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   "cell_type": "markdown",
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   "metadata": {},
   "source": [
    "# Blender"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cffb7e10-1aa1-46d9-8eac-7fa9fab3daae",
   "metadata": {},
   "source": [
    "## Rotation formalisms"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "id": "df40f778-f020-4026-a5c8-2ede7957a2c2",
   "metadata": {},
   "source": [
    "See [Rotation formalisms in three dimensions](https://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions). Blender's user interface only allows for rotations to be entered as as Quaternions, Euler rotations, or an Euler axis-angle. If you have a rotation in some other form, how do you enter it in Blender? See [Rotation — SciPy Manual](https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.transform.Rotation.html#scipy.spatial.transform.Rotation):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "d4248180-dbdc-4f1c-8cc0-89ea294e6676",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.spatial.transform import Rotation as R\n",
    "\n",
    "def show_rot(rot: R):\n",
    "    print('Matrix:')\n",
    "    display(rot.as_matrix())\n",
    "    print('\\nBlender \"Quaternion\":')\n",
    "    display(rot.as_quat(canonical=True, scalar_first=True))\n",
    "    print('\\nBlender \"XYZ Euler\":')\n",
    "    display(rot.as_euler('xyz', degrees=True))\n",
    "    print('\\nBlender \"Axis Angle\":')\n",
    "    rot_vec = rot.as_rotvec(degrees=True)\n",
    "    norm = np.linalg.norm(rot_vec)\n",
    "    display(norm, rot_vec / norm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "d65d3481-2753-4ff0-be25-fb991548c20c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[-2.77555756e-17, -6.42962682e-01, -7.65897506e-01],\n",
       "       [ 0.00000000e+00, -7.65897506e-01,  6.42962682e-01],\n",
       "       [-1.00000000e+00,  0.00000000e+00, -2.77555756e-17]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Blender \"Quaternion\":\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.2419207 , -0.66443538,  0.2419207 ,  0.66443538])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Blender \"XYZ Euler\":\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-139.98690433,   90.        ,    0.        ])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Blender \"Axis Angle\":\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(152.00014158445592)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "array([-0.68477595,  0.24932669,  0.68477595])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_rot(R.from_matrix([\n",
    "[ 0.000, -0.643, -0.766],\n",
    "[ 0.000, -0.766,  0.643],\n",
    "[-1.000,  0.000,  0.000],]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "8e632615-e826-48b4-b88b-d921eee33ef0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  1.],\n",
       "       [-1.,  0.,  0.],\n",
       "       [ 0., -1.,  0.]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Blender \"Quaternion\":\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([ 0.5, -0.5,  0.5, -0.5])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Blender \"XYZ Euler\":\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([-90.,   0., -90.])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Blender \"Axis Angle\":\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "np.float64(119.99999999999999)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_rot(R.from_matrix([\n",
    "[ 0.000,  0.000,  1.000],\n",
    "[-1.000,  0.000,  0.000],\n",
    "[ 0.000, -1.000,  0.000],]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f4269d8-0a90-4a53-8b2e-1b940ec8fbc4",
   "metadata": {},
   "source": [
    "See also [Rotation Modes - Blender 4.5 LTS Manual](https://docs.blender.org/manual/en/latest/advanced/appendices/rotations.html). Many Blender tutorials try to explain Gimbal lock, but the best references still seem to be [Euler (gimbal lock) Explained - YouTube](https://www.youtube.com/watch?v=zc8b2Jo7mno) and [Gimbal lock - Wikipedia](https://en.wikipedia.org/wiki/Gimbal_lock)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bb2fea7-61d9-4d6c-aab8-7b72e4290ff5",
   "metadata": {},
   "source": [
    "In Eigen, quaternion-vector multiplication is [just multiplication](https://stackoverflow.com/a/52239772/622049). In Eigen the coeffs command [produces XYZW](https://eigen.tuxfamily.org/dox/classEigen_1_1QuaternionBase.html#a193e79f616335a0067e3e784c7cf85fa), but internally the data is XYZW. If you [install the Eigen pretty printers](https://stackoverflow.com/a/25088214/622049), it's explicit:\n",
    "```\n",
    "$1 = Eigen::Quaternion<double> (data ptr: 0x7fffffffd7d0) = {[x] = 0, [y] = 0.7071067811865841, [z] = 0, [w] = 0.70710678118651094}\n",
    "```"
   ]
  }
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