{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basic usage of geo3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from geo3d import frame_wizard, Vector, Point, RotationMatrix, Frame, transformation_between_frames"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Frame creation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Manual Frame cration\n",
    "Manually create frame from given rotation Euler angles and translation vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <table>\n",
       "                <tr>\n",
       "                    <th>rotation matrix</th>\n",
       "                    <th>Fixed angles<br>(xyz, extr., deg.)</th>\n",
       "                    <th>Euler angles<br>(xyz, intr., deg.)</th>\n",
       "                    <th>translation<br></th>\n",
       "                </tr>\n",
       "                <tr><td><table><tr><td>0.19245009</td><td>0.41147560</td><td>-0.89087081</td></tr><tr><td>0.19245009</td><td>0.87438565</td><td>0.44543540</td></tr><tr><td>0.96225045</td><td>-0.25717225</td><td>0.08908708</td></tr></table></td><td><table><tr><td>θx</td><td>-70.89339</td></tr><tr><td>θy</td><td>-74.20683</td></tr><tr><td>θz</td><td>45.00000</td></tr></table></td><td><table><tr><td>θx</td><td>-78.69007</td></tr><tr><td>θy</td><td>-62.98288</td></tr><tr><td>θz</td><td>-64.93417</td></tr></table></td><td><table><tr><td>x</td><td>3.00000</td></tr><tr><td>y</td><td>4.00000</td></tr><tr><td>z</td><td>6.00000</td></tr></table></td></tr></table>"
      ],
      "text/plain": [
       "<geo3d.frame.Frame at 0x10bf2df00>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rot = RotationMatrix.from_euler_angles('xyz', [-70.89339465, -74.20683095,  45], degrees=True)\n",
    "vec = Vector([3,4,6])\n",
    "Frame(rot,vec)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Frame Wizard\n",
    "Create two frames using a Frame Wizard (comparable to the one in Spatial Analyzer).\n",
    "Frames are defined as transformations starting from a unit frame (no translation and rotation)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# rotation only from UnitFrame\n",
    "fa = frame_wizard(Vector([1, 1, 0]), Vector([1, -1, 0]), \"x\", \"y\", origin=[0, 0, 0])\n",
    "# translation only from UnitFrame\n",
    "fb = frame_wizard(Vector([1, 0, 0]), Vector([0, 1, 0]), \"x\", \"y\", origin=[1, 1, 4])\n",
    "# rotation and translation from UnitFrame\n",
    "fc = frame_wizard(Vector([1, 1, 0]), Vector([1, -1, 0]), \"x\", \"y\", origin=[1, 1, 4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <table>\n",
       "                <tr>\n",
       "                    <th>rotation matrix</th>\n",
       "                    <th>Fixed angles<br>(xyz, extr., deg.)</th>\n",
       "                    <th>Euler angles<br>(xyz, intr., deg.)</th>\n",
       "                    <th>translation<br></th>\n",
       "                </tr>\n",
       "                <tr><td><table><tr><td>0.70710678</td><td>0.70710678</td><td>0.00000000</td></tr><tr><td>0.70710678</td><td>-0.70710678</td><td>0.00000000</td></tr><tr><td>0.00000000</td><td>-0.00000000</td><td>-1.00000000</td></tr></table></td><td><table><tr><td>θx</td><td>180.00000</td></tr><tr><td>θy</td><td>0.00000</td></tr><tr><td>θz</td><td>45.00000</td></tr></table></td><td><table><tr><td>θx</td><td>180.00000</td></tr><tr><td>θy</td><td>0.00000</td></tr><tr><td>θz</td><td>-45.00000</td></tr></table></td><td><table><tr><td>x</td><td>0.00000</td></tr><tr><td>y</td><td>0.00000</td></tr><tr><td>z</td><td>0.00000</td></tr></table></td></tr></table>"
      ],
      "text/plain": [
       "<geo3d.frame.Frame at 0x10bf2d390>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<Frame instance at 4508522128>\n",
      "rotation\n",
      "[[ 1. -0.  0.]\n",
      " [ 0.  1.  0.]\n",
      " [ 0. -0.  1.]]\n",
      "Fixed angles (xyz, extrinsic, deg.)\n",
      "[0. 0. 0.]\n",
      "Euler angles (XYZ, intrinsic, deg.)\n",
      "[0. 0. 0.]\n",
      "translation\n",
      "[1 1 4]\n"
     ]
    }
   ],
   "source": [
    "print(fb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "They have a rotation and translation component:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><td>x</td><td>1.00000</td></tr><tr><td>y</td><td>1.00000</td></tr><tr><td>z</td><td>4.00000</td></tr></table>"
      ],
      "text/plain": [
       "<Vector at 4495432416> [1 1 4]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fc.translation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><td>0.70710678</td><td>0.70710678</td><td>0.00000000</td></tr><tr><td>0.70710678</td><td>-0.70710678</td><td>0.00000000</td></tr><tr><td>0.00000000</td><td>-0.00000000</td><td>-1.00000000</td></tr></table>"
      ],
      "text/plain": [
       "<geo3d.rotation.RotationMatrix at 0x10bf2ef80>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fc.rotation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rotation can be expressed as Euler angles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([180.,   0.,  45.])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fc.euler_angles('xyz', degrees='True')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Frame from 4x4 matrix string"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Construct Frame from 4x4 matrix (SA style) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <table>\n",
       "                <tr>\n",
       "                    <th>rotation matrix</th>\n",
       "                    <th>Fixed angles<br>(xyz, extr., deg.)</th>\n",
       "                    <th>Euler angles<br>(xyz, intr., deg.)</th>\n",
       "                    <th>translation<br></th>\n",
       "                </tr>\n",
       "                <tr><td><table><tr><td>0.00000003</td><td>0.00000026</td><td>-1.00000000</td></tr><tr><td>-0.13057024</td><td>-0.99143906</td><td>-0.00000026</td></tr><tr><td>-0.99143906</td><td>0.13057024</td><td>0.00000000</td></tr></table></td><td><table><tr><td>θx</td><td>90.00000</td></tr><tr><td>θy</td><td>82.49745</td></tr><tr><td>θz</td><td>-89.99998</td></tr></table></td><td><table><tr><td>θx</td><td>89.99689</td></tr><tr><td>θy</td><td>-89.99998</td></tr><tr><td>θz</td><td>-82.50056</td></tr></table></td><td><table><tr><td>x</td><td>634.99979</td></tr><tr><td>y</td><td>784.03196</td></tr><tr><td>z</td><td>747.50609</td></tr></table></td></tr></table>"
      ],
      "text/plain": [
       "<geo3d.frame.Frame at 0x10bf2e5c0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frame_from_SA = Frame.from_SA_pastable_string(\n",
    "    \"0.0000000344 0.0000002614 -1.0000000000 634.9997932029 -0.1305702435 -0.9914390609 -0.0000002637 784.0319609308 -0.9914390609 0.1305702435 0.0000000000 747.5060850385 0.0000000000 0.0000000000 0.0000000000 1.0000000000 \"\n",
    ")\n",
    "frame_from_SA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Convert Frame back to 4x4 matrix string"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.000000034400 0.000000261400 -1.000000000000 634.999793202900\n",
      "-0.130570243500 -0.991439060900 -0.000000263700 784.031960930800\n",
      "-0.991439060900 0.130570243500 0.000000000000 747.506085038500\n",
      "0.000000000000 0.000000000000 0.000000000000 1.000000000000\n"
     ]
    }
   ],
   "source": [
    "print(frame_from_SA.SA_pastable_string())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Frame to frame transformations "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A frame can be expressed in a different frame. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <table>\n",
       "                <tr>\n",
       "                    <th>rotation matrix</th>\n",
       "                    <th>Fixed angles<br>(xyz, extr., deg.)</th>\n",
       "                    <th>Euler angles<br>(xyz, intr., deg.)</th>\n",
       "                    <th>translation<br></th>\n",
       "                </tr>\n",
       "                <tr><td><table><tr><td>0.70710678</td><td>0.70710678</td><td>0.00000000</td></tr><tr><td>0.70710678</td><td>-0.70710678</td><td>0.00000000</td></tr><tr><td>0.00000000</td><td>0.00000000</td><td>-1.00000000</td></tr></table></td><td><table><tr><td>θx</td><td>180.00000</td></tr><tr><td>θy</td><td>0.00000</td></tr><tr><td>θz</td><td>45.00000</td></tr></table></td><td><table><tr><td>θx</td><td>180.00000</td></tr><tr><td>θy</td><td>0.00000</td></tr><tr><td>θz</td><td>-45.00000</td></tr></table></td><td><table><tr><td>x</td><td>1.41421</td></tr><tr><td>y</td><td>0.00000</td></tr><tr><td>z</td><td>-4.00000</td></tr></table></td></tr></table>"
      ],
      "text/plain": [
       "<geo3d.frame.Frame at 0x10bf2e230>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fb.express_in_frame(fa)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This yields the frame-to-frame transformation from fA to fB, represented in fA."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same frame-to-frame transformation matrix, but given in the original (unit) frame is "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "            <table>\n",
       "                <tr>\n",
       "                    <th>rotation matrix</th>\n",
       "                    <th>Fixed angles<br>(xyz, extr., deg.)</th>\n",
       "                    <th>Euler angles<br>(xyz, intr., deg.)</th>\n",
       "                    <th>translation<br></th>\n",
       "                </tr>\n",
       "                <tr><td><table><tr><td>0.70710678</td><td>0.70710678</td><td>0.00000000</td></tr><tr><td>0.70710678</td><td>-0.70710678</td><td>0.00000000</td></tr><tr><td>0.00000000</td><td>0.00000000</td><td>-1.00000000</td></tr></table></td><td><table><tr><td>θx</td><td>180.00000</td></tr><tr><td>θy</td><td>0.00000</td></tr><tr><td>θz</td><td>45.00000</td></tr></table></td><td><table><tr><td>θx</td><td>180.00000</td></tr><tr><td>θy</td><td>0.00000</td></tr><tr><td>θz</td><td>-45.00000</td></tr></table></td><td><table><tr><td>x</td><td>1.00000</td></tr><tr><td>y</td><td>1.00000</td></tr><tr><td>z</td><td>4.00000</td></tr></table></td></tr></table>"
      ],
      "text/plain": [
       "<geo3d.frame.Frame at 0x10bf2da80>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transformation_between_frames(fa, fb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Expression of vectors and points in frames"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Express a vector given in `original_frame` in a new frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><td>x</td><td>2.82843</td></tr><tr><td>y</td><td>-1.41421</td></tr><tr><td>z</td><td>0.00000</td></tr></table>"
      ],
      "text/plain": [
       "<Vector at 4405009840> [ 2.82842712 -1.41421356  0.        ]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Vector([1,3,0]).express_in_frame(fa, original_frame=fb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Express a point given in `original_frame` in a new frame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table><tr><td>x</td><td>7.07107</td></tr><tr><td>y</td><td>1.41421</td></tr><tr><td>z</td><td>-24.00000</td></tr></table>"
      ],
      "text/plain": [
       "<Point at 4495430688> [  7.07106781   1.41421356 -24.        ]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Point([5,3,20]).express_in_frame(fa, original_frame=fb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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