{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4404ab81-3b3e-459c-b722-ac376fc826d2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e0ab07d7-0f0e-44e1-a37e-6885d8bb34c4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def createXYGrid(bbox, meshsize):\n",
    "    x1, y1, x2, y2 = bbox\n",
    "    xgrid, ygrid =np.meshgrid(np.linspace(x1, x2 ,meshsize), np.linspace(y1,y2,meshsize))\n",
    "    \n",
    "    zeroes = np.zeros(xgrid.shape)\n",
    "    \n",
    "    # create the individual position vectors\n",
    "    vecs = np.dstack((xgrid, ygrid, zeroes))\n",
    "    return xgrid, ygrid,vecs\n",
    "\n",
    "def createXZGrid(bbox, meshsize):\n",
    "    x1, z1, x2, z2 = bbox\n",
    "    xgrid, zgrid =np.meshgrid(np.linspace(x1, x2 ,meshsize), np.linspace(z1,z2,meshsize))\n",
    "    \n",
    "    zeroes = np.zeros(xgrid.shape)\n",
    "    \n",
    "    # create the individual position vectors\n",
    "    vecs = np.dstack((xgrid, zeroes, zgrid))\n",
    "    return xgrid, zgrid, vecs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1d089355-e77d-435f-961a-b471e2126d10",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-3,  6, -3])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cross([1,2,3],[4,5,6])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "813faaf7-3df2-4a79-9cb6-815dad5ea1ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3,  6, -3],\n",
       "       [-6, 12, -6]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cross([1,2,],[[4,5,6],[7,8,9]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e7b65392-0447-4c72-94de-3db7756482d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[1, 4],\n",
       "        [2, 5],\n",
       "        [3, 6]]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.dstack(([1,2,3],[4,5,6]))\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "edec09a0-a99b-4c6b-9c8c-dce6061fca80",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 3, 2)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1d5ffa0a-53af-49b2-ac7a-b1f2b54831a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 4],\n",
       "       [2, 5],\n",
       "       [3, 6]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.stack(([1,2,3],[4,5,6]), axis=1); x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9a579aca-c318-4490-90e8-73b6494c857c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 2)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "de47f268-ab14-42a9-897a-18d6ba1eb47d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 4]\n",
      "[2 5]\n",
      "[3 6]\n"
     ]
    }
   ],
   "source": [
    "for zz in x: print (zz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1e37913c-4d29-4f8b-ac09-76936abba983",
   "metadata": {},
   "outputs": [],
   "source": [
    "meshsize = 100\n",
    "bbox = (-.03,-.03, .03, .03)  # bounding box of visual area in meters\n",
    "\n",
    "# create the individual position vectors\n",
    "xgrid, ygrid, vecs = createXYGrid(bbox, meshsize)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "31a7be65-d588-483f-bf66-2263d7122f1f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100, 3)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vecs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "3f8a36c3-0250-4231-8bdd-1da0ad8e1202",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.03, -0.03,  0.  ])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vecs[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "1fce0842-6218-48c0-a722-bf7661812049",
   "metadata": {},
   "outputs": [],
   "source": [
    "radius = .03\n",
    "angnum = 720  # The number of evenly spaced angle values around a circumference of length 2*pi*R\n",
    "\n",
    "\n",
    "angles = np.linspace(0, 2*np.pi, angnum, endpoint=False)\n",
    "\n",
    "# create an array of the vector l\n",
    "coss = np.cos(angles)\n",
    "sins = np.sin(angles)\n",
    "zz = np.zeros_like(angles)\n",
    "l = np.stack((coss, sins, zz), axis=-1)*radius"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "3455ea5d-04c5-48c6-93c0-a6e16a52147f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.03      ,  0.        ,  0.        ],\n",
       "       [ 0.02999886,  0.0002618 ,  0.        ],\n",
       "       [ 0.02999543,  0.00052357,  0.        ],\n",
       "       ...,\n",
       "       [ 0.02998972, -0.00078531,  0.        ],\n",
       "       [ 0.02999543, -0.00052357,  0.        ],\n",
       "       [ 0.02999886, -0.0002618 ,  0.        ]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f2336b6f-4764-4755-8b5c-08a07a5f36ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "dl = np.diff(l, n=1, axis=0)\n",
    "dl = np.append(dl, [dl[0]], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "83baf809-301c-4f24-9e01-cacb9c039ca7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((720, 3), (720, 3))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(l.shape, dl.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "59f1c892-189b-491c-b596-2ad3fb8bd10b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(720, 2, 3)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.stack((l, dl), axis=1)\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f60780ad-3731-4537-a1a5-fa08d896ab8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "a,b = x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "3674b37b-3e73-4643-8b62-5ad563aba87f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.03, 0.  , 0.  ])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "ba871b06-904c-4d77-a709-ae75083191c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(720, 3)"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x[:,0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "1f37fccc-29d3-46bb-8de6-9c69169ee15d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100, 3)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vecs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "957eea1a-2a69-41f7-8318-0bdef2fb1730",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100, 720, 3)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rp = vecs[:,:,np.newaxis] - x[:,0]\n",
    "rp.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "9ff820bc-20ba-44b3-bb09-e75bb696d9a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.06, -0.03,  0.  ])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rp[0,0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "1556eea6-d6e3-45d2-8d49-5bf16bdc1909",
   "metadata": {},
   "outputs": [],
   "source": [
    "cp = np.cross(dl,rp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "aed0cdd3-c9ec-4c7f-bb10-37a0e19bd832",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100, 720, 3)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cp.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "33f13442-72ea-4b73-adef-59cd65d93248",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 100, 3)"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cp[:,:,0,:].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "81ee59eb-42d6-4bbe-8bc7-e88401cb6078",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-0.06, -0.03,  0.  ]),\n",
       " array([[ 0.03      ,  0.        ,  0.        ],\n",
       "        [ 0.02999886,  0.0002618 ,  0.        ],\n",
       "        [ 0.02999543,  0.00052357,  0.        ],\n",
       "        ...,\n",
       "        [ 0.02998972, -0.00078531,  0.        ],\n",
       "        [ 0.02999543, -0.00052357,  0.        ],\n",
       "        [ 0.02999886, -0.0002618 ,  0.        ]]))"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aa[0,0,0], x[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "ce7423bc-5347-4eb4-8e07-a2d960f29a0e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.03, -0.03,  0.  ])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vecs[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "694a89cc-eb23-445d-b62a-3d7bf334cec6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 1],\n",
       "       [2, 2],\n",
       "       [3, 3],\n",
       "       [4, 4]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array([[1,1],[2,2],[3,3],[4,4]]); a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "02c4e7ca-544f-48be-b6fa-bad56ca98466",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 2)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "c860c660-68dd-472b-b4f2-3e4593a5d3d8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3,  3],\n",
       "       [ 2,  2],\n",
       "       [ 1,  1],\n",
       "       [ 0,  0],\n",
       "       [-1, -1],\n",
       "       [-2, -2]])"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array([[3,3],[2,2],[1,1],[0,0],[-1, -1], [-2, -2]]);b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "01d8d48a-a2ae-4327-b1c9-483e3b908e32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 2)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "9cc873bb-7ae9-4b80-ab51-b78035ca8dfd",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "operands could not be broadcast together with shapes (4,2) (6,2) ",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[58], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43ma\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mb\u001b[49m\n",
      "\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (4,2) (6,2) "
     ]
    }
   ],
   "source": [
    "a - b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "d0cf3914-992b-45dc-b1ee-efd5b2c05deb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 1, 2)"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1 = a[:, np.newaxis]\n",
    "a1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "c33433da-b4ab-4d4b-8093-f7e868b009aa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 2)"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "876fb3fa-b1a1-4252-a278-0213d24d5217",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 6, 2)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = a1 - b\n",
    "c.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "273e3008-659f-4103-9d28-aaf96fd0b7ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c.ndim\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "bad40882-ad09-4ea9-a902-e5db2bd7b826",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "87b48a14-32bd-4015-b0f3-1989654653c8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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   "pygments_lexer": "ipython3",
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