src/generator-pattern.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "373c9c0a",
   "metadata": {},
   "source": [
    "This notebook describes the math used in the `get_pattern_frame_offset_adjustments()` function in `generate-fake-recording.py`. See the comments in that function for context."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6d1183db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t.grid-container {\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t\tdisplay: inline-grid;\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t\tgrid-template-columns: auto;\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t}\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t</style>\n",
       "\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t<div><div class=\"grid-container\"><div class=\"grid-item\"><img alt=\"Output\" 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class=\"grid-item\"><img alt=\"Output\" 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class=\"grid-item\"><img alt=\"Output\" src=\"data:image/png;base64,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\"></div><div class=\"grid-item\"><img alt=\"Output\" 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\"></div></div></div>"
      ],
      "text/plain": [
       "{maxDeviation -> 0.5}\n",
       "{start -> 0.5}\n",
       "{end -> 1.5, start -> 0.5}\n",
       "start ∈ Reals && start > 0 && end ∈ Reals && end > 0 && end > start && \n",
       " \n",
       ">   offsetIntoCycle ∈ Reals && offsetIntoCycle >= 0 && \n",
       " \n",
       ">   cumulativeOffsetIntoCycle ∈ Reals && cumulativeOffsetIntoCycle >= 0"
      ]
     },
     "execution_count": 29,
     "metadata": {
      "text/html": [],
      "text/plain": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exampleMaxDeviation = {maxDeviation -> 0.5}\n",
    "exampleWithoutEnd = {start -> 1-maxDeviation} /. exampleMaxDeviation\n",
    "example = Join[{end -> 1+maxDeviation} /. exampleMaxDeviation, exampleWithoutEnd]\n",
    "assumptions =\n",
    "    Element[start, PositiveReals] && Element[end, PositiveReals] && end > start &&\n",
    "    Element[offsetIntoCycle, NonNegativeReals] &&\n",
    "    Element[cumulativeOffsetIntoCycle, NonNegativeReals]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "216b5e01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><img alt=\"Output\" src=\"data:image/png;base64,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\"></div>"
      ],
      "text/plain": [
       "       end  offsetIntoCycle\n",
       "-1 + (-----)                start\n",
       "      start"
      ]
     },
     "execution_count": 33,
     "metadata": {
      "text/html": [],
      "text/plain": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frameDurationAdjustment = (start (end/start)^offsetIntoCycle - 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "e3a344ae",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t.grid-container {\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t\tdisplay: inline-grid;\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t\tgrid-template-columns: auto;\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t}\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t</style>\n",
       "\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t<div><div class=\"grid-container\"><div class=\"grid-item\"><img alt=\"Output\" 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\"></div><div class=\"grid-item\"><img alt=\"Output\" src=\"data:image/png;base64,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\"></div><div class=\"grid-item\"><img alt=\"Output\" src=\"data:image/png;base64,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\"></div></div></div>"
      ],
      "text/plain": [
       "-Graphics-\n",
       "-0.5\n",
       "0.5"
      ]
     },
     "execution_count": 34,
     "metadata": {
      "text/html": [],
      "text/plain": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Plot[frameDurationAdjustment /. example, {offsetIntoCycle, 0, 1} /. example]\n",
    "frameDurationAdjustment /. {offsetIntoCycle -> 0} /. example\n",
    "frameDurationAdjustment /. {offsetIntoCycle -> 1} /. example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "6e638a05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><img alt=\"Output\" src=\"data:image/png;base64,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\"></div>"
      ],
      "text/plain": [
       "                                     end  cumulativeOffsetIntoCycle\n",
       "                             (-1 + (-----)                         ) start\n",
       "                                    start\n",
       "-cumulativeOffsetIntoCycle + ---------------------------------------------\n",
       "                                                   end\n",
       "                                              Log[-----]\n",
       "                                                  start"
      ]
     },
     "execution_count": 37,
     "metadata": {
      "text/html": [],
      "text/plain": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "frameOffsetAdjustment = Integrate[frameDurationAdjustment, {offsetIntoCycle, 0, cumulativeOffsetIntoCycle}]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "1adc7d4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><img alt=\"Output\" 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\"></div>"
      ],
      "text/plain": [
       "-Graphics-"
      ]
     },
     "execution_count": 38,
     "metadata": {
      "text/html": [],
      "text/plain": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Plot[frameOffsetAdjustment /. example, {cumulativeOffsetIntoCycle, 0, 1.5} /. example]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "b0732b5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t.grid-container {\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t\tdisplay: inline-grid;\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t\tgrid-template-columns: auto;\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t}\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t</style>\n",
       "\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t<div><div class=\"grid-container\"><div class=\"grid-item\"><img alt=\"Output\" 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\"></div></div></div>"
      ],
      "text/plain": [
       "     end - start\n",
       "-1 + -----------\n",
       "          end\n",
       "     Log[-----]\n",
       "         start\n",
       "-Graphics-"
      ]
     },
     "execution_count": 39,
     "metadata": {
      "text/html": [],
      "text/plain": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "finalFrameOffsetAdjustment = FullSimplify[frameOffsetAdjustment /. {cumulativeOffsetIntoCycle -> 1}, assumptions]\n",
    "Plot[finalFrameOffsetAdjustment /. {exampleWithoutEnd}, {end, 1, 2}]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "2d9d47c6",
   "metadata": {},
   "outputs": [
    {
     "ename": "Reduce::useq",
     "evalue": "                                                                                                start\n                                                                             ProductLog[C[1], -(------)]\n                                                                                                 start\n                                                                                                E                               start\nThe answer found by Reduce contains unsolved equation(s) {0 == start + Log[-(---------------------------)] + ProductLog[C[1], -(------)]}. A likely reason for this is that the solution set depends on branch cuts of Wolfram Language functions.\n                                                                                        start                                    start\n                                                                                                                                E",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m                                                                                                              start\n                                                                                           ProductLog[C[1], -(------)]\n                                                                                                               start\n                                                                                                              E                               start\nReduce::useq: The answer found by Reduce contains unsolved equation(s) {0 == start + Log[-(---------------------------)] + ProductLog[C[1], -(------)]}. A likely reason for this is that the solution set depends on branch cuts of Wolfram Language functions.\n                                                                                                      start                                    start\n                                                                                                                                              E\u001b[0m"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t.grid-container {\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t\tdisplay: inline-grid;\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t\tgrid-template-columns: auto;\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t\t}\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t</style>\n",
       "\n",
       "\t\t\t\t\t\t\t\t\t\t\t\t<div><div class=\"grid-container\"><div class=\"grid-item\"><img alt=\"Output\" 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\"></div><div class=\"grid-item\"><img alt=\"Output\" 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      ],
      "text/plain": [
       "start != 0 && end != 0 && (end - start) start != 0 && \n",
       " \n",
       "                                        start\n",
       "                       ProductLog[-1, -(------)]\n",
       "                                         start\n",
       "                                        E                             start\n",
       ">   0 == start + Log[-(-------------------------)] + ProductLog[-1, -(------)] && \n",
       "                                 start                                 start\n",
       "                                                                      E\n",
       " \n",
       "                             start\n",
       ">   end == -ProductLog[-1, -(------)]\n",
       "                              start\n",
       "                             E\n",
       "end == 1.75643"
      ]
     },
     "execution_count": 41,
     "metadata": {
      "text/html": [],
      "text/plain": []
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "endSolution = Reduce[finalFrameOffsetAdjustment == 0, end] /. {C[1] -> -1}\n",
    "FullSimplify[endSolution /. exampleWithoutEnd]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1788764e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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