k11)\n",
    "\n",
    "k21 = np.linspace(-0.5, 0.5, 100)\n",
    "k22 = np.ones_like(k21) * np.sqrt(3) / 2\n",
    "k23 = np.ones_like(k21)\n",
    "\n",
    "k31 = np.linspace(-0.5, 0.5, 100)\n",
    "k32 = - np.ones_like(k31) * np.sqrt(3) / 2\n",
    "k33 = np.ones_like(k31)\n",
    "\n",
    "k41 = np.linspace(1,0.5,100)\n",
    "k42 = - k41*np.sqrt(3) + np.sqrt(3)\n",
    "k43 = np.ones_like(k41)\n",
    "\n",
    "k51 = np.linspace(-1,-0.5,100)\n",
    "k52 = - k51*np.sqrt(3) - np.sqrt(3)\n",
    "k53 = np.ones_like(k51)\n",
    "\n",
    "k61 = np.linspace(-1,-0.5,100)\n",
    "k62 = k61*np.sqrt(3) + np.sqrt(3)\n",
    "k63 = np.ones_like(k61)\n",
    "\n",
    "\n",
    "\n",
    "v11 = np.ones_like(x) * 0.5\n",
    "v12 = np.ones_like(x) * np.sqrt(3) / 2\n",
    "v13 = np.linspace(0, 1, 100)\n",
    "\n",
    "v21 = - np.ones_like(x) * 0.5\n",
    "v22 = np.ones_like(x) * np.sqrt(3) / 2\n",
    "v23 = np.linspace(0, 1, 100)\n",
    "\n",
    "v31 = - np.ones_like(x) * 0.5\n",
    "v32 = - np.ones_like(x) * np.sqrt(3) / 2\n",
    "v33 = np.linspace(0, 1, 100)\n",
    "\n",
    "v41 = np.ones_like(x) * 0.5\n",
    "v42 = - np.ones_like(x) * np.sqrt(3) / 2\n",
    "v43 = np.linspace(0, 1, 100)\n",
    "\n",
    "v51 = - np.ones_like(x)\n",
    "v52 = np.zeros_like(x)\n",
    "v53 = np.linspace(0, 1, 100)\n",
    "\n",
    "v61 = np.ones_like(x)\n",
    "v62 = np.zeros_like(x)\n",
    "v63 = np.linspace(0, 1, 100)\n",
    "\n",
    "# Plot the line\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(x, y, z)\n",
    "ax.plot(x1, y1, z1)\n",
    "#ax.plot(x2, y2, z2)\n",
    "ax.plot(h11, h12, h13, 'k-')\n",
    "ax.plot(h21, h22, h23, 'k-')\n",
    "ax.plot(h31, h32, h33, 'k-')\n",
    "ax.plot(h41, h42, h43, 'k-')\n",
    "ax.plot(h51, h52, h53, 'k-')\n",
    "ax.plot(h61, h62, h63, 'k-')\n",
    "ax.plot(k11, k12, k13, 'k-')\n",
    "ax.plot(k21, k22, k23, 'k-')\n",
    "ax.plot(k31, k32, k33, 'k-')\n",
    "ax.plot(k41, k42, k43, 'k-')\n",
    "ax.plot(k51, k52, k53, 'k-')\n",
    "ax.plot(k61, k62, k63, 'k-')\n",
    "ax.plot(v11, v12, v13, 'k-')\n",
    "ax.plot(v21, v22, v23, 'k-')\n",
    "ax.plot(v31, v32, v33, 'k-')\n",
    "ax.plot(v41, v42, v43, 'k-')\n",
    "ax.plot(v51, v52, v53, 'k-')\n",
    "ax.plot(v61, v62, v63, 'k-')\n",
    "\n",
    "ax.set_xticks([])\n",
    "ax.set_yticks([])\n",
    "ax.set_zticks([])\n",
    "\n",
    "ax.set_xlabel('')\n",
    "ax.set_ylabel('')\n",
    "ax.set_zlabel('')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "a523f432-ce0a-4506-9d83-bd469e1c9ba3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the rotation angles (in radians)\n",
    "alpha = radians(phi_1)  # Rotation around the x-axis\n",
    "beta = radians(phi_)   # Rotation around the y-axis\n",
    "gamma = radians(phi_2)  # Rotation around the z-axis\n",
    "\n",
    "# Create the rotation matrices\n",
    "Rx = np.array([[1, 0, 0],\n",
    "               [0, cos(alpha), -sin(alpha)],\n",
    "               [0, sin(alpha), cos(alpha)]])\n",
    "\n",
    "Ry = np.array([[cos(beta), 0, sin(beta)],\n",
    "               [0, 1, 0],\n",
    "               [-sin(beta), 0, cos(beta)]])\n",
    "\n",
    "Rz = np.array([[cos(gamma), -sin(gamma), 0],\n",
    "               [sin(gamma), cos(gamma), 0],\n",
    "               [0, 0, 1]])\n",
    "\n",
    "# Combine the rotation matrices\n",
    "R = Rz @ Ry @ Rx\n",
    "\n",
    "# Apply the rotation to the line\n",
    "point1 = np.column_stack((x, y, z))\n",
    "point2 = np.column_stack((x1, y1, z1))\n",
    "point3 = np.column_stack((h11,h12,h13))\n",
    "point4 = np.column_stack((h21, h22, h23))\n",
    "point5 = np.column_stack((h31, h32, h33))\n",
    "point6 = np.column_stack((h41, h42, h43))\n",
    "point7 = np.column_stack((h51, h52, h53))\n",
    "point8 = np.column_stack((h61, h62, h63))\n",
    "point9 = np.column_stack((k11, k12, k13))\n",
    "point10 = np.column_stack((k21, k22, k23))\n",
    "point11 = np.column_stack((k31, k32, k33))\n",
    "point12 = np.column_stack((k41, k42, k43))\n",
    "point13 = np.column_stack((k51, k52, k53))\n",
    "point14 = np.column_stack((k61, k62, k63))\n",
    "point15 = np.column_stack((v11, v12, v13))\n",
    "point16 = np.column_stack((v21, v22, v23))\n",
    "point17 = np.column_stack((v31, v32, v33))\n",
    "point18 = np.column_stack((v41, v42, v43))\n",
    "point19 = np.column_stack((v51, v52, v53))\n",
    "point20 = np.column_stack((v61, v62, v63))\n",
    "point21 = np.column_stack((x2, y2, z2))\n",
    "\n",
    "rotated_point1 = np.dot(R, point1.T).T\n",
    "rotated_point2 = np.dot(R, point2.T).T\n",
    "rotated_point3 = np.dot(R, point3.T).T\n",
    "rotated_point4 = np.dot(R, point4.T).T\n",
    "rotated_point5 = np.dot(R, point5.T).T\n",
    "rotated_point6 = np.dot(R, point6.T).T\n",
    "rotated_point7 = np.dot(R, point7.T).T\n",
    "rotated_point8 = np.dot(R, point8.T).T\n",
    "rotated_point9 = np.dot(R, point9.T).T\n",
    "rotated_point10 = np.dot(R, point10.T).T\n",
    "rotated_point11 = np.dot(R, point11.T).T\n",
    "rotated_point12 = np.dot(R, point12.T).T\n",
    "rotated_point13 = np.dot(R, point13.T).T\n",
    "rotated_point14 = np.dot(R, point14.T).T\n",
    "rotated_point15 = np.dot(R, point15.T).T\n",
    "rotated_point16 = np.dot(R, point16.T).T\n",
    "rotated_point17 = np.dot(R, point17.T).T\n",
    "rotated_point18 = np.dot(R, point18.T).T\n",
    "rotated_point19 = np.dot(R, point19.T).T\n",
    "rotated_point20 = np.dot(R, point20.T).T\n",
    "rotated_point21 = np.dot(R, point21.T).T\n",
    "\n",
    "# Extract the rotated coordinates\n",
    "x_rotated1, y_rotated1, z_rotated1 = rotated_point1.T\n",
    "x_rotated2, y_rotated2, z_rotated2 = rotated_point2.T\n",
    "x_rotated3, y_rotated3, z_rotated3 = rotated_point3.T\n",
    "x_rotated4, y_rotated4, z_rotated4 = rotated_point4.T\n",
    "x_rotated5, y_rotated5, z_rotated5 = rotated_point5.T\n",
    "x_rotated6, y_rotated6, z_rotated6 = rotated_point6.T\n",
    "x_rotated7, y_rotated7, z_rotated7 = rotated_point7.T\n",
    "x_rotated8, y_rotated8, z_rotated8 = rotated_point8.T\n",
    "x_rotated9, y_rotated9, z_rotated9 = rotated_point9.T\n",
    "x_rotated10, y_rotated10, z_rotated10 = rotated_point10.T\n",
    "x_rotated11, y_rotated11, z_rotated11 = rotated_point11.T\n",
    "x_rotated12, y_rotated12, z_rotated12 = rotated_point12.T\n",
    "x_rotated13, y_rotated13, z_rotated13 = rotated_point13.T\n",
    "x_rotated14, y_rotated14, z_rotated14 = rotated_point14.T\n",
    "x_rotated15, y_rotated15, z_rotated15 = rotated_point15.T\n",
    "x_rotated16, y_rotated16, z_rotated16 = rotated_point16.T\n",
    "x_rotated17, y_rotated17, z_rotated17 = rotated_point17.T\n",
    "x_rotated18, y_rotated18, z_rotated18 = rotated_point18.T\n",
    "x_rotated19, y_rotated19, z_rotated19 = rotated_point19.T\n",
    "x_rotated20, y_rotated20, z_rotated20 = rotated_point20.T\n",
    "x_rotated21, y_rotated21, z_rotated21 = rotated_point21.T\n",
    "\n",
    "\n",
    "# Plot the line\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(projection='3d')\n",
    "ax.plot(x_rotated1, y_rotated1, z_rotated1)\n",
    "ax.plot(x_rotated2, y_rotated2, z_rotated2)\n",
    "#ax.plot(x_rotated21, y_rotated21, z_rotated21)\n",
    "ax.plot(x_rotated3, y_rotated3, z_rotated3, 'k-')\n",
    "ax.plot(x_rotated4, y_rotated4, z_rotated4, 'k-')\n",
    "ax.plot(x_rotated5, y_rotated5, z_rotated5, 'k-')\n",
    "ax.plot(x_rotated6, y_rotated6, z_rotated6, 'k-')\n",
    "ax.plot(x_rotated7, y_rotated7, z_rotated7, 'k-')\n",
    "ax.plot(x_rotated8, y_rotated8, z_rotated8, 'k-')\n",
    "ax.plot(x_rotated9, y_rotated9, z_rotated9, 'k-')\n",
    "ax.plot(x_rotated10, y_rotated10, z_rotated10, 'k-')\n",
    "ax.plot(x_rotated11, y_rotated11, z_rotated11, 'k-')\n",
    "ax.plot(x_rotated12, y_rotated12, z_rotated12, 'k-')\n",
    "ax.plot(x_rotated13, y_rotated13, z_rotated13, 'k-')\n",
    "ax.plot(x_rotated14, y_rotated14, z_rotated14, 'k-')\n",
    "ax.plot(x_rotated15, y_rotated15, z_rotated15, 'k-')\n",
    "ax.plot(x_rotated16, y_rotated16, z_rotated16, 'k-')\n",
    "ax.plot(x_rotated17, y_rotated17, z_rotated17, 'k-')\n",
    "ax.plot(x_rotated18, y_rotated18, z_rotated18, 'k-')\n",
    "ax.plot(x_rotated19, y_rotated19, z_rotated19, 'k-')\n",
    "ax.plot(x_rotated20, y_rotated20, z_rotated20, 'k-')\n",
    "\n",
    "ax.set_xticks([])\n",
    "ax.set_yticks([])\n",
    "ax.set_zticks([])\n",
    "\n",
    "ax.set_xlabel('')\n",
    "ax.set_ylabel('')\n",
    "ax.set_zlabel('')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "0f461c1e-f9db-4880-8ed3-2a4c841b2251",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the rotation angles (in radians)\n",
    "alpha = damask.Orientation.from_matrix(R=np.linalg.inv(R_),family='hexagonal',lattice='hP',a=1.0,b=1.0,c=1.6235).as_Euler_angles(degrees=False)[0] \n",
    "beta = damask.Orientation.from_matrix(R=np.linalg.inv(R_),family='hexagonal',lattice='hP',a=1.0,b=1.0,c=1.6235).as_Euler_angles(degrees=False)[1] \n",
    "gamma = damask.Orientation.from_matrix(R=np.linalg.inv(R_),family='hexagonal',lattice='hP',a=1.0,b=1.0,c=1.6235).as_Euler_angles(degrees=False)[2] \n",
    "\n",
    "# Create the rotation matrices\n",
    "Rx = np.array([[1, 0, 0],\n",
    "               [0, cos(alpha), -sin(alpha)],\n",
    "               [0, sin(alpha), cos(alpha)]])\n",
    "\n",
    "Ry = np.array([[cos(beta), 0, sin(beta)],\n",
    "               [0, 1, 0],\n",
    "               [-sin(beta), 0, cos(beta)]])\n",
    "\n",
    "Rz = np.array([[cos(gamma), -sin(gamma), 0],\n",
    "               [sin(gamma), cos(gamma), 0],\n",
    "               [0, 0, 1]])\n",
    "\n",
    "# Combine the rotation matrices\n",
    "R = Rz @ Ry @ Rx\n",
    "\n",
    "# Apply the rotation to the line\n",
    "point21 = np.column_stack((x_rotated1, y_rotated1, z_rotated1))\n",
    "point22 = np.column_stack((x_rotated2, y_rotated2, z_rotated2))\n",
    "point23 = np.column_stack((x_rotated3, y_rotated3, z_rotated3))\n",
    "point24 = np.column_stack((x_rotated4, y_rotated4, z_rotated4))\n",
    "point25 = np.column_stack((x_rotated5, y_rotated5, z_rotated5))\n",
    "point26 = np.column_stack((x_rotated6, y_rotated6, z_rotated6))\n",
    "point27 = np.column_stack((x_rotated7, y_rotated7, z_rotated7))\n",
    "point28 = np.column_stack((x_rotated8, y_rotated8, z_rotated8))\n",
    "point29 = np.column_stack((x_rotated9, y_rotated9, z_rotated9))\n",
    "point30 = np.column_stack((x_rotated10, y_rotated10, z_rotated10))\n",
    "point31 = np.column_stack((x_rotated11, y_rotated11, z_rotated11))\n",
    "point32 = np.column_stack((x_rotated12, y_rotated12, z_rotated12))\n",
    "point33 = np.column_stack((x_rotated13, y_rotated13, z_rotated13))\n",
    "point34 = np.column_stack((x_rotated14, y_rotated14, z_rotated14))\n",
    "point35 = np.column_stack((x_rotated15, y_rotated15, z_rotated15))\n",
    "point36 = np.column_stack((x_rotated16, y_rotated16, z_rotated16))\n",
    "point37 = np.column_stack((x_rotated17, y_rotated17, z_rotated17))\n",
    "point38 = np.column_stack((x_rotated18, y_rotated18, z_rotated18))\n",
    "point39 = np.column_stack((x_rotated19, y_rotated19, z_rotated19))\n",
    "point40 = np.column_stack((x_rotated20, y_rotated20, z_rotated20))\n",
    "point41 = np.column_stack((x_rotated21, y_rotated21, z_rotated21))\n",
    "\n",
    "rotated_point21 = np.dot(R, point21.T).T\n",
    "rotated_point22 = np.dot(R, point22.T).T\n",
    "rotated_point23 = np.dot(R, point23.T).T\n",
    "rotated_point24 = np.dot(R, point24.T).T\n",
    "rotated_point25 = np.dot(R, point25.T).T\n",
    "rotated_point26 = np.dot(R, point26.T).T\n",
    "rotated_point27 = np.dot(R, point27.T).T\n",
    "rotated_point28 = np.dot(R, point28.T).T\n",
    "rotated_point29 = np.dot(R, point29.T).T\n",
    "rotated_point30 = np.dot(R, point30.T).T\n",
    "rotated_point31 = np.dot(R, point31.T).T\n",
    "rotated_point32 = np.dot(R, point32.T).T\n",
    "rotated_point33 = np.dot(R, point33.T).T\n",
    "rotated_point34 = np.dot(R, point34.T).T\n",
    "rotated_point35 = np.dot(R, point35.T).T\n",
    "rotated_point36 = np.dot(R, point36.T).T\n",
    "rotated_point37 = np.dot(R, point37.T).T\n",
    "rotated_point38 = np.dot(R, point38.T).T\n",
    "rotated_point39 = np.dot(R, point39.T).T\n",
    "rotated_point40 = np.dot(R, point40.T).T\n",
    "rotated_point41 = np.dot(R, point41.T).T\n",
    "\n",
    "# Extract the rotated coordinates\n",
    "x_rotated21, y_rotated21, z_rotated21 = rotated_point21.T\n",
    "x_rotated22, y_rotated22, z_rotated22 = rotated_point22.T\n",
    "x_rotated23, y_rotated23, z_rotated23 = rotated_point23.T\n",
    "x_rotated24, y_rotated24, z_rotated24 = rotated_point24.T\n",
    "x_rotated25, y_rotated25, z_rotated25 = rotated_point25.T\n",
    "x_rotated26, y_rotated26, z_rotated26 = rotated_point26.T\n",
    "x_rotated27, y_rotated27, z_rotated27 = rotated_point27.T\n",
    "x_rotated28, y_rotated28, z_rotated28 = rotated_point28.T\n",
    "x_rotated29, y_rotated29, z_rotated29 = rotated_point29.T\n",
    "x_rotated30, y_rotated30, z_rotated30 = rotated_point30.T\n",
    "x_rotated31, y_rotated31, z_rotated31 = rotated_point31.T\n",
    "x_rotated32, y_rotated32, z_rotated32 = rotated_point32.T\n",
    "x_rotated33, y_rotated33, z_rotated33 = rotated_point33.T\n",
    "x_rotated34, y_rotated34, z_rotated34 = rotated_point34.T\n",
    "x_rotated35, y_rotated35, z_rotated35 = rotated_point35.T\n",
    "x_rotated36, y_rotated36, z_rotated36 = rotated_point36.T\n",
    "x_rotated37, y_rotated37, z_rotated37 = rotated_point37.T\n",
    "x_rotated38, y_rotated38, z_rotated38 = rotated_point38.T\n",
    "x_rotated39, y_rotated39, z_rotated39 = rotated_point39.T\n",
    "x_rotated40, y_rotated40, z_rotated40 = rotated_point40.T\n",
    "x_rotated41, y_rotated41, z_rotated41 = rotated_point41.T\n",
    "\n",
    "\n",
    "# Plot the line\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "ax.plot(x_rotated21, y_rotated21, z_rotated21)\n",
    "ax.plot(x_rotated22, y_rotated22, z_rotated22)\n",
    "ax.plot(x_rotated23, y_rotated23, z_rotated23, 'k-')\n",
    "ax.plot(x_rotated24, y_rotated24, z_rotated24, 'k-')\n",
    "ax.plot(x_rotated25, y_rotated25, z_rotated25, 'k-')\n",
    "ax.plot(x_rotated26, y_rotated26, z_rotated26, 'k-')\n",
    "ax.plot(x_rotated27, y_rotated27, z_rotated27, 'k-')\n",
    "ax.plot(x_rotated28, y_rotated28, z_rotated28, 'k-')\n",
    "ax.plot(x_rotated29, y_rotated29, z_rotated29, 'k-')\n",
    "ax.plot(x_rotated30, y_rotated30, z_rotated30, 'k-')\n",
    "ax.plot(x_rotated31, y_rotated31, z_rotated31, 'k-')\n",
    "ax.plot(x_rotated32, y_rotated32, z_rotated32, 'k-')\n",
    "ax.plot(x_rotated33, y_rotated33, z_rotated33, 'k-')\n",
    "ax.plot(x_rotated34, y_rotated34, z_rotated34, 'k-')\n",
    "ax.plot(x_rotated35, y_rotated35, z_rotated35, 'k-')\n",
    "ax.plot(x_rotated36, y_rotated36, z_rotated36, 'k-')\n",
    "ax.plot(x_rotated37, y_rotated37, z_rotated37, 'k-')\n",
    "ax.plot(x_rotated38, y_rotated38, z_rotated38, 'k-')\n",
    "ax.plot(x_rotated39, y_rotated39, z_rotated39, 'k-')\n",
    "ax.plot(x_rotated40, y_rotated40, z_rotated40, 'k-')\n",
    "ax.plot(x_rotated40, y_rotated40, z_rotated40, 'k-')\n",
    "#ax.plot(x_rotated41, y_rotated41, z_rotated41)\n",
    "\n",
    "ax.set_xticks([])\n",
    "ax.set_yticks([])\n",
    "ax.set_zticks([])\n",
    "\n",
    "ax.set_xlabel('')\n",
    "ax.set_ylabel('')\n",
    "ax.set_zlabel('')\n",
    "plt.show()"
   ]
  }
 ],
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