diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..b3133b9
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,3 @@
+.jupyter_cache
+*.log
+*.tex
\ No newline at end of file
diff --git a/.jupyter_cache/__version__.txt b/.jupyter_cache/__version__.txt
deleted file mode 100644
index 79a2734..0000000
--- a/.jupyter_cache/__version__.txt
+++ /dev/null
@@ -1 +0,0 @@
-0.5.0
\ No newline at end of file
diff --git a/.jupyter_cache/executed/2f3f010a51c40fce4d85e1fa29ada8c0/base.ipynb b/.jupyter_cache/executed/2f3f010a51c40fce4d85e1fa29ada8c0/base.ipynb
deleted file mode 100644
index 5139368..0000000
--- a/.jupyter_cache/executed/2f3f010a51c40fce4d85e1fa29ada8c0/base.ipynb
+++ /dev/null
@@ -1,248 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "id": "a45c1344",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "(process:28652): GLib-GIO-WARNING **: 12:50:31.472: Unexpectedly, UWP app `KDEe.V.Okular_21.1203.941.0_x64__7vt06qxq7ptv8' (AUMId `KDEe.V.Okular_7vt06qxq7ptv8!KDEe.V.Okular') supports 5 extensions but has no verbs\n"
-     ]
-    }
-   ],
-   "source": [
-    "import IJulia\n",
-    "\n",
-    "# The julia kernel has built in support for Revise.jl, so this is the \n",
-    "# recommended approach for long-running sessions:\n",
-    "# https://github.com/JuliaLang/IJulia.jl/blob/9b10fa9b879574bbf720f5285029e07758e50a5e/src/kernel.jl#L46-L51\n",
-    "\n",
-    "# Users should enable revise within .julia/config/startup_ijulia.jl:\n",
-    "# https://timholy.github.io/Revise.jl/stable/config/#Using-Revise-automatically-within-Jupyter/IJulia-1\n",
-    "\n",
-    "# clear console history\n",
-    "IJulia.clear_history()\n",
-    "\n",
-    "# Intialize Plots w/ default fig width/height\n",
-    "try\n",
-    "  fig_width = 7\n",
-    "  fig_height = 5\n",
-    "  fig_format = :retina\n",
-    "  fig_dpi = 96\n",
-    "  # no retina format type, use svg for high quality type/marks\n",
-    "  if fig_format == :retina\n",
-    "    fig_format = :svg\n",
-    "  # IJulia doesn't support PDF output so use png (if the DPI \n",
-    "  # remains the default of 300 then set to 96)\n",
-    "  elseif fig_format == :pdf\n",
-    "    fig_format = :png\n",
-    "    fig_dpi = 96\n",
-    "  end\n",
-    "  # convert inches to pixels\n",
-    "  fig_width = fig_width * fig_dpi\n",
-    "  fig_height = fig_height * fig_dpi\n",
-    "  using Plots\n",
-    "  gr(size=(fig_width, fig_height), fmt = fig_format, dpi = fig_dpi)\n",
-    "catch e\n",
-    "  # @warn \"Plots init\" exception=(e, catch_backtrace())\n",
-    "end\n",
-    "\n",
-    "# Set run_path if specified\n",
-    "try\n",
-    "  run_path = \"\"\n",
-    "  if !isempty(run_path)\n",
-    "    cd(run_path)\n",
-    "  end\n",
-    "catch e\n",
-    "  @warn \"Run path init:\" exception=(e, catch_backtrace())\n",
-    "end\n",
-    "\n",
-    "# don't return kernel dependencies (b/c Revise should take care of dependencies)\n",
-    "nothing\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "id": "189db2ad",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "#| code-fold: true\n",
-    "#| output: false\n",
-    "using FileIO\n",
-    "using MeshIO\n",
-    "\n",
-    "using stlProcess\n",
-    "\n",
-    "using CSV\n",
-    "using DataFrames\n",
-    "\n",
-    "using LinearAlgebra"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "id": "5e47d862",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div class=\"data-frame\"><p>0 rows × 8 columns (omitted printing of 1 columns)</p><table class=\"data-frame\"><thead><tr><th></th><th>surface_area</th><th>characteristic_length</th><th>sbx</th><th>sby</th><th>sbz</th><th>Ix</th><th>Iy</th></tr><tr><th></th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody></tbody></table></div>"
-      ],
-      "text/latex": [
-       "\\begin{tabular}{r|cccccccc}\n",
-       "\t& surface\\_area & characteristic\\_length & sbx & sby & sbz & Ix & Iy & \\\\\n",
-       "\t\\hline\n",
-       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
-       "\t\\hline\n",
-       "\\end{tabular}\n"
-      ],
-      "text/plain": [
-       "\u001b[1m0×8 DataFrame\u001b[0m"
-      ]
-     },
-     "execution_count": 3,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# local path to https://gitlab.com/orbital-debris-research/fake-satellite-dataset\n",
-    "dataset_path = raw\"C:\\Coding\\fake-satellite-dataset\"\n",
-    "\n",
-    "folders = [\"1_5U\", \"assembly1\", \"cubesat\"]\n",
-    "\n",
-    "df = DataFrame(;\n",
-    "    surface_area=Float64[],\n",
-    "    characteristic_length=Float64[],\n",
-    "    sbx=Float64[],\n",
-    "    sby=Float64[],\n",
-    "    sbz=Float64[],\n",
-    "    Ix=Float64[],\n",
-    "    Iy=Float64[],\n",
-    "    Iz=Float64[],\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "id": "6c55224d",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Processing Path: C:\\Coding\\fake-satellite-dataset\\1_5U\n",
-      "Processing Path: C:\\Coding\\fake-satellite-dataset\\assembly1\n",
-      "Processing Path: C:\\Coding\\fake-satellite-dataset\\cubesat\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "┌ Warning: Characteristic Length Algorithm failed to converge, this usually means stl is flat. Setting length in dir to 0.\n",
-      "└ @ stlProcess C:\\Users\\albig\\.julia\\packages\\stlProcess\\8rsc7\\src\\stlProcess.jl:153\n"
-     ]
-    }
-   ],
-   "source": [
-    "for path in dataset_path * \"\\\\\" .* folders\n",
-    "    println(\"Processing Path: \", path)\n",
-    "    Threads.@threads for file in readdir(path)\n",
-    "        stl = load(path * \"\\\\\" * file)\n",
-    "        scale = find_scale(stl)\n",
-    "        props = get_mass_properties(stl; scale=scale)\n",
-    "\n",
-    "        eigs = eigvals(props.inertia)\n",
-    "        sort_index = sortperm(eigs)\n",
-    "        Ix, Iy, Iz = eigs[sort_index]\n",
-    "        sbx, sby, sbz = props.sb_values[sort_index]\n",
-    "\n",
-    "        push!(\n",
-    "            df,\n",
-    "            [props.surface_area, props.characteristic_length, sbx, sby, sbz, Ix, Iy, Iz],\n",
-    "        )\n",
-    "    end\n",
-    "end"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "id": "2e520bb3",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div class=\"data-frame\"><p>8 rows × 7 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>variable</th><th>mean</th><th>min</th><th>median</th><th>max</th><th>nmissing</th><th>eltype</th></tr><tr><th></th><th title=\"Symbol\">Symbol</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th><th title=\"DataType\">DataType</th></tr></thead><tbody><tr><th>1</th><td>surface_area</td><td>25.2002</td><td>5.60865</td><td>13.3338</td><td>159.406</td><td>0</td><td>Float64</td></tr><tr><th>2</th><td>characteristic_length</td><td>79.5481</td><td>0.158521</td><td>1.55816</td><td>1582.23</td><td>0</td><td>Float64</td></tr><tr><th>3</th><td>sbx</td><td>1.40222</td><td>0.0417367</td><td>0.967078</td><td>10.0663</td><td>0</td><td>Float64</td></tr><tr><th>4</th><td>sby</td><td>3.3367</td><td>0.0125824</td><td>2.68461</td><td>9.68361</td><td>0</td><td>Float64</td></tr><tr><th>5</th><td>sbz</td><td>3.91184</td><td>0.29006</td><td>1.8185</td><td>14.7434</td><td>0</td><td>Float64</td></tr><tr><th>6</th><td>Ix</td><td>1.58725</td><td>0.0311782</td><td>0.23401</td><td>11.1335</td><td>0</td><td>Float64</td></tr><tr><th>7</th><td>Iy</td><td>3.74345</td><td>0.178598</td><td>1.01592</td><td>24.6735</td><td>0</td><td>Float64</td></tr><tr><th>8</th><td>Iz</td><td>5.20207</td><td>0.178686</td><td>1.742</td><td>32.0083</td><td>0</td><td>Float64</td></tr></tbody></table></div>"
-      ],
-      "text/latex": [
-       "\\begin{tabular}{r|ccccccc}\n",
-       "\t& variable & mean & min & median & max & nmissing & eltype\\\\\n",
-       "\t\\hline\n",
-       "\t& Symbol & Float64 & Float64 & Float64 & Float64 & Int64 & DataType\\\\\n",
-       "\t\\hline\n",
-       "\t1 & surface\\_area & 25.2002 & 5.60865 & 13.3338 & 159.406 & 0 & Float64 \\\\\n",
-       "\t2 & characteristic\\_length & 79.5481 & 0.158521 & 1.55816 & 1582.23 & 0 & Float64 \\\\\n",
-       "\t3 & sbx & 1.40222 & 0.0417367 & 0.967078 & 10.0663 & 0 & Float64 \\\\\n",
-       "\t4 & sby & 3.3367 & 0.0125824 & 2.68461 & 9.68361 & 0 & Float64 \\\\\n",
-       "\t5 & sbz & 3.91184 & 0.29006 & 1.8185 & 14.7434 & 0 & Float64 \\\\\n",
-       "\t6 & Ix & 1.58725 & 0.0311782 & 0.23401 & 11.1335 & 0 & Float64 \\\\\n",
-       "\t7 & Iy & 3.74345 & 0.178598 & 1.01592 & 24.6735 & 0 & Float64 \\\\\n",
-       "\t8 & Iz & 5.20207 & 0.178686 & 1.742 & 32.0083 & 0 & Float64 \\\\\n",
-       "\\end{tabular}\n"
-      ],
-      "text/plain": [
-       "\u001b[1m8×7 DataFrame\u001b[0m\n",
-       "\u001b[1m Row \u001b[0m│\u001b[1m variable              \u001b[0m\u001b[1m mean     \u001b[0m\u001b[1m min       \u001b[0m\u001b[1m median    \u001b[0m\u001b[1m max        \u001b[0m\u001b[1m nmis\u001b[0m ⋯\n",
-       "\u001b[1m     \u001b[0m│\u001b[90m Symbol                \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Int6\u001b[0m ⋯\n",
-       "─────┼──────────────────────────────────────────────────────────────────────────\n",
-       "   1 │ surface_area           25.2002   5.60865    13.3338     159.406         ⋯\n",
-       "   2 │ characteristic_length  79.5481   0.158521    1.55816   1582.23\n",
-       "   3 │ sbx                     1.40222  0.0417367   0.967078    10.0663\n",
-       "   4 │ sby                     3.3367   0.0125824   2.68461      9.68361\n",
-       "   5 │ sbz                     3.91184  0.29006     1.8185      14.7434        ⋯\n",
-       "   6 │ Ix                      1.58725  0.0311782   0.23401     11.1335\n",
-       "   7 │ Iy                      3.74345  0.178598    1.01592     24.6735\n",
-       "   8 │ Iz                      5.20207  0.178686    1.742       32.0083\n",
-       "\u001b[36m                                                               2 columns omitted\u001b[0m"
-      ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "describe(df)"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Julia 1.8.0-beta3",
-   "language": "julia",
-   "name": "julia-1.8"
-  },
-  "language_info": {
-   "file_extension": ".jl",
-   "mimetype": "application/julia",
-   "name": "julia",
-   "version": "1.8.0"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
\ No newline at end of file
diff --git a/.jupyter_cache/executed/fd2f73547cc85cb9d5d855720bd105d3/base.ipynb b/.jupyter_cache/executed/fd2f73547cc85cb9d5d855720bd105d3/base.ipynb
deleted file mode 100644
index a0ebec1..0000000
--- a/.jupyter_cache/executed/fd2f73547cc85cb9d5d855720bd105d3/base.ipynb
+++ /dev/null
@@ -1,237 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "id": "129f639c",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import IJulia\n",
-    "\n",
-    "# The julia kernel has built in support for Revise.jl, so this is the \n",
-    "# recommended approach for long-running sessions:\n",
-    "# https://github.com/JuliaLang/IJulia.jl/blob/9b10fa9b879574bbf720f5285029e07758e50a5e/src/kernel.jl#L46-L51\n",
-    "\n",
-    "# Users should enable revise within .julia/config/startup_ijulia.jl:\n",
-    "# https://timholy.github.io/Revise.jl/stable/config/#Using-Revise-automatically-within-Jupyter/IJulia-1\n",
-    "\n",
-    "# clear console history\n",
-    "IJulia.clear_history()\n",
-    "\n",
-    "# Intialize Plots w/ default fig width/height\n",
-    "try\n",
-    "  fig_width = 7\n",
-    "  fig_height = 5\n",
-    "  fig_format = :retina\n",
-    "  fig_dpi = 96\n",
-    "  # no retina format type, use svg for high quality type/marks\n",
-    "  if fig_format == :retina\n",
-    "    fig_format = :svg\n",
-    "  # IJulia doesn't support PDF output so use png (if the DPI \n",
-    "  # remains the default of 300 then set to 96)\n",
-    "  elseif fig_format == :pdf\n",
-    "    fig_format = :png\n",
-    "    fig_dpi = 96\n",
-    "  end\n",
-    "  # convert inches to pixels\n",
-    "  fig_width = fig_width * fig_dpi\n",
-    "  fig_height = fig_height * fig_dpi\n",
-    "  using Plots\n",
-    "  gr(size=(fig_width, fig_height), fmt = fig_format, dpi = fig_dpi)\n",
-    "catch e\n",
-    "  # @warn \"Plots init\" exception=(e, catch_backtrace())\n",
-    "end\n",
-    "\n",
-    "# Set run_path if specified\n",
-    "try\n",
-    "  run_path = \"\"\n",
-    "  if !isempty(run_path)\n",
-    "    cd(run_path)\n",
-    "  end\n",
-    "catch e\n",
-    "  @warn \"Run path init:\" exception=(e, catch_backtrace())\n",
-    "end\n",
-    "\n",
-    "# don't return kernel dependencies (b/c Revise should take care of dependencies)\n",
-    "nothing\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "id": "8b15e8a8",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "#| code-fold: true\n",
-    "#| output: false\n",
-    "\n",
-    "using FileIO\n",
-    "using MeshIO\n",
-    "\n",
-    "using stlProcess\n",
-    "\n",
-    "using CSV\n",
-    "using DataFrames\n",
-    "\n",
-    "using LinearAlgebra"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "id": "f40c9594",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div class=\"data-frame\"><p>0 rows × 8 columns (omitted printing of 1 columns)</p><table class=\"data-frame\"><thead><tr><th></th><th>surface_area</th><th>characteristic_length</th><th>sbx</th><th>sby</th><th>sbz</th><th>Ix</th><th>Iy</th></tr><tr><th></th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th></tr></thead><tbody></tbody></table></div>"
-      ],
-      "text/latex": [
-       "\\begin{tabular}{r|cccccccc}\n",
-       "\t& surface\\_area & characteristic\\_length & sbx & sby & sbz & Ix & Iy & \\\\\n",
-       "\t\\hline\n",
-       "\t& Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & Float64 & \\\\\n",
-       "\t\\hline\n",
-       "\\end{tabular}\n"
-      ],
-      "text/plain": [
-       "\u001b[1m0×8 DataFrame\u001b[0m"
-      ]
-     },
-     "execution_count": 14,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "#| code-fold: true\n",
-    "#| output: false\n",
-    "\n",
-    "# local path to https://gitlab.com/orbital-debris-research/fake-satellite-dataset\n",
-    "dataset_path = raw\"C:\\Coding\\fake-satellite-dataset\"\n",
-    "\n",
-    "folders = [\"1_5U\", \"assembly1\", \"cubesat\"]\n",
-    "\n",
-    "df = DataFrame(;\n",
-    "    surface_area=Float64[],\n",
-    "    characteristic_length=Float64[],\n",
-    "    sbx=Float64[],\n",
-    "    sby=Float64[],\n",
-    "    sbz=Float64[],\n",
-    "    Ix=Float64[],\n",
-    "    Iy=Float64[],\n",
-    "    Iz=Float64[],\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "id": "bb8f7086",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Processing Path: C:\\Coding\\fake-satellite-dataset\\1_5U\n",
-      "Processing Path: C:\\Coding\\fake-satellite-dataset\\assembly1\n",
-      "Processing Path: C:\\Coding\\fake-satellite-dataset\\cubesat\n"
-     ]
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "┌ Warning: Characteristic Length Algorithm failed to converge, this usually means stl is flat. Setting length in dir to 0.\n",
-      "└ @ stlProcess C:\\Users\\albig\\.julia\\packages\\stlProcess\\8rsc7\\src\\stlProcess.jl:153\n"
-     ]
-    }
-   ],
-   "source": [
-    "for path in dataset_path * \"\\\\\" .* folders\n",
-    "    println(\"Processing Path: \", path)\n",
-    "    Threads.@threads for file in readdir(path)\n",
-    "        stl = load(path * \"\\\\\" * file)\n",
-    "        scale = find_scale(stl)\n",
-    "        props = get_mass_properties(stl; scale=scale)\n",
-    "\n",
-    "        eigs = eigvals(props.inertia)\n",
-    "        sort_index = sortperm(eigs)\n",
-    "        Ix, Iy, Iz = eigs[sort_index]\n",
-    "        sbx, sby, sbz = props.sb_values[sort_index]\n",
-    "\n",
-    "        push!(\n",
-    "            df,\n",
-    "            [props.surface_area, props.characteristic_length, sbx, sby, sbz, Ix, Iy, Iz],\n",
-    "        )\n",
-    "    end\n",
-    "end"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "id": "a51a601f",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div class=\"data-frame\"><p>8 rows × 7 columns</p><table class=\"data-frame\"><thead><tr><th></th><th>variable</th><th>mean</th><th>min</th><th>median</th><th>max</th><th>nmissing</th><th>eltype</th></tr><tr><th></th><th title=\"Symbol\">Symbol</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Float64\">Float64</th><th title=\"Int64\">Int64</th><th title=\"DataType\">DataType</th></tr></thead><tbody><tr><th>1</th><td>surface_area</td><td>25.2002</td><td>5.60865</td><td>13.3338</td><td>159.406</td><td>0</td><td>Float64</td></tr><tr><th>2</th><td>characteristic_length</td><td>79.5481</td><td>0.158521</td><td>1.55816</td><td>1582.23</td><td>0</td><td>Float64</td></tr><tr><th>3</th><td>sbx</td><td>1.40222</td><td>0.0417367</td><td>0.967078</td><td>10.0663</td><td>0</td><td>Float64</td></tr><tr><th>4</th><td>sby</td><td>3.3367</td><td>0.0125824</td><td>2.68461</td><td>9.68361</td><td>0</td><td>Float64</td></tr><tr><th>5</th><td>sbz</td><td>3.91184</td><td>0.29006</td><td>1.8185</td><td>14.7434</td><td>0</td><td>Float64</td></tr><tr><th>6</th><td>Ix</td><td>1.58725</td><td>0.0311782</td><td>0.23401</td><td>11.1335</td><td>0</td><td>Float64</td></tr><tr><th>7</th><td>Iy</td><td>3.74345</td><td>0.178598</td><td>1.01592</td><td>24.6735</td><td>0</td><td>Float64</td></tr><tr><th>8</th><td>Iz</td><td>5.20207</td><td>0.178686</td><td>1.742</td><td>32.0083</td><td>0</td><td>Float64</td></tr></tbody></table></div>"
-      ],
-      "text/latex": [
-       "\\begin{tabular}{r|ccccccc}\n",
-       "\t& variable & mean & min & median & max & nmissing & eltype\\\\\n",
-       "\t\\hline\n",
-       "\t& Symbol & Float64 & Float64 & Float64 & Float64 & Int64 & DataType\\\\\n",
-       "\t\\hline\n",
-       "\t1 & surface\\_area & 25.2002 & 5.60865 & 13.3338 & 159.406 & 0 & Float64 \\\\\n",
-       "\t2 & characteristic\\_length & 79.5481 & 0.158521 & 1.55816 & 1582.23 & 0 & Float64 \\\\\n",
-       "\t3 & sbx & 1.40222 & 0.0417367 & 0.967078 & 10.0663 & 0 & Float64 \\\\\n",
-       "\t4 & sby & 3.3367 & 0.0125824 & 2.68461 & 9.68361 & 0 & Float64 \\\\\n",
-       "\t5 & sbz & 3.91184 & 0.29006 & 1.8185 & 14.7434 & 0 & Float64 \\\\\n",
-       "\t6 & Ix & 1.58725 & 0.0311782 & 0.23401 & 11.1335 & 0 & Float64 \\\\\n",
-       "\t7 & Iy & 3.74345 & 0.178598 & 1.01592 & 24.6735 & 0 & Float64 \\\\\n",
-       "\t8 & Iz & 5.20207 & 0.178686 & 1.742 & 32.0083 & 0 & Float64 \\\\\n",
-       "\\end{tabular}\n"
-      ],
-      "text/plain": [
-       "\u001b[1m8×7 DataFrame\u001b[0m\n",
-       "\u001b[1m Row \u001b[0m│\u001b[1m variable              \u001b[0m\u001b[1m mean     \u001b[0m\u001b[1m min       \u001b[0m\u001b[1m median    \u001b[0m\u001b[1m max        \u001b[0m\u001b[1m nmis\u001b[0m ⋯\n",
-       "\u001b[1m     \u001b[0m│\u001b[90m Symbol                \u001b[0m\u001b[90m Float64  \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64   \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Int6\u001b[0m ⋯\n",
-       "─────┼──────────────────────────────────────────────────────────────────────────\n",
-       "   1 │ surface_area           25.2002   5.60865    13.3338     159.406         ⋯\n",
-       "   2 │ characteristic_length  79.5481   0.158521    1.55816   1582.23\n",
-       "   3 │ sbx                     1.40222  0.0417367   0.967078    10.0663\n",
-       "   4 │ sby                     3.3367   0.0125824   2.68461      9.68361\n",
-       "   5 │ sbz                     3.91184  0.29006     1.8185      14.7434        ⋯\n",
-       "   6 │ Ix                      1.58725  0.0311782   0.23401     11.1335\n",
-       "   7 │ Iy                      3.74345  0.178598    1.01592     24.6735\n",
-       "   8 │ Iz                      5.20207  0.178686    1.742       32.0083\n",
-       "\u001b[36m                                                               2 columns omitted\u001b[0m"
-      ]
-     },
-     "execution_count": 16,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "describe(df)"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Julia 1.8.0-beta3",
-   "language": "julia",
-   "name": "julia-1.8"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
\ No newline at end of file
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@@ -0,0 +1 @@
+{"rule":"UPPERCASE_SENTENCE_START","sentence":"^\\Qmodels that are in the \\E(?:Dummy|Ina|Jimmy-)[0-9]+\\Q format.\\E$"}
diff --git a/report.html b/report.html
index de012f2..a9b0ac6 100644
--- a/report.html
+++ b/report.html
@@ -2514,75 +2514,94 @@ vertical-align: -.125em;
 
 
 
-<div class="cell" data-execution_count="1">
-<details>
-<summary>Code</summary>
-<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">FileIO</span></span>
-<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">MeshIO</span></span>
-<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">stlProcess</span></span>
-<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">CSV</span></span>
-<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">DataFrames</span></span>
-<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">LinearAlgebra</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
-</details>
-</div>
-<div class="cell" data-execution_count="2">
+<section id="introduction" class="level2 page-columns page-full">
+<h2 class="anchored" data-anchor-id="introduction">Introduction</h2>
+<p>Orbital debris is a form of pollution that is growing at an exponential pace and puts current and future space infrastructure at risk. Satellites are critical to military, commercial, and civil operations. Unfortunately, the space that debris occupies is increasingly becoming more crowded and dangerous, potentially leading to a cascade event that could turn orbit around the Earth into an unusable wasteland for decades unless proper mitigation is not introduced. Existing models employed by NASA rely on a dataset created from 2D images and are missing many crucial features required for correctly modeling the space debris environment. This approach aims to use high-resolution 3D scanning to fully capture the geometry of a piece of debris and allow a more advanced analysis of each piece. Coupled with machine learning methods, the scans will allow advances to the current cutting edge. Physical and photograph-based measurements are time-consuming, hard to replicate, and lack precision. 3D scanning allows much more advanced and accurate analysis of each debris sample, focusing on properties such as moment of inertia, cross-section, and drag. Once the characteristics of space debris are more thoroughly understood, we can begin mitigating the creation and danger of future space debris by implementing improved satellite construction methods and more advanced debris avoidance measures.</p>
+<section id="current-progress" class="level3 page-columns page-full">
+<h3 class="anchored" data-anchor-id="current-progress">Current Progress</h3>
+<div class="page-columns page-full"><p>This project aims to fix very difficult issues, and although great progress has been made there is still plenty of work to be done. Currently, algorithms have been made that are capable of getting many key features from solid <a href="#fn1" class="footnote-ref" id="fnref1" role="doc-noteref"><sup>1</sup></a> models that are in the <code>stl</code> format. The algorithm for processing the 3D meshes is implemented in the Julia programming language. Syntactically the language is very similar to Python and Matlab. Julia was chosen because it is nearly as performant as compiled languages like C, while still having tooling geared towards engineers and scientists. The code produces a struct with all the calculated properties as follows:</p><div class="no-row-height column-margin column-container"><li id="fn1" role="doc-endnote"><p><sup>1</sup>&nbsp;A mesh with a surface that is fully closed and has no holes in its geometry.</p></li></div></div>
+<div class="sourceCode" id="cb1"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> Properties</span>
+<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Volume of the mesh</span></span>
+<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a>    volume<span class="op">::</span><span class="dt">Float64</span></span>
+<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Center of gravity, meshes are not always center at [0,0,0]</span></span>
+<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a>    center_of_gravity<span class="op">::</span><span class="dt">Vector{Float64}</span></span>
+<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Moment of inertia tensor</span></span>
+<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a>    inertia<span class="op">::</span><span class="dt">Matrix{Float64}</span></span>
+<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Surface area of mesh</span></span>
+<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a>    surface_area<span class="op">::</span><span class="dt">Float64</span></span>
+<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Average orthogonal dimension of the mesh</span></span>
+<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a>    characteristic_length<span class="op">::</span><span class="dt">Float64</span></span>
+<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a>    <span class="co"># Projected length of farthest two points in [x,y,z] directions</span></span>
+<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a>    solidbody_values<span class="op">::</span><span class="dt">Vector{Float64}</span></span>
+<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="cell" data-execution_count="3">
 <details>
 <summary>Code</summary>
 <div class="sourceCode cell-code" id="cb2"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="co"># local path to https://gitlab.com/orbital-debris-research/fake-satellite-dataset</span></span>
 <span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>dataset_path <span class="op">=</span> <span class="st">raw"C:\Coding\fake-satellite-dataset"</span></span>
 <span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a>folders <span class="op">=</span> [<span class="st">"1_5U"</span>, <span class="st">"assembly1"</span>, <span class="st">"cubesat"</span>]</span>
-<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a>df <span class="op">=</span> <span class="fu">DataFrame</span>(;</span>
-<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a>    surface_area<span class="op">=</span><span class="dt">Float64</span>[],</span>
-<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a>    characteristic_length<span class="op">=</span><span class="dt">Float64</span>[],</span>
-<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a>    sbx<span class="op">=</span><span class="dt">Float64</span>[],</span>
-<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a>    sby<span class="op">=</span><span class="dt">Float64</span>[],</span>
-<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a>    sbz<span class="op">=</span><span class="dt">Float64</span>[],</span>
-<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a>    Ix<span class="op">=</span><span class="dt">Float64</span>[],</span>
-<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a>    Iy<span class="op">=</span><span class="dt">Float64</span>[],</span>
-<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a>    Iz<span class="op">=</span><span class="dt">Float64</span>[],</span>
-<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="co"># folders = ["1_5U", "assembly1", "cubesat"]</span></span>
+<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a>folders <span class="op">=</span> [<span class="st">"cubesat"</span>]</span>
+<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a>df <span class="op">=</span> <span class="fu">DataFrame</span>(;</span>
+<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a>    surface_area<span class="op">=</span><span class="dt">Float64</span>[],</span>
+<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a>    characteristic_length<span class="op">=</span><span class="dt">Float64</span>[],</span>
+<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a>    sbx<span class="op">=</span><span class="dt">Float64</span>[],</span>
+<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a>    sby<span class="op">=</span><span class="dt">Float64</span>[],</span>
+<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a>    sbz<span class="op">=</span><span class="dt">Float64</span>[],</span>
+<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a>    Ix<span class="op">=</span><span class="dt">Float64</span>[],</span>
+<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a>    Iy<span class="op">=</span><span class="dt">Float64</span>[],</span>
+<span id="cb2-15"><a href="#cb2-15" aria-hidden="true" tabindex="-1"></a>    Iz<span class="op">=</span><span class="dt">Float64</span>[],</span>
+<span id="cb2-16"><a href="#cb2-16" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 </details>
 </div>
-<div class="cell" data-execution_count="3">
-<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> path <span class="kw">in</span> dataset_path <span class="op">*</span> <span class="st">"</span><span class="sc">\\</span><span class="st">"</span> <span class="op">.*</span> folders</span>
-<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>    <span class="fu">println</span>(<span class="st">"Processing Path: "</span>, path)</span>
-<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>    <span class="bu">Threads</span>.<span class="pp">@threads</span> <span class="cf">for</span> file <span class="kw">in</span> <span class="fu">readdir</span>(path)</span>
-<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a>        stl <span class="op">=</span> <span class="fu">load</span>(path <span class="op">*</span> <span class="st">"</span><span class="sc">\\</span><span class="st">"</span> <span class="op">*</span> file)</span>
-<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a>        scale <span class="op">=</span> <span class="fu">find_scale</span>(stl)</span>
-<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a>        props <span class="op">=</span> <span class="fu">get_mass_properties</span>(stl; scale<span class="op">=</span>scale)</span>
-<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a>        eigs <span class="op">=</span> <span class="fu">eigvals</span>(props.inertia)</span>
-<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a>        sort_index <span class="op">=</span> <span class="fu">sortperm</span>(eigs)</span>
-<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a>        Ix, Iy, Iz <span class="op">=</span> eigs[sort_index]</span>
-<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a>        sbx, sby, sbz <span class="op">=</span> props.sb_values[sort_index]</span>
-<span id="cb3-12"><a href="#cb3-12" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb3-13"><a href="#cb3-13" aria-hidden="true" tabindex="-1"></a>        <span class="fu">push!</span>(</span>
-<span id="cb3-14"><a href="#cb3-14" aria-hidden="true" tabindex="-1"></a>            df,</span>
-<span id="cb3-15"><a href="#cb3-15" aria-hidden="true" tabindex="-1"></a>            [props.surface_area, props.characteristic_length, sbx, sby, sbz, Ix, Iy, Iz],</span>
-<span id="cb3-16"><a href="#cb3-16" aria-hidden="true" tabindex="-1"></a>        )</span>
-<span id="cb3-17"><a href="#cb3-17" aria-hidden="true" tabindex="-1"></a>    <span class="cf">end</span></span>
-<span id="cb3-18"><a href="#cb3-18" aria-hidden="true" tabindex="-1"></a><span class="cf">end</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
-<div class="cell-output cell-output-stdout">
-<pre><code>Processing Path: C:\Coding\fake-satellite-dataset\1_5U
-Processing Path: C:\Coding\fake-satellite-dataset\assembly1
-Processing Path: C:\Coding\fake-satellite-dataset\cubesat</code></pre>
-</div>
-<div class="cell-output cell-output-stderr">
-<pre><code>┌ Warning: Characteristic Length Algorithm failed to converge, this usually means stl is flat. Setting length in dir to 0.
-└ @ stlProcess C:\Users\albig\.julia\packages\stlProcess\8rsc7\src\stlProcess.jl:153</code></pre>
-</div>
-</div>
 <div class="cell" data-execution_count="4">
-<div class="sourceCode cell-code" id="cb6"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">describe</span>(df)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
-<div class="cell-output cell-output-display" data-execution_count="16">
-<div class="data-frame"><p>8 rows × 7 columns</p><table class="data-frame table table-sm table-striped"><thead><tr><th></th><th>variable</th><th>mean</th><th>min</th><th>median</th><th>max</th><th>nmissing</th><th>eltype</th></tr><tr><th></th><th title="Symbol">Symbol</th><th title="Float64">Float64</th><th title="Float64">Float64</th><th title="Float64">Float64</th><th title="Float64">Float64</th><th title="Int64">Int64</th><th title="DataType">DataType</th></tr></thead><tbody><tr><th>1</th><td>surface_area</td><td>25.2002</td><td>5.60865</td><td>13.3338</td><td>159.406</td><td>0</td><td>Float64</td></tr><tr><th>2</th><td>characteristic_length</td><td>79.5481</td><td>0.158521</td><td>1.55816</td><td>1582.23</td><td>0</td><td>Float64</td></tr><tr><th>3</th><td>sbx</td><td>1.40222</td><td>0.0417367</td><td>0.967078</td><td>10.0663</td><td>0</td><td>Float64</td></tr><tr><th>4</th><td>sby</td><td>3.3367</td><td>0.0125824</td><td>2.68461</td><td>9.68361</td><td>0</td><td>Float64</td></tr><tr><th>5</th><td>sbz</td><td>3.91184</td><td>0.29006</td><td>1.8185</td><td>14.7434</td><td>0</td><td>Float64</td></tr><tr><th>6</th><td>Ix</td><td>1.58725</td><td>0.0311782</td><td>0.23401</td><td>11.1335</td><td>0</td><td>Float64</td></tr><tr><th>7</th><td>Iy</td><td>3.74345</td><td>0.178598</td><td>1.01592</td><td>24.6735</td><td>0</td><td>Float64</td></tr><tr><th>8</th><td>Iz</td><td>5.20207</td><td>0.178686</td><td>1.742</td><td>32.0083</td><td>0</td><td>Float64</td></tr></tbody></table></div>
+<div class="sourceCode cell-code" id="cb3"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> path <span class="kw">in</span> dataset_path <span class="op">*</span> <span class="st">"</span><span class="sc">\\</span><span class="st">"</span> <span class="op">.*</span> folders</span>
+<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>    <span class="bu">Threads</span>.<span class="pp">@threads</span> <span class="cf">for</span> file <span class="kw">in</span> <span class="fu">readdir</span>(path)</span>
+<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>        stl <span class="op">=</span> <span class="fu">load</span>(path <span class="op">*</span> <span class="st">"</span><span class="sc">\\</span><span class="st">"</span> <span class="op">*</span> file)</span>
+<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a>        scale <span class="op">=</span> <span class="fu">find_scale</span>(stl)</span>
+<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a>        props <span class="op">=</span> <span class="fu">get_mass_properties</span>(stl; scale<span class="op">=</span>scale)</span>
+<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a>        eigs <span class="op">=</span> <span class="fu">eigvals</span>(props.inertia)</span>
+<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a>        sort_index <span class="op">=</span> <span class="fu">sortperm</span>(eigs)</span>
+<span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a>        I1, I2, I3 <span class="op">=</span> eigs[sort_index]</span>
+<span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a>        sbx, sby, sbz <span class="op">=</span> props.sb_values[sort_index]</span>
+<span id="cb3-11"><a href="#cb3-11" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb3-12"><a href="#cb3-12" aria-hidden="true" tabindex="-1"></a>        <span class="fu">push!</span>(</span>
+<span id="cb3-13"><a href="#cb3-13" aria-hidden="true" tabindex="-1"></a>            df,</span>
+<span id="cb3-14"><a href="#cb3-14" aria-hidden="true" tabindex="-1"></a>            [props.surface_area, props.characteristic_length, sbx, sby, sbz, I3, I2, I1],</span>
+<span id="cb3-15"><a href="#cb3-15" aria-hidden="true" tabindex="-1"></a>        )</span>
+<span id="cb3-16"><a href="#cb3-16" aria-hidden="true" tabindex="-1"></a>    <span class="cf">end</span></span>
+<span id="cb3-17"><a href="#cb3-17" aria-hidden="true" tabindex="-1"></a><span class="cf">end</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+</div>
+<div class="column-body-outset">
+<div class="cell" data-execution_count="5">
+<div class="cell-output cell-output-display" data-execution_count="20">
+<div class="data-frame"><p>8 rows × 7 columns</p><table class="data-frame table table-sm table-striped"><thead><tr><th></th><th>variable</th><th>mean</th><th>min</th><th>median</th><th>max</th><th>nmissing</th><th>eltype</th></tr><tr><th></th><th title="Symbol">Symbol</th><th title="Float64">Float64</th><th title="Float64">Float64</th><th title="Float64">Float64</th><th title="Float64">Float64</th><th title="Int64">Int64</th><th title="DataType">DataType</th></tr></thead><tbody><tr><th>1</th><td>surface_area</td><td>17.6375</td><td>6.62244</td><td>14.4423</td><td>52.2496</td><td>0</td><td>Float64</td></tr><tr><th>2</th><td>characteristic_length</td><td>35.3451</td><td>0.2662</td><td>1.50102</td><td>434.102</td><td>0</td><td>Float64</td></tr><tr><th>3</th><td>sbx</td><td>1.69789</td><td>0.198322</td><td>1.48948</td><td>3.60402</td><td>0</td><td>Float64</td></tr><tr><th>4</th><td>sby</td><td>2.30204</td><td>0.135151</td><td>1.00749</td><td>8.0472</td><td>0</td><td>Float64</td></tr><tr><th>5</th><td>sbz</td><td>2.25255</td><td>0.29006</td><td>1.48957</td><td>7.76479</td><td>0</td><td>Float64</td></tr><tr><th>6</th><td>Ix</td><td>1.79204</td><td>0.178686</td><td>1.57634</td><td>6.83016</td><td>0</td><td>Float64</td></tr><tr><th>7</th><td>Iy</td><td>1.50921</td><td>0.178598</td><td>0.844538</td><td>6.54812</td><td>0</td><td>Float64</td></tr><tr><th>8</th><td>Iz</td><td>0.507267</td><td>0.0311782</td><td>0.279339</td><td>2.19511</td><td>0</td><td>Float64</td></tr></tbody></table></div>
 </div>
 </div>
+</div>
+<div class="cell" data-execution_count="6">
+<div class="sourceCode cell-code" id="cb4"><pre class="sourceCode julia code-with-copy"><code class="sourceCode julia"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>S <span class="op">=</span> <span class="fu">cov</span>(<span class="fu">Matrix</span>(df))</span>
+<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>eig_vals <span class="op">=</span> <span class="fu">eigvals</span>(S);</span>
+<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a><span class="co"># sorting eigenvalues from largest to smallest</span></span>
+<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a>sort_index <span class="op">=</span> <span class="fu">sortperm</span>(eig_vals; rev<span class="op">=</span><span class="cn">true</span>)</span>
+<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a>lambda <span class="op">=</span> eig_vals[sort_index]</span>
+<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a>names_sorted <span class="op">=</span> <span class="fu">names</span>(df)[sort_index]</span>
+<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a>lambda_ratio <span class="op">=</span> <span class="fu">cumsum</span>(lambda) <span class="op">./</span> <span class="fu">sum</span>(lambda)</span>
+<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a><span class="fu">plot</span>(lambda_ratio, marker<span class="op">=:</span>x)</span>
+<span id="cb4-14"><a href="#cb4-14" aria-hidden="true" tabindex="-1"></a><span class="fu">xticks!</span>(sort_index,<span class="fu">names</span>(df), xrotation <span class="op">=</span> <span class="fl">15</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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+</div>
+</div>
+</section>
+</section>
 <section id="gathering-data" class="level2">
 <h2 class="anchored" data-anchor-id="gathering-data">Gathering Data</h2>
 <p>To get started on the project before any scans of the actual debris are made available, I opted to find 3D models online and process them as if they were data collected by my team. GrabCAD is an excellent source of high-quality 3D models, and all the models have, at worst, a non-commercial license making them suitable for this study. The current dataset uses three separate satellite assemblies found on GrabCAD, below is an example of one of the satellites that was used.</p>
@@ -2607,16 +2626,16 @@ Murray, James, Heather Cowardin, J-C Liou, Marlon Sorge, Norman Fitz-Coy, and To
 </figure>
 </div>
 <p>The algorithm’s speed is critical not only for the eventual large number of debris pieces that have to be processed, but many of the data science algorithms we plan on performing on the compiled data need the data to be normalized. For the current dataset and properties, it makes the most sense to normalize the dataset based on volume. Volume was chosen for multiple reasons, namely because it was easy to implement an efficient algorithm to calculate volume, and currently, volume produces the least amount of variation out of the current set of properties calculated. Unfortunately, scaling a model to a specific volume is an iterative process, but can be done very efficiently using derivative-free numerical root-finding algorithms. The current implementation can scale and process all the properties using only 30% more time than getting the properties without first scaling.</p>
-<div class="sourceCode" id="cb7"><pre class="sourceCode txt code-with-copy"><code class="sourceCode default"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a> Row │ variable               mean      min        median     max</span>
-<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>─────┼───────────────────────────────────────────────────────────────────</span>
-<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>   1 │ surface_area           25.2002   5.60865     13.3338     159.406</span>
-<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>   2 │ characteristic_length  79.5481   0.158521    1.55816     1582.23</span>
-<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>   3 │ sbx                     1.40222  0.0417367   0.967078    10.0663</span>
-<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a>   4 │ sby                     3.3367   0.0125824   2.68461     9.68361</span>
-<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a>   5 │ sbz                     3.91184  0.29006     1.8185      14.7434</span>
-<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a>   6 │ Ix                      1.58725  0.0311782   0.23401     11.1335</span>
-<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a>   7 │ Iy                      3.74345  0.178598    1.01592     24.6735</span>
-<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a>   8 │ Iz                      5.20207  0.178686    1.742       32.0083</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode" id="cb5"><pre class="sourceCode txt code-with-copy"><code class="sourceCode default"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a> Row │ variable               mean      min        median     max</span>
+<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>─────┼───────────────────────────────────────────────────────────────────</span>
+<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>   1 │ surface_area           25.2002   5.60865     13.3338     159.406</span>
+<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a>   2 │ characteristic_length  79.5481   0.158521    1.55816     1582.23</span>
+<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a>   3 │ sbx                     1.40222  0.0417367   0.967078    10.0663</span>
+<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a>   4 │ sby                     3.3367   0.0125824   2.68461     9.68361</span>
+<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a>   5 │ sbz                     3.91184  0.29006     1.8185      14.7434</span>
+<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a>   6 │ Ix                      1.58725  0.0311782   0.23401     11.1335</span>
+<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a>   7 │ Iy                      3.74345  0.178598    1.01592     24.6735</span>
+<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a>   8 │ Iz                      5.20207  0.178686    1.742       32.0083</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <p>Above is a summary of the current 108 part with scaling. Since all the volumes are the same it is left out of the dataset, the center of gravity is also left out of the dataset since it currently is just an artifact of the <code>stl</code> file format. There are many ways to determine the ‘center’ of a 3D mesh, but since only one is being implemented at the moment comparisons to other properties doesn’t make sense. The other notable part of the data is the model is rotated so that the magnitudes of <code>Iz</code>, <code>Iy</code>, and <code>Ix</code> are in descending order. This makes sure that the rotation of a model doesn’t matter for characterization. The dataset is available for download here:</p>
 <ul>
 <li><a href="https://gitlab.com/orbital-debris-research/directed-study/report-3/-/blob/main/scaled_dataset.csv">scaled_dataset.csv</a></li>
@@ -2625,18 +2644,18 @@ Murray, James, Heather Cowardin, J-C Liou, Marlon Sorge, Norman Fitz-Coy, and To
 <section id="characterization" class="level2">
 <h2 class="anchored" data-anchor-id="characterization">Characterization</h2>
 <p>The first step toward characterization is to perform a principal component analysis to determine what properties of the data capture the most variation. <code>PCA</code> also requires that the data is scaled, so as discussed above the dataset that is scaled by <code>volume</code> will be used. <code>PCA</code> is implemented manually instead of the Matlab built-in function as shown below:</p>
-<div class="sourceCode" id="cb8"><pre class="sourceCode matlab code-with-copy"><code class="sourceCode matlab"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="co">% covaraince matrix of data points</span></span>
-<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="va">S</span><span class="op">=</span><span class="va">cov</span>(<span class="va">scaled_data</span>)<span class="op">;</span></span>
-<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a><span class="co">% eigenvalues of S</span></span>
-<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a><span class="va">eig_vals</span> <span class="op">=</span> <span class="va">eig</span>(<span class="va">S</span>)<span class="op">;</span></span>
-<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a><span class="co">% sorting eigenvalues from largest to smallest</span></span>
-<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a>[<span class="va">lambda</span><span class="op">,</span> <span class="va">sort_index</span>] <span class="op">=</span> <span class="va">sort</span>(<span class="va">eig_vals</span><span class="op">,</span><span class="ss">'descend'</span>)<span class="op">;</span></span>
-<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a></span>
-<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a><span class="va">lambda_ratio</span> <span class="op">=</span> <span class="va">cumsum</span>(<span class="va">lambda</span>) <span class="op">./</span> <span class="va">sum</span>(<span class="va">lambda</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
-<p>Then plotting <code>lambda_ratio</code>, which is the <code>cumsum</code>/<code>sum</code> produces the following plot:</p>
+<div class="sourceCode" id="cb6"><pre class="sourceCode matlab code-with-copy"><code class="sourceCode matlab"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="co">% covaraince matrix of data points</span></span>
+<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="va">S</span><span class="op">=</span><span class="va">cov</span>(<span class="va">scaled_data</span>)<span class="op">;</span></span>
+<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a><span class="co">% eigenvalues of S</span></span>
+<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a><span class="va">eig_vals</span> <span class="op">=</span> <span class="va">eig</span>(<span class="va">S</span>)<span class="op">;</span></span>
+<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb6-7"><a href="#cb6-7" aria-hidden="true" tabindex="-1"></a><span class="co">% sorting eigenvalues from largest to smallest</span></span>
+<span id="cb6-8"><a href="#cb6-8" aria-hidden="true" tabindex="-1"></a>[<span class="va">lambda</span><span class="op">,</span> <span class="va">sort_index</span>] <span class="op">=</span> <span class="va">sort</span>(<span class="va">eig_vals</span><span class="op">,</span><span class="ss">'descend'</span>)<span class="op">;</span></span>
+<span id="cb6-9"><a href="#cb6-9" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb6-10"><a href="#cb6-10" aria-hidden="true" tabindex="-1"></a></span>
+<span id="cb6-11"><a href="#cb6-11" aria-hidden="true" tabindex="-1"></a><span class="va">lambda_ratio</span> <span class="op">=</span> <span class="va">cumsum</span>(<span class="va">lambda</span>) <span class="op">./</span> <span class="va">sum</span>(<span class="va">lambda</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<p>Then plotting <code>lambda_ratio</code>, which is the <code>cumsum ./ sum</code> produces the following plot:</p>
 <div class="quarto-figure quarto-figure-center">
 <figure class="figure">
 <p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAjAAAAGkCAIAAACgjIjwAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAB3RJTUUH5gQPBRkteT7TLwAAACR0RVh0U29mdHdhcmUATUFUTEFCLCBUaGUgTWF0aFdvcmtzLCBJbmMuPFjdGAAAACJ0RVh0Q3JlYXRpb24gVGltZQAxNC1BcHItMjAyMiAyMjoyNTo0NRsMJN4AACAASURBVHic7d1pQFNX2gfwYwADikyIW9GhYIEgoDIg6IAL4I64VtxX6grC2Lq0ztS6zKjVgTqKiOO0Fmipy9jWqXbeiqUsKkwFFJXFskSCCGgpCQJCRJL7fridTISAJITcm+T/+5R7cpI8N8b7cJZ7Ti+KoggAAADTOEwHAAAAQAgSEgAAsAQSEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsAISEgAAsIIp0wEAgDESiaUiSbO/gzXTgahHJJbGZ1fb8839Hazt+eZMh6MGReR08EyHo1oviqKYjqFbrl+/PmHCBKajANA1+vqSLpSIJFJ/B+u4JS5MR9RV8dnVIefu2/PN7a3NRRLpai+bvdOHMR1UlwTE3qa/bUJIfHZ13BKXNd42TAfVJfoSuX4npNjY2LNnz16/fp3pQEBfKS7rhBA/B2t9uTKKxNKAk7dXe9n4O/IIIWmldQk51amhnuz/mz0+u3rf1bKy933pQ8WJsP+bDzl3XyRuTg3zpA9FYmnIuUK9+M20jzw+u5oQwsbIKf0kkUh27tzp4eExfvx4pmOBX5XVNqeWipmOQg1ltc32+zP2XHmQWipOLRXvufLAfn9GWW0z03G9mv3+jDZfdVxWlf3+DKbi6Tqy9Yc2JWW1ze0LWaijyNn/m1cZefufEBvoawtp7969ffv2HTly5IEDBzpqIa1cuTIrK0vHgRmnpv6CRz7vmDXVmjbXtlr0t3r0n/7F/2Y6qFcrm7R/8N3P+tQWK0rqf+tTKwgalrKLwaheqf63Pk9tf2/7n7+1Ka/wead/8b+VT6eLXvTpr1kkLyzUe2Fzf6em/oL+xf9uffmFtYIgq0f/MWsSaxaGBl704atX36J/c3+B1aP/tCmv/62PRW2xWXOt9kLTMuXIx4wZ+38fLKbLA2Jv75k+jG2DSfqakORyOYfDSU9P37VrV0cJydnZuaioSMeBaYV+RU53wtD9Rc7Ozkn/uasXnTDx2dUJ2dWKfgzFd97Rf1SRWKryfUSSZhWFqip39A6EkHKJyvqq3lkiFYmlyl1zlY8qh/52aOfv3zmNO/rsrdV7IR28vwPPnm9BCPn666/ffPNNQkiaUGJvbU4X6oadmpGXS6RpQslqr1/HXWJijoeHRxBCEnKq/R2s1X03XVKOPCbm+C+Xj9DlIefu+znw2DaSpK8JiYaExAa9tqVQH02iH9OR0wMDinECrWh/tVXOBG2ebXPY5nJPX+hFEikhhB5XJ124rHd01VZ5UVZ5be3ksqXyzVUXWluIJM0h5+6nhv6aSidNnpTyQwohJORc4WpvG7ZdYpS1+WEofufDDmSyfADMMCJXvrCwM3JM+4Zuic+uVlwBRWJpU39BmlBCX9P3JpXZ883bX9+V00ObRoDopadeemH7/znKmaBNAmhz6fdz4CkfrvZ+jX7/fVfL9kwfZm9tQQiZNHm7vlzWCSH+DtaKOdNmTbX2fPM0oSRNWKdo8LETPbNub1KZcus55Nx9e2tztl0Z27Dnm++ZNizk3H3l2YwBsbcRuXYhIYF20B13tYKgfUlldHpIF0rKJRbtmwXK6YHODQp0bvj1cQ//bxFZS9Md6uytLegPoi/rIrFULy7rfg68kHP36X7RF3360xOpU8M8mA7t1eKWuIacKwyIlfg5WNcKgoYdyLS3Nmf5F07zd7AWiaXDDmT6O1jXCoJ6bUtZ422jF7PtFZGL3VftTSrbd7WMvZEzPKmie9LS0jqZZScQCHQZjBZFR0czHUJX0dN1/E/coiftKCLXi+lq9Mw0eq7Rtn1/TS0V68WkKVpqqdj/xC2y9Qf6+9eXsKn/zsZcc7Zw/8VsPQqbVlbbHJdVtf9iNtOBqK2stvm1SavjsqqYDqQzGEOCbqH/4LLnmyuPGIWcu08IYemfYC9LE0r2JZUpZgrELXFh27wjAG1h/yVRvxNS59j/7es1+sZAkUQat8Ql5Nx9fwdrPweeSCxNyKkmhGh3RgMAdB/7L4lYXBU0sTepbNiBTD8H67L3ff0drFNDPf0ceOnCOkLIai8bZCMA0AAmNYB66IYRIaTsfV/FvAN7vvkaPttnpgEAyyEhgRr2JpUl5FSz/6ZXANBHSEjQJfTtdfbW5uiOA4AegoQEr0Y3jDADDQB6FBISdCZNKKFvpEfDCAB6GhISdAgNIwDQJSQkUIFuGPk7WKNhBAA6g4QEL6F3k0TDCAB0DzfGwv+kCSXDDmQSQujbXZkOBwCMC1pIQIjSOkCpYR5IRQDACCQkIPTmBXumDUvF7a4AwBwkJKOGhhEAsAcSkvGid45AwwgAWAIJyRgpGkbKC6QCADALs+yMjvLOEchGAMAeaCEZEZU7RwAAsARaSMZC0TBKDfNENgIAFkILyfChYQQAegEJycBhSz0A0BdISAYLW+oBgH5BQjJM2DkCAPQOEpKhwc4RAKCnkJAMChpGAKC/MO3bQKQJJb22pRDsHAEAegstJL2n2FIPC6QCgF5DC0m/YUs9ADAYaCHpK+wcAQAGBglJL2FLPQAwPEhIegYNIwAwVEhI+gRb6gGAAUNC0g/YUg8ADB4SErvsTSqjH9jzzdd42ygK0TACAIOHhMQWIrF039WyNKFktZeNPd88XVi372pZ3BKXfUllBDtHAIARQEJii31Xf0089OEab5thBzIDYnP3TBuGnSMAwBggIbFCmlASn11NfTSJPqRHjOytze2tzf0deczGBgCgG1ipgRVEYqlixIjex4jea9zPwVokljIbGwCAbiAhsYI931wkbqYf0/MX6G66cgmyEQAYCyQkVrC3thBJpHRjKE0ooe94FYmliscAAAYPCYkV7Pnmq71sAk7ejs+uFoml9nxzehhpz7RhmFwHAEZCp5MaKioqioqKbG1tnZ2dVVYoLS0ViUROTk52dnavLBeJRKWlpUOHDnVxcenZuHVi7/Rh9nzzfVfL7Pnmvbal2PPNsc8eABiVXhRF6eaTLl++fOjQIV9f31u3bs2dO3fLli1tKkRGRl68eHHcuHF5eXmzZs0KDw/vpDwuLu6TTz7x9fXNy8vz8vLav39/+090dnYuKirq6fPSrpBz9/0ceP4O1mgYAYB26cElkdKJ1tZWDw+PkpISiqJqa2vd3d3LysqUK9y7d2/EiBFVVVUURUml0oCAgHv37nVULpPJXF1di4uLKYp6+vSpq6trYWFh+w8VCAQ9f2ZaZr8/o6y2mekoAMAAsf+SqKMxpGvXrvF4PEdHR0IIn8+fOHHijRs3lCuUlpZOmDDBxsaGEMLlckePHp2UlNRJOUVR5ubmhBALCwsOh9PS0qKbE+lp9AAS01EAADBAR2NIdXV1w4cPVxxaWloWFxcrV+ByuZWVlYrD+vp6DofTUTmHw9mzZ09YWNiUKVMyMzMXL17s7u6u8nMVg1Xh4eERERFaPKOeEJ9drbgbCQCg+44fPx4TE8N0FF2loxaSTCajE8yvn8rhyOVy5Qq+vr5PnjyJjIzMyspKSEjIz8+nK3RUnpOT06dPn4EDB/J4PKFQ2NTUpPJzi/6L/dmIEJIurPNzwLoMAKA1ERERissg07G8mo4SEpfLlclkikO5XG5q+lLjjMfjJSYmlpeXR0dHNzQ0zJkzh8vldlSekpKSm5t75syZZcuWnTp1ihDy6aef6uZEehTuOgIAY6ajLrtBgwbl5+crDiUSycyZM5UrNDY2Pnv2TNG0DA0NnTJlSkflEolEIBCYmJjQhXZ2dhUVFbo4jR6GASQAMGY6aiF5e3sTQtLT0wkhJSUlmZmZPj4+hJC7d+9WV1cTQhoaGpYtW/bkyRNCSG5ubk5OztSpUzsqd3V1zcjIePDgASGkvr4+JydnzJgxujmRnoMBJAAwcjpqIXE4nKioqK1btzo6OhYUFBw+fHjAgAGEkKNHjwYFBQUHB9vY2Lz33nuBgYFubm6PHj2KiYmxsrIihKgst7Ky+tOf/rRo0SI3N7eCgoIFCxYsWLBANyfSczCABABGTnc3xuqeHtwFpmTYgczUUE902QFAD2H/JRFr2bEFBpAAwMghIbECBpAAAJCQWCFdWGdnjeYRABg1JCRWSBNK0F8HAEYOCYkVlLcwBwAwTkhIzMMAEgAAQUICAACWQEJiHm6JBQAgSEhsEJ9djTVVAQCQkBhGz6/DFDsAACQkhonEUjSPAAAIEhLjMIAEAEBDQmIYNuUDAKAhITEMa6oCANCQkJiEW2IBABSQkJiEASQAAAUkJCZhAAkAQAEJiUkYQAIAUEBCYgwGkAAAlCEhMQYDSAAAypCQGIMBJAAAZUhIjMEAEgCAMiQkZmAACQCgDSQkZmAACQCgDSQkZmAACQCgDSQkZmAACQCgDSQkBmAACQCgPSQkBojEUjtrNI8AAF6ChMSAdKEE/XUAAG1onpDkcnl0dPTMmTNzc3OLiopu376txbAMW5qwDl12AABtaJiQmpqaXFxczp8/LxQKCSGVlZVLly6NiYnRamyGKT672h8TvgEA2tEwIb355pvr1q3LyMgYPnw4IWTSpEmnT5+OjY3VamwGy55vwXQIAACso2FCevz48fr165VLxo8fb2JiUl9fr42oDBluiQUAUEnDhGRqatrc3KxcIpfLW1paTE1NtRGVIcMtsQAAKmmYkGbNmjV79myxWEwfNjU1rVixYujQoX369NFebAYoTSjBLbEAACpp2KDZu3dvWVmZj48PISQkJKS5udnCwiI7O1ursRkgkViK+XUAACpp3sOWkJBACMnLy5PL5dbW1q+//rr2ojJYGEACAOiIhl12MpnM09Nz/vz5I0eOdHd3X7lypZubm0gk0mpsBggDSAAAHdEwIQUHB3t4eHz++ef0YXp6+ubNm4ODg7UXmGHCABIAQEc0TEhlZWUfffSRpaWloiQsLOz58+eNjY1aCswAYU1VAIBOaD7tu6mpqU1hS0sLh4PF8TqEASQAgE5omD9mzJgxZ86cmpoa+rCxsTEsLGzIkCGdT/uuqKhITk4uKirqqEJpaWlycnJ5eXlXysVicUpKys2bNzU7Bd3DABIAQCc0nGW3f//+0tLS8ePH03fCtra29uvXLycnp5OXXL58+dChQ76+vrdu3Zo7d+6WLVvaVIiMjLx48eK4ceOioqJmzZoVHh7eSXl6evof//hHX1/f8vJyLpf72Wefsb9xhgEkAIDOUN1QW1tbUlLy008/VVVVdV6ztbXVw8OjpKSEfpW7u3tZWZlyhXv37o0YMYJ+H6lUGhAQcO/evY7KW1tbfXx8bt68Sb82KCjou+++a/+hAoGgO2enXXFZVWvOFjIdBQAYL1ZdElXS/D6kpqamhoYGDofD4XCam5sfPHhACHnjjTdUVr527RqPx3N0dCSE8Pn8iRMn3rhxw97eXlGhtLR0woQJNjY2hBAulzt69OikpKSRI0eqLK+pqRk6dOiYMWPo13777bcdBens7Ew/CA8Pj4iI0Phkuw8DSACge8ePH9ejfRg0TEjffvvttm3b2hSamJgUFhaqrF9XV0evC06ztLQsLi5WrsDlcisrKxWH9fX1dBecynKJRGJra7t79+5vvvnGxMRk8+bNa9euVfm5nYxX6ViaULJn2jCmowAA4xIREaH4W1zxBzpraTju8uGHHy5dujQ/P79ISUfZiBAik8mUx3g4HI5cLleu4Ovr++TJk8jIyKysrISEhPz8fLqCyvLS0tKkpCQ3N7e7d++ePXv273//+40bNzQ7EZ3BABIAQOc0TEiNjY3h4eFmZmZdrM/lcmUymeJQLpe3WRecx+MlJiaWl5dHR0c3NDTMmTOHy+V2VP7666/b2dktXryYEOLs7Dx16tT/+7//0+xEdAN3IAEAvJKGXXY2NjYFBQV+fn5drD9o0KD8/HzFoUQimTlzpnKFxsbGZ8+eKfo6Q0NDp0yZ0lF5v379lF/L/vl16cI6O2s0jwAAOqPhpTwxMXHDhg2nT59+8LKO6nt7exNC0tPTCSElJSWZmZn0SuF3796trq4mhDQ0NCxbtuzJkyeEkNzc3JycnKlTp3ZUHhAQIBaLU1NTCSFisfj69euzZ8/W7ER0I00o8XfEjAYAgM70oihKg5f5+fk9fvy4TWEnkxoIITdv3ty6daujo2NBQcH+/ftnzJhBCAkJCQkKCqIXwfvss8+OHj3q5ub26NGjQ4cOjR07ln6hyvKcnJwdO3YMHjy4tLT0rbfeCgsLa/+Jzs7OLJnU0GtbCvXRJKajAACjxp5LYkc0TEh6gSXffnx2dbqwLm6JC9OBAIBRY8klsRNsH30xACKxlOkQAAD0gOY3xtbX1z99+lQxe/vFixdXrlxRrPcDCuUSKW6JBQB4JQ0T0sWLF3fu3NmmcMCAAUhI7cVnV+OWWACAV9Kwy+7IkSObNm0qLCwcNGjQ1atXs7Ozx4wZs3HjRu0GZwDis6v9HXi4JRYA4JU0TEj19fUrV640MTF57bXXMjIyrKys4uPjIyMjtRucYbDnWzAdAgCAHtAwIZmZmdG3o65ater8+fOEEBMTk759+9bX12szOv2HNVUBALpIw4Tk6Oi4b9++pqamUaNGPXjwQCaTlZeXSyQSer0fUMCmfAAAXaRhQjpz5kxGRsahQ4fs7OwGDhzo6uo6bdo0b29vJCRlaUIJ1lQFAOgiDWfZcTgcxf6wKSkpBQUFvXv3dnJy0l5ghkAklmJNVQCALlIvISl24WuzbJ2FhQX9bEcb9BknDCABAHSdeglp06ZNcrk8OTl57dq19IKnynr16lVQUKC92PQeNuUDAOg69RLS1atX6QdfffUVn8/vgXgMCgaQAAC6TsNJDTNnztSjfdoZgU35AADUomFCam1ttbOz024oBgYDSAAAatFwlt2JEydWrVpVVVU1depUExMTRTmylAIGkAAA1KK7Dfp0j9nNP7ApHwCwCvv3Q9KwhURvRg4dwQASAIC6sB9Sj8AAEgCAurAfUo/AABIAgLqwH1KPwB1IAADqwn5I2ocBJAAADWA/JO1LF9bZWaN5BACgHuyHpH1pQgn66wAA1IX9kLQPu04AAGgA+yFpGQaQAAA0o14LacWKFYoFv5W5ubkhG9FEYinTIQAA6CX1EhKPx4uIiHB2dl6/fn11dXUPxaTXyiVS3BILAKAB9RJSTExMUVHR6dOnhUKhv7+/r6/vmTNnXrx40UPB6aP47Gp/B2umowAA0D+aTGoYP358SkpKdnb2smXLjhw5MmLEiPnz51dUVGg9OL2TJpT4O/AwxQ4AQAMazrIjhFhZWYWHh+fk5KSmpr722muzZs3y9vbWYmT6SCSW2vMtmI4CAEAvaZ6QFHr37j106FALCwup1NjH87GmKgCAxjRf7bupqen8+fOffPLJL7/8Ymtr+/HHH48cOVKLkekjrKkKAKAxtROSTCZLTU09ePBgZWVl375933rrrTVr1lhaWvZEcHoHa6oCAGhMvYS0cePGtLQ0Qoibm1tCQoKtrW2PBKWfcEssAEB3qJeQ6urq/vznP7/55ptmZmY9FJD+wgASAEB3qJeQ6IW9QSUMIAEAdIcWZtkBDQNIAADdgYSkHRhAAgDoJiQk7cAAEgBAN2mekORyeXR09MyZM3Nzc4uKim7fvq3FsPROmlCCJewAALpDw4TU1NTk4uJy/vx5oVBICKmsrFy6dGlMTEznr6qoqEhOTi4qKuqoQmlpaXJycnl5eRfLCSF3796tqalR/wy0DANIAADdpGFCevPNN9etW5eRkTF8+HBCyKRJk06fPh0bG9vJSy5fvrxkyZKkpKTQ0NBjx461rxAZGblq1aqkpKSNGzcq57aOygkhpaWlK1asuHv3rmZnoS0YQAIA6D4Nlw56/Pjx+vXrlUvGjx9vYmJSX19vZWXVvr5MJtuzZ88///lPR0dHsVg8adKkuXPn2tvbKyrk5eV99tlnV69etbGxef78eWBgoJ+f38iRIzsqJ4S8ePFi27ZtAwYM0OwUtAgDSAAA3adhC8nU1LS5uVm5RC6Xt7S0mJqqznDXrl3j8XiOjo6EED6fP3HixBs3bihXKC0tnTBhgo2NDSGEy+WOHj06KSmpk3JCyJEjRyZPniwQCDQ7BS3CABIAQPdpmJBmzZo1e/ZssVhMHzY1Na1YsWLo0KF9+vRRWb+uro7u3KNZWloWFxcrV+ByuZWVlYrD+vp6emSoo/KsrKybN2/+4Q9/6DxO5/86fvy4emeoDgwgAQA7HT9+XHEZZDqWV9Owy27v3r1lZWU+Pj6EkJCQkObmZgsLi+zs7I7qy2QyDud/yY/D4cjlcuUKvr6+f/7znyMjI/38/O7fv5+fn+/r69tReX19/e7du//+97+/Ms5OJlBoCwaQAIC1IiIiIiIi6Mfsz0kaJqSampqEhITq6upffvlFLpfzeDw7O7tO6nO5XJlMpjiUy+W9e/dWrsDj8RITE48ePRodHf373/9+zpw5DQ0NHZX/9a9/dXV1LS8vLy8vF4vFBQUFtra2TH3XIrHUzhrNIwCA7tIwIQUHB7e2toaGhi5cuJDL5b6y/qBBg/Lz8xWHEolk5syZyhUaGxufPXummEQXGho6ZcqUjsofPXpUWFh45swZQkhlZWV6erqVlRVTCSldKFmNFhIAQPdRGmloaIiNjfXy8hIIBNOnTy8uLu68vkwmGz9+fFpaGkVRxcXFo0aNqqmpoSjqzp07VVVVFEVVVVW5uro+fvyYoqjbt297eXk9ffq0k3KFDRs2fP/99yo/VCAQaHZ2aiFbf9DBpwAAdJNuLondoWELydLSMjQ0NDQ0tLq6+sMPP5w3b56pqenMmTM//PBDlfU5HE5UVNTWrVsdHR0LCgoOHz5MT9c+evRoUFBQcHCwjY3Ne++9FxgY6Obm9ujRo5iYGHr6eEflLBGfXe2PCd8AANrQi6Kobr5FY2PjpUuX9u3bZ2JiUlhYqJWwtMLZ2bmnJzXEZ1enC+vilrj06KcAAHSfDi6J3aRhC4kQIpPJfvjhh0OHDlVWVg4ZMuTEiRP0qI9RwS2xAADaomFCWrt27Y0bNywsLBYuXBgaGsrn87Ublr7ApnwAANqieQspKSlJee0fI5QmlOCWWAAAbVEvIT148IAQ8sYbb7z//vtyuZw+VPbGG29oLTTWE4mluCUWAEBb1EtImzZtksvlycnJa9euffLkSZtne/XqVVBQoL3Y2A4DSAAAWqReQrp69Sr9IDU1tQeC0TMYQAIA0CLNF1etrq5WLqmvr3d1dX3+/Lk2otIPGEACANAi9VpIWVlZR48eJYSUlJRs27ZN+anm5maZTNbR9hOGB2uqAgBol3r5Y8yYMVKptK6ujhDy+PHjl97I1HTnzp0mJibajI7FMIAEAKBdajdovv76a0LIihUrIiMj6X3zjBMGkAAAtEvDHrbExETtxqF3MIAEAKBdmg/51NfXP336VLHP3osXL65cuRIeHq6lwFgNA0gAAFqnYUK6ePHizp072xQOGDDASBISBpAAALROw2nfR44c2bRpU2Fh4aBBg65evZqdnT1mzJiNGzdqNzjWShNK/B2smY4CAMCgaJiQ6uvrV65caWJi8tprr2VkZFhZWcXHx0dGRmo3ONbCABIAgNZpmJDMzMw4HA4hZNWqVefPnyeEmJiY9O3bt76+XpvRsRIGkAAAeoKGCcnR0XHfvn1NTU2jRo168OCBTCYrLy+XSCRcLle78bFQurDOzhrNIwAALdMwIZ05cyYjI+PQoUN2dnYDBw50dXWdNm2at7e3MSSkNKHE3xEzGgAAtEzDWXYcDicnJ4d+nJKSUlBQ0Lt3bycnJ+0Fxl4isRQzGgAAtE69hFReXq6y3NLSkn7Wzs5OC0GxGAaQAAB6iHoJae3atRUVFR09a2JiUlhY2O2QWE0kljIdAgCAYVIvISUlJfVQHPoiXShZjRYSAEAPUC8hKRbzrqqqUllhyJAh3Y2I3dKEdXFLXJmOAgDAAGk4qWHp0qVttp8ghFhZWWVnZ3c7JPaKz672d+DhllgAgJ6gYUJKSUlRPmxoaNixY4eHh4c2QmI1e74F0yEAABgmDe9DMnkZj8eLjY09duyYdoNjG6ypCgDQczRMSO2ZmZkRQujNZA0V1lQFAOg5GnbZtb8h6eDBg7179+bxDLYBkSaUYE1VAICeo2FCWrVqVZtJDf369Tt16pQ2QmIpkViKW2IBAHqOdiY1KKaDGzAMIAEA9CgNE5KJiUleXt7hw4cVW5gTQjgcTmJiopYCY500oWTPtGFMRwEAYLA0TEhbtmy5cuXKa6+9ptw2ondIMlQYQAIA6FEaJqT09PR//OMffn5+2o2GtbCmKgBAT9OwTWNqaurqakQr6GAACQCgp2mYkD744IN3331XJpNpNxrWwh1IAAA9TcMuuxkzZrz77ruurq4WFv9bSofD4dy+fVtLgbELBpAAAHqa5gnJ2to6Ojq6X79+2g2IhTCABACgAxomJLFYfOXKFRsbo7hMYwAJAEAHNBxD6t+//8OHD7UbCmthAAkAQAc0bCF98cUX/v7+b7/99vTp05XL33jjDW1ExS4YQAIA0IFeFEVp8DI/P7/2G/SZmJgUFhZqIyrtcHZ2Lioq6uabxGdXpwvr4pa4aCUkAACmaOWS2KM0vzFWg1dVVFQUFRXZ2to6OzurrFBaWioSiZycnOzs7F5ZThfy+XxPT08NgumidGGdnTWaRwAAPU7DhFRVVaWyfMiQIR295PLly4cOHfL19b1169bcuXO3bNnSpkJkZOTFixfHjRsXFRU1a9as8PDwTsr379+fkpIyevTo4uLivn37xsXFcblczc6lc2lCCZpHAAA6oGFCWrp0xONM7AAAIABJREFUafsuOysrq+zsbJX1ZTLZnj17/vnPfzo6OorF4kmTJs2dO9fe3l5RIS8v77PPPrt69aqNjc3z588DAwP9/PxGjhypstzU1PT8+fPXr1+nt1+aPXv25cuXg4ODNTuXzonEUsxoAADQAe1sP9HQ0LBjxw4PD4+O6l+7do3H4zk6OhJC+Hz+xIkTb9y4oZyQSktLJ0yYQM8j53K5o0ePTkpKGjlypMry5cuXnzp1SrEZ4LBhwzpqsSn6BsPDwyMiItQ9TdyBBAB67fjx4zExMUxH0VWabz+hfMjj8WJjY0eMGBEWFqayfl1d3fDhwxWHlpaWxcXFyhW4XG5lZaXisL6+nl47XGW5jY2N4hao8vLy1NTU0NBQlZ/bzRE8kVjanZcDADArIiJC8bd4R4P37KG1DSPMzMwIIXV1dSqflclkyptTcDgc5Y2UCCG+vr5PnjyJjIzMyspKSEjIz8+nK3RUTnvy5MmaNWvCwsJcXHpkmKdcIsUtsQAAuqFhQipvZ+PGjb1791Z0o7XB5XKVV2KVy+Wmpi81zng8XmJiYnl5eXR0dENDw5w5c+hJCh2VE0Ly8vLmz5+/atWqjppH3RefXY0BJAAA3dCwy27VqlVtJjX069fv1KlTHdUfNGhQfn6+4lAikcycOVO5QmNj47NnzxR9naGhoVOmTOmkPDMzc8uWLQcOHJg2bZpmp/BKaUKJvwMPt8QCAOgIpZHWl72yvkwmGz9+fFpaGkVRxcXFo0aNqqmpoSjqzp07VVVVFEVVVVW5uro+fvyYoqjbt297eXk9ffq0o/KHDx96eHikpKS0/JfKGAQCgWZnR4vLqlpztrA77wAAwB7dvCTqgHYmNbwSh8OJioraunWro6NjQUHB4cOHBwwYQAg5evRoUFBQcHCwjY3Ne++9FxgY6Obm9ujRo5iYGCsrK0KIyvKTJ08+e/Zs06ZNivdfvnz57t27NTuXjmBNVQAAXVJ76aDy8vJly5YlJCTQc7gJIatXr75z505kZGTP9Z5pppvrZAw7kJka6okuOwAwDOxfOki9SQ2NjY3Tpk3jcDh8Pl9R+OGHH3p5eUVERKSmpmo7PCZhTVUAAF1SLyGtW7duyJAh169fV05IQ4YMOX369NKlS3fs2KHt8BiDW2IBAHRMvYRUWlr697//XeVT27dvb2hoaGpq0kZUzMMAEgCAjqmXkORyeUdrmFpYWBBCWlpatBAUC2BTPgAAHVMvIfF4vKSkJJVPPXnyhBBCT40zABhAAgDQMfUSUkRExJEjR1SuD7RixQonJyfl9YH0FwaQAAB0T737kObPn3/+/PmxY8fOmDHjnXfe4XK5LS0tFy5cSExMbG5uvnXrVg9FqWMYQAIA0D21b4w9d+5cZGTkZ599duXKFbrExMTE39//2LFj9PqqBiBNKNkzbRjTUQAAGBdNVmrYsWPHjh07xGLx8+fPzczM6DUXDAkGkAAAdE/DpYMIIcq3IhkSDCABADDCEOYgaBcGkAAAGIGE1BbuQAIAYAQSUlsYQAIAYAQS0kswgAQAwBQkpJeIxFI7azSPAAAYgIT0knShBP11AACMQEJ6SZqwDl12AACMQEL6n/jsan9M+AYAYAgS0kvs+RZMhwAAYKSQkP4Ht8QCADAICel/cEssAACDkJB+lSaU4JZYAAAGISH9SiSWYn4dAACDkJB+hQEkAABmISH9CgNIAADMQkL6FQaQAACYhYRECNZUBQBgASQkQjCABADAAkhIhGAACQCABZCQCMEAEgAACyAhYQAJAIAVkJAwgAQAwApISBhAAgBgBSQkDCABALCCsSckDCABALCEsSekdGGdnTWaRwAAzDP2hJQmlPg7YkYDAADzjD0hicRSzGgAAGADo05IGEACAGAPo05IIrGU6RAAAOBXrEhIFRUVycnJRUVFHVUoLS1NTk4uLy/vYnkXpQsluCUWAIAlmE9Ily9fXrJkSVJSUmho6LFjx9pXiIyMXLVqVVJS0saNG2NiYl5Z3nVpwjoMIAEAsAXFqNbWVg8Pj5KSEoqiamtr3d3dy8rKlCvcu3dvxIgRVVVVFEVJpdKAgIB79+51Uq5MIBB08tFxWVX+J25p9WwAANir80siGzDcQrp27RqPx3N0dCSE8Pn8iRMn3rhxQ7lCaWnphAkTbGxsCCFcLnf06NFJSUmdlKvFnm+hndMAAIBuM2X24+vq6oYPH644tLS0LC4uVq7A5XIrKysVh/X19RwOp5PyNpydnekH4eHhERERyk9hTVUAMHjHjx/XbESDEQy3kGQymXIi4XA4crlcuYKvr++TJ08iIyOzsrISEhLy8/PpCh2Vt1H0X22yEcGaqgBgBCIiIhSXQaZjeTWGExKXy5XJZIpDuVxuavpSo43H4yUmJpaXl0dHRzc0NMyZM4fL5XZS3kVpQgnWVAUAYBWGu+wGDRqUn5+vOJRIJDNnzlSu0NjY+OzZM0WTMzQ0dMqUKZ2Ud5FILMUtsQAArMJwC8nb25sQkp6eTggpKSnJzMz08fEhhNy9e7e6upoQ0tDQsGzZsidPnhBCcnNzc3Jypk6d2kl5F2EACQCAbRhuIXE4nKioqK1btzo6OhYUFBw+fHjAgAGEkKNHjwYFBQUHB9vY2Lz33nuBgYFubm6PHj2KiYmxsrIihHRU3kVpQsmeacN66qwAAEB9vSiKYjqGnuLs7NzROF6vbSnUR5N0HA8AAIM6uSSyBPMrNege1lQFAGAhY0xIGEACAGAhY0xIuAMJAICFjDEh4Q4kAAAWMrqEhAEkAAB2MrqEhAEkAAB2MrqEhAEkAAB2MrqEhAEkAAB2Mq6EhAEkAADWYnjpIB1LF9bZWaN5BNDjVq5cmZWVxXQUxmXMmDGff/4501F0i3ElpDShJG6JC9NRABi+rKwslq9SY3gU+5HqL+PqshOJpZjRAADATkaUkDCABADAZkaUkERiKdMhAABAh4woIZVLpLglFgCAtYxoUkN8djU25QMwQrW1tbm5uW0KhwwZ4urqSj++dOlS//79x40bRwi5cuWKr6+vWht+dkVTU1NkZOSePXvaPxUdHT1t2rThw4d3MdoeipANjKWFlCaU+DvwcEssgBFqampatGhRcnIyfdja2nrv3r3du3fThxKJ5PDhw3Q2IoT89re/DQwM1HoMffr0efr0aWpqavunPv30U4FA0MVoey5CNjCWFpJILLXnWzAdBQB0lUgsjc+utueb2/PNuzk51tbW9sSJE9u3b9+xY0f//v0JITNmzOBwfv1z/OjRoytXrlRUHjFiRGtra3FxsXKS0IotW7YsWLAgJydHubCystLR0VERzCuj7dEIGWcsLSSsqQqgRwJibwecvF0ukaYL6wJic+Ozq7v5hkuXLh03blxoaKiiZNKkSfSDf/zjH3Pnzm1T+YsvvujmJ7ZnZ2fX2tpaWFioXPjvf/972rRpXY+2RyNknLEkJKypCqAvQs7dJ4SUve8bt8QlbolL2fu+IrF0b1JZN9/21KlTGRkZirUMRo0aRQipqKh49uyZjc1LN4QsX748MTGxmx+nkru7e3Z2tnLJ1atXVfa/qYxWBxEyy1gSEtZUBdAX8dnVqWGeikN7vvkab5uEnOo0oaQ7b2ttbR0eHj5y5EjlwoKCgjYlhJCffvrJxMQkIyOjOx+nUr9+/W7evKk4lMvlxcXFtra2XYxWBxEyyygSEm6JBdAXaUJJ+/+t9nxz+26vQnn16tXRo0f/7ne/ow+//vprQgiHw3n69KlytdTU1Ly8vPfff//8+fPd/MT25HK5ufn/TiQ9Pd3f37/r0eogQmYZxaQGDCABMGhvUtm+q+p1uKkcNEqLbTsZunN7pg3bO/3XOz1u3br19OnThQsXKp69cePGm2++6evrW1paqii8evXqpUuXYmJiWlpa3n333aNHj7a2tra0tFhaWnb0KaWlpY6OjorDlpaWhoaGfv369e7dmy5pbGwkhNDvIJFI5s2bp6icnJzcfgCpk2hVRqg830HfGUVCShNKcAcSAFP2Tv9fYnglkVgacPJ22fu+bcqHHchMDfXUrOO9oqJi7dq148ePT09PJ4S8ePHizp07dnZ2hBBLS0tXV9fCwkJXV9dbt25FR0d/++23hJDevXvPmjXrq6++6tu377Vr1w4dOqTynS9cuHD27Fnl5ktycnJQUFB8fPzq1avpEicnp1mzZn388ceEkBs3bkRFRSkqp6Sk7Nu3r+vRqoxQOW/pO6NISBhAAtAX9nzzPdOGhZy7r7wwf0DsbXtrc43/F9va2t65c6ejZzdt2nT27Nm//OUv7u7uly5dUpSfOnWqtbX12bNniltW23j77bdLS0vplpBcLr9586aPjw8h5Pe///2FCxfohJSammpvb0/Xv3nzpre399ChQxXv8P3335uatr0IdxKtygg7O3N9YzhtvY5gAAlAv/g7WNtZmw87kBly7v7epLJe21Ls+RbK0xy0a926dSkpKU1NTaampsrdX6ampubm5tevXz9y5EhqauosJfRMucWLFyckJNCV5XL5hx9+SD+2t7evra2le+rOnDmzePFiuvyjjz7av3+/8kd30hOoksoI1T5hFjP8FhIGkAD0iz3ffO/0YWu8behpddRHk175ku7gcDjR0dG5ubmKxRraCwgICAgIaFPo4+NTW1tLPzY1NVVuuyxcuPCrr75auXKlSCQKCgoqKCiora2dPXu2YvkfUMnwExIGkAD0kT3ffA1fR30bo0eP7rzChQsX3n77bcVhYmJi+/ykbPHixRs3buzfv//s2bPpkv79+yuvBwEqGX5CwgASAHTTwoUL1Zo7MHTo0IaGhs8+++z48eP/+c9/ei4wA2PgY0gYQAIAHWhpaWmz/PaCBQtqa2sHDx7MVEj6qBdFUUzH0FOcnZ199/3Lz4GHnASgY87OzkVFRUxHYVxe+Z2z/x/FwFtIWMIOAEBfGHhCwgASAIC+MOSEVP9bH3TWAQDoCwOcZUfv65UulNQKgpiOBcBIjRkzxtnZmekojMuYMWOYDqG7DG1SA70Q1movG39H3rSo5HEjHUQSqcZLYAEAGAxMatC1gJO36SV+/R2sX/TpnxrmudrLJuRc4atfCQAAjDKohBSfXS0SS+lxo/jsaovaYkIIvcxwN7f2AgCAnmZQCYkQopjFYM8371NbTD/2c7AWiaXMBQUAAK9mUAnJnm8uEjfTj/0drPsX/5t+nI7mEQAA6xlWQrK2IIS0aQyJxNI0YZ1+zf8+fvw40yFoCJHrHiLXPf2NnOV0mpAqKiqSk5M7meZRWlqanJxcXl7eplwkEiUnJ9+/f7/zQnu++Wpvm4CTtxUjRiKxdNiBzNQwD+2dhC7ExMQwHYKGELnuIXLd09/IWU539yFdvnz50KFDvr6+t27dmjt37pYtW9pUiIyMvHjx4rhx46KiombNmhUeHk6Xx8XFffLJJ76+vnl5eV5eXvQOVyoLCSFrvG3s+eb7kspCJPdFs04GnLydGuaB1YMAAPQApROtra0eHh4lJSUURdXW1rq7u5eVlSlXuHfv3ogRI6qqqiiKkkqlAQEB9+7doyhKJpO5uroWFxdTFPX06VNXV9fCwkKVhe0/VCAQ9PyZ9QhErnuIXPcQuY6xP2wdtZCuXbvG4/EcHR0JIXw+f+LEiTdu3FBsNU8IKS0tnTBhgo2NDSGEy+WOHj06KSlp5MiRdMqkt+m1sLDgcDgtLS0dFbah1/eKI3LdQ+S6h8h1if1LOegoIdXV1Q0fPlxxaGlpWVxcrFyBy+VWVlYqDuvr6+mt4zkczp49e8LCwqZMmZKZmbl48WJ3d3dCiMrCNj7//POeOh8AANA2HU1qkMlkdIL59VM5HLlcrlzB19f3yZMnkZGRWVlZCQkJ+fn5igo5OTl9+vQZOHAgj8cTCoVNTU0dFQIAgP7SUULicrkymUxxKJfLTU1fapzxeLzExMTy8vLo6OiGhoY5c+ZwuVxCSEpKSm5u7pkzZ5YtW3bq1ClCyKeffqqyUDcnAgAAPURHXXaDBg3Kz89XHEokkpkzZypXaGxsfPbsmWIyZWho6JQpU+iaAoHAxMSELrezs6uoqLCxsWlfqIvTAACAHqOjFpK3tzchJD09nRBSUlKSmZnp4+NDCLl79251dTUhpKGhYdmyZU+ePCGE5Obm5uTkTJ06lRDi6uqakZHx4MEDQkh9fX1OTs6YMWNUFurmRAAAoIfoqIXE4XCioqK2bt3q6OhYUFBw+PDhAQMGEEKOHj0aFBQUHBxsY2Pz3nvvBQYGurm5PXr0KCYmxsrKihDi4uLypz/9adGiRW5ubgUFBQsWLFiwYAEhRGUhAADoL0PbDwkAAPSUQa1lBwAA+gsJCQAAWAEJCQAAWAEJCQAAWAEJCQAAWMHAE9Lz58/Xr1/fZpkifREWFkbfmKV3FFuH6Bf8Whihj7+WpqamX375hekoNFFTU9PJjnSM091+SD2tpqZm4MCByiUxMTEnT55sbW1ts5Ie27SPnPbw4UOxWDx48GDdh9RFKiOvqqq6ffs2I/F0h778WjrC/l+LSvr4awkPD//xxx+fP38+cuTIM2fOMB2OGjZu3JiXl2dmZlZXV3f37l2mw1FB//7jqXTx4kV6ZQfa9evXf/e739XV1aWnp/fr18/MzIzB2DrXJnLl/5wzZsyIiopiIqguaRN5ampqbGwsIaSpqalPnz7MxaU2Pfq1tKFHv5Y29PfX8qc//YnP5+fk5OTl5dGnoC9CQkK8vLwyMzPT09P5fD47fy0GkpDmz59PCDl58iR9+OOPP6alpe3ataumpoZeEoK12kR+4cIFZ2dnehP3GTNmtN/NnT3aRD5kyBA6+FOnTvXr14/R0LqK7ubSo1+LAh25Hv1aFOjI9fHXQrty5crmzZvpxzwej9lg1HLz5s3ly5cTQo4dO9arV6+PP/64ubmZ6aDaYXiDQO1JS0sTCARSqVS5cMOGDR988AFTIXVRm8i/+OILgUDw/fff19bWenh4MBtb59p/51VVVe7u7gKBICIi4unTpwzG1kZra2v7wqCgIOW9htn5a+k8cjb/Wl75nbP210JR1PLly99555325QEBAZcuXVIcbt68+f3339dhXOppaGh4/Pgx/ZjeYnvRokWhoaEURU2ePHnNmjVMBqeKgbSQCCF+fn62trZvv/22cmFJScmqVasIIWKxeMaMGXV1dQxF15k2kS9btuyf//zn5s2bv/rqK5lM9uLFC2bD60T779zGxmbYsGFxcXE8Hs/b23vhwoXK244wpampydXVlR7z76Sbi4W/lldGztpfS1e+c3b+WmiRkZH//ve/a2pq2pTv2rVr165dikMbG5vevXvrNrSuCg0NnTZtWnBwsKen5y+//OLk5LRr167XX3+d7mk0NTXNzMxMSEhgOsyXMZ0RtammpkYgECj+IqAoytXVVSKRbNu2zcXF5fLlywzG1rn2kUulUi8vL4FAUFVVxWBgr9Q+8qlTp/70008URUmlUuX2B7P++te/Tpw4kaKonTt3CgQCkUhEUVRJScnkyZMVddj5a+lK5Oz8tXQlcnb+WmihoaHKoSosWrRo3rx5lZWV33//vUAgaGlp0X1sr7Rnz54//vGP9OMjR46MGjWKoqipU6ceOXKEoqjLly8vXrxYZROWWQaVkCiKeuedd+j/AxRFPX36VCAQuLi4HDp0iNmoukI5coWAgID8/HxG4um6NpFPnDixrKyMuXA6NGLEiO+//57qoJuLzb+WziNXYOGv5ZWRs/bXQlFUS0uLQCC4du1a+6f+8pe/TJw4MTQ0tKmpSfeBdWLTpk3BwcEURY0dO5b+M/HIkSMuLi7/+te/KIq6c+eOQCAYMWLE0qVLGQ60A4aWkGQyGf27pw+XL1/e0NDAbEhd1CZyWkpKyltvvcVUSF3UJvJNmzYxG09769atGz16NP1fkS6h/2f+4x//GDVqlOIvXBb+WroYOY1Vv5YuRs7CX4uy2NhYd3d3pqNQ4ccff2xTkpGR8cknn0yePJluJY8fP/7IkSMjRozYv38/RVHFxcW+vr4URbW2trLtR67M0BISRVGffPKJ4v+AfmkTuVQqnTNnzrFjxxgMqYvY/J2vW7fu6NGjFEU1NTX5+vrSjym2dnMpUytyVv1a9Pc7b8/DwyM2NpZ+fOvWrdGjR9NNEAYdO3bMy8tr/vz5yoV05/mtW7fowy+++MLDw0MxVeTy5ctTp07VdaDqM8CERFEUm/8E6Jxy5Ldu3WLPH7yvxJ7vXHlmEUVRI0aMqK2tpR/T/XLK3Sys6ubqTuTM/lr09zt/pYyMDIFAUFNTM2/ePJYMLhYXF0+fPv3dd98VCAT03DnaO++8ExAQoDicPn16YGDgw4cP6bEuvfgjwDATEhit0NDQsWPHjh07dsSIEfRouY+PT3Z2tqJCYGCg8mxX9nRzIXLWmj59ukAgOHjwINOB/Ornn3+mx+Hi4+MFAkF8fDxdTnee0/8EtA8++CAgIGDz5s1sm1XfESQkMBzbt29XXDXoUXSZTHbixAkvLy9FnTlz5ggEgsrKSopN3VyInM1kMhmrLuh04qHH4W7duiUQCDZs2EA/9emnn/r4+DAaXbcgIYHhcHd3//nnnxWHAQEB9IXP399/+fLlVVVV3333nZeXV0lJCV2BPZ2iiBzU4uXlRS8D6OXltWjRIg8PDw8PD4lEQlHU6NGjv/zyS6YD1BASEuifefPmff311/RjiURC/+lNUdTYsWOVe4pu3ryp6FKn5+m+9dZbzN41gshBK6ZOnTp58mQvLy/FaNyaNWsEAoFQKCwuLn727Bmz4WkMCQn0D71kEUVRO3fu9PHx8fX1HTVqVGVl5YkTJ8aOHauoFh8f32YmEuMQOWjF8uXL20/2U/yVoL+QkEAvTZ48OSIiYtasWfRhbGysq6srRVG+vr6LFi2qqqpKSkoSCATsmfungMih69pMX1TIz89XnlBnMJCQQC/Rd13cuXNHUTJx4sQzZ85QFLVz50523kVPQ+TQRZs2bfLx8Rk/fryHh0dNTY3yU5WVlay98687kJBAX73zzjvLly9XHH733XdBQUEMxtN1iBxeSeVidApNTU2LFi1iIq6eZTirfYOxiYqKys7Orqqqog+rq6tff/11ZkPqIkQOKinvjH7lypUtW7YQQv72t799/PHHf/7zn5VrWlhYnD9/noEQe5jhbGEOxobD4ezcuTMgIODEiROEkEOHDmVkZDAdVJcgcmivzc7oZmZmZ86c+fTTT5csWVJYWFhSUjJu3DiD/7aRkECPhYSEnDhxorCwUCaTZWdnW1lZMR1RVyFyUKbYGZ0QQm/EFRoaGhUVlZGRQX/DRUVFffv2ZTjKnteLoiimYwDQXElJyeDBg/XxsojIQcHT0/O7774bPHiwcuGMGTM4HM6pU6eKioo2b96clpZmY2PDVIS6gRYS6DcnJyemQ9AQIjdyNTU1YrHY2dmZEMLj8bKysmbPnk0/FR4ezuPxrly5snv37tWrV7u6uhpJYxQJCQCgZyUmJv7lL3+5d+8el8ulSzZu3JiXl2dmZlZXV3f37t1du3a98847ioRkY2ND7+beZi6DwUOXHQBAD6qvr/f29lbucAsJCfH19V2/fj0hJCAgICgoaPv27YsXL25paaHH5zZv3pyfn29mZsZo4AzAtG8AgB5Ed7XV19efPXuWLrl58+by5csJIceOHevVq9fHH3/c3Nx8/vz50aNHL1269Ouvv75z544RZiOChAQA0NPmzZs3Z84cevocIeSbb77p06fP4sWLi4qKUlJSbG1tw8LCCCG7du1KT0+PjY21sLBgNF7GICEBAPSg7du3p6am9uvX7ze/+Q1d4uTktGvXrtdffz02NpYQYmpqmpmZmZCQwGiYrIBJDQAAPSIzM/P+/ft37tz55ptvKioqVq5cuWzZMvqprKyswMBAQsi3337L4/EKCwtNTEwYDZYVMKkBAKBH/PLLL+PGjTt79qynpychZPbs2e7u7vv37yeE3L17d9GiRb1796bXZWA6UrZAQgIA0Kb169cvW7YsICCAELJ169Y7d+6kpKQQQurq6saOHXvz5k0ej0cIkclkzc3NlpaWDIfLJhhDAgDQpvnz57/99tv046ioqMrKyqKiIkIIj8dbsGDBypUr6adMTEyQjdpAQgIAUM+OHTs8PT3d3d1PnjxJl6SmpkZHR9OPZ86caWVlRR/Sy9GGhITQTx08eFAx+RvaQ0ICAOgqerEfiqK+++67uLi4U6dOPX/+nBDi7Ox84sSJpqYmutr58+dPnDjR3NxMCAkJCWlpafnqq6/op9Aq6gTGkAAAumrcuHGbN29WTJZTFhYW9vz589OnT9OHU6ZMsbW1jYuLI4SUlJQMHTq0T58+Oo1VD6GFBADQVfX19ZMnT6YfP3/+vKSkJDc3l96x8NixYzdu3CgvL6efNTc3z8rKop9ycnJCNuoK3IcEANBVEyZMCAwMdHJy+vnnn6uqqszNzfl8flVV1d69e5cuXfr2228HBgb+8MMPaWlpra2tycnJBr9hhHahyw4AQA2nT5++dOnSypUr/fz8Bg4cSAi5cePG9u3bf/zxR0JIWFhYZmamq6sr7i7SABISAEC3lJaWrlixgk5I0B0YQwIAUE9paanicX19fVBQ0B/+8AcG4zEYaCEBAKhn/fr1165dc3Nza2xsLC8v37JlC71cN3QTEhIAgNquX7/+t7/9bdKkSWvWrMGtRdqChAQAAKyAMSQAAGAFJCQAAGAFJCQAAGAFJCQAAGAFJCQAAGAFJCQAAGAFJCQAAGAFJCQAAGAFJCQAAGAF7IcExuXLL7/87rvv7t27Z2lp6ePjExoaamtry3RQ3SKXy+/fv+/m5sZ0IADdhaWDwFjIZLJ169bl5+evXr16+PDhUqn0888/f/DgwZkzZ5ycnJiOTnPbt2+3srLavXv4j6IqAAAFIElEQVQ304EAdBdaSGAsTp48effu3YsXL9rZ2dElgYGBwcHBH3zwwblz55iNrTsaGhqsrKyYjgJACzCGBMYiMTFx6dKlimxECDExMTl48OBbb71FHzY2Nh44cGDcuHFeXl5hYWEPHjygyzdu3JicnLxy5UpPT88lS5aUl5d/9dVXU6ZM8fb2/vDDDxV1vv322yVLlnh6ei5btqygoOCV75mSkhISEuLp6Tl79uzk5GS6/Pnz55GRkX5+fnT98vJyRbQqX3Ly5Mm8vLy0tLStW7cSQlJSUhYuXOjp6Tlt2rTY2Nie+zIBegQFYASEQqFAIPjhhx86qbN48eL58+dnZ2eXlJTs3LnTy8urqqqKoiiBQODr63vp0qWMjIx58+aNHz9+w4YNGRkZX3/9tYuLS1JSEl3Hy8vrhx9+ePbs2aFDhzw8PB4/ftz5e44fP/7LL7+8fv36zp07XVxcfv75Z4qiNm/eHBQUlJ2dXVlZuWfPHh8fn9raWjo8lS/Jz88PDg6m4xGJRAKB4MKFCw0NDSkpKR4eHhcuXOjpLxZAi5CQwChcv35dIBBkZGR0VOHHH38UCASVlZWKkqCgoIMHD1IUJRAIPvnkE7rwyy+/dHFxaWhooA8XL168f//+NnXo1x4/fryL7ymVSgUCQVpaWmFhoUAgKCkpUa4fGxtLP1b5EoqiNmzYsG/fPoqi0tLSXFxcFB93+/btn376SYPvCoApGEMCozB48GBCyIsXLzqq8OjRIysrqyFDhihKRo0a9fDhQ/qxoqPPwsLC3NxcsSHbb37zG5lMRj92cXFRvNbFxaW4uNjGxqYr78nlcunYiouLCSEff/yxov6zZ89++uknxWH7lyifwvjx44cPHz5lypRRo0b5+vpOnTrV2dn5Fd8LAJsgIYFRcHBwMDU1LS4u9vPzUy7Pzc395ptvtm7d2tLSYmJi0p2PMDVt+79J3fdsbW3t3bu3t7e3osTb21s5n3XOxMTkyy+/TE9P//777//1r3+dOHHi3XffXbt2bdcDAGAWJjWAUeBwOAsWLDh//vzz58+Vy7/44ovU1FRLS8v+/fvX19c3NjYqnnr48KG1tXXXP+Lnn39Wfq2tra2678nn81taWvz8/IL/a+DAgRYWFl0M4MGDB1euXAkICDh48GBKSsqaNWuUG1sA7IeEBMZi8+bNTU1Nq1evzs3NlcvlT548OXDgwOXLl//4xz9yOJzJkycPHjx49+7ddMY6f/58dnb28uXLu/7+sbGxNTU19Gvz8/MXLFig7nv6+fnZ2tru2rWrqamJEJKSkrJhwwaJRNL555qYmFRUVNTX1//yyy/bt2+/efMmIUQulz98+FCv768CI4QuOzAWgwcPPnv27N69e5csWUKXDB069NixYzNmzCCEmJiYnD59etu2bZ6enqampjwe79ixY2otf+Dk5DR9+nS5XN63b9+YmJg33niDEKLWe3I4nLi4uK1bt3p7e5uZmRFC3n333UmTJnX+uZMmTdq9e/e4cePy8vLCwsLeeustMzMzmUzm5OR04sSJrscPwDis1ABG58WLFyKRyNraesCAAe2fff78eXNzM4/HU+s9nZ2dT5w4ERAQIJFI2r+tuu/54sULsVg8cOBADqdLfRhyuZyiKHq8Si6X19TU8Hg8euIDgB5BCwmMjpmZWSd9WVwuV+NLuYmJicokp+57mpmZ0dMCu0g5b3E4HLVeC8AeGEMC0ILevXt3sTUDAB1Blx0AALDC/wNP8eF7YV9fiQAAAABJRU5ErkJggg==" class="img-fluid figure-img"></p>
@@ -2645,10 +2664,10 @@ Murray, James, Heather Cowardin, J-C Liou, Marlon Sorge, Norman Fitz-Coy, and To
 </div>
 <p>The current dataset can be described incredibly well just by looking at <code>Iz</code>, which again the models are rotated so that <code>Iz</code> is the largest moment of inertia. Then including <code>Iy</code> and <code>Iz</code> means that a 3D plot of the principle moments of inertia almost capture all the variation in the data.</p>
 <p>The next step for characterization is to get only the inertia’s from the dataset. Since the current dataset is so small, the scaled dataset will be used for rest of the characterization process. Once more parts are added to the database it will make sense to start looking at the raw dataset. Now we can proceed to cluster the data using the k-means method of clustering. To properly use k-means a value of k, which is the number of clusters, needs to be determined. This can be done by creating an elbow plot using the following code:</p>
-<div class="sourceCode" id="cb9"><pre class="sourceCode matlab code-with-copy"><code class="sourceCode matlab"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="kw">for</span> <span class="va">ii</span><span class="op">=</span><span class="fl">1</span><span class="op">:</span><span class="fl">20</span></span>
-<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>    [<span class="va">idx</span><span class="op">,~,</span><span class="va">sumd</span>] <span class="op">=</span> <span class="va">kmeans</span>(<span class="va">inertia</span><span class="op">,</span><span class="va">ii</span>)<span class="op">;</span></span>
-<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>    <span class="va">J</span>(<span class="va">ii</span>)<span class="op">=</span><span class="va">norm</span>(<span class="va">sumd</span>)<span class="op">;</span></span>
-<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
+<div class="sourceCode" id="cb7"><pre class="sourceCode matlab code-with-copy"><code class="sourceCode matlab"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a><span class="kw">for</span> <span class="va">ii</span><span class="op">=</span><span class="fl">1</span><span class="op">:</span><span class="fl">20</span></span>
+<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>    [<span class="va">idx</span><span class="op">,~,</span><span class="va">sumd</span>] <span class="op">=</span> <span class="va">kmeans</span>(<span class="va">inertia</span><span class="op">,</span><span class="va">ii</span>)<span class="op">;</span></span>
+<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>    <span class="va">J</span>(<span class="va">ii</span>)<span class="op">=</span><span class="va">norm</span>(<span class="va">sumd</span>)<span class="op">;</span></span>
+<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
 <p>Which produces the following plot:</p>
 <div class="quarto-figure quarto-figure-center">
 <figure class="figure">
@@ -2671,6 +2690,7 @@ Murray, James, Heather Cowardin, J-C Liou, Marlon Sorge, Norman Fitz-Coy, and To
 
 </section>
 
+
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diff --git a/report.qmd b/report.qmd
index 310f694..9574dcb 100644
--- a/report.qmd
+++ b/report.qmd
@@ -18,8 +18,54 @@ execute:
   cache: true
 ---
 
+## Introduction
+
+Orbital debris is a form of pollution that is growing at an exponential pace and puts current and
+future space infrastructure at risk. Satellites are critical to military, commercial, and civil
+operations. Unfortunately, the space that debris occupies is increasingly becoming more crowded and
+dangerous, potentially leading to a cascade event that could turn orbit around the Earth into an
+unusable wasteland for decades unless proper mitigation is not introduced. Existing models employed
+by NASA rely on a dataset created from 2D images and are missing many crucial features required for
+correctly modeling the space debris environment. This approach aims to use high-resolution 3D
+scanning to fully capture the geometry of a piece of debris and allow a more advanced analysis of
+each piece. Coupled with machine learning methods, the scans will allow advances to the current
+cutting edge. Physical and photograph-based measurements are time-consuming, hard to replicate, and
+lack precision. 3D scanning allows much more advanced and accurate analysis of each debris sample,
+focusing on properties such as moment of inertia, cross-section, and drag. Once the characteristics
+of space debris are more thoroughly understood, we can begin mitigating the creation and danger of
+future space debris by implementing improved satellite construction methods and more advanced debris
+avoidance measures.
+
+### Current Progress
+
+This project aims to fix very difficult issues, and although great progress has been made there is
+still plenty of work to be done. Currently, algorithms have been made that are capable of getting
+many key features from solid ^[A mesh with a surface that is fully closed and has no holes in its
+geometry.] models that are in the `stl` format. The algorithm for processing the 3D meshes is
+implemented in the Julia programming language. Syntactically the language is very similar to Python
+and Matlab. Julia was chosen because it is nearly as performant as compiled languages like C, while
+still having tooling geared towards engineers and scientists. The code produces a struct with all
+the calculated properties as follows:
+
+```julia
+struct Properties
+    # Volume of the mesh
+    volume::Float64
+    # Center of gravity, meshes are not always center at [0,0,0]
+    center_of_gravity::Vector{Float64}
+    # Moment of inertia tensor
+    inertia::Matrix{Float64}
+    # Surface area of mesh
+    surface_area::Float64
+    # Average orthogonal dimension of the mesh
+    characteristic_length::Float64
+    # Projected length of farthest two points in [x,y,z] directions
+    solidbody_values::Vector{Float64}
+end
+```
+
 ```{julia}
-#| code-fold: true
+#| echo: false
 #| output: false
 
 using FileIO
@@ -29,8 +75,11 @@ using stlProcess
 
 using CSV
 using DataFrames
+using Plots
+theme(:ggplot2)
 
 using LinearAlgebra
+using Statistics
 ```
 
 ```{julia}
@@ -40,7 +89,8 @@ using LinearAlgebra
 # local path to https://gitlab.com/orbital-debris-research/fake-satellite-dataset
 dataset_path = raw"C:\Coding\fake-satellite-dataset"
 
-folders = ["1_5U", "assembly1", "cubesat"]
+# folders = ["1_5U", "assembly1", "cubesat"]
+folders = ["cubesat"]
 
 df = DataFrame(;
     surface_area=Float64[],
@@ -55,8 +105,9 @@ df = DataFrame(;
 ```
 
 ```{julia}
+#| output: false
+
 for path in dataset_path * "\\" .* folders
-    println("Processing Path: ", path)
     Threads.@threads for file in readdir(path)
         stl = load(path * "\\" * file)
         scale = find_scale(stl)
@@ -64,21 +115,44 @@ for path in dataset_path * "\\" .* folders
 
         eigs = eigvals(props.inertia)
         sort_index = sortperm(eigs)
-        Ix, Iy, Iz = eigs[sort_index]
+        I1, I2, I3 = eigs[sort_index]
         sbx, sby, sbz = props.sb_values[sort_index]
 
         push!(
             df,
-            [props.surface_area, props.characteristic_length, sbx, sby, sbz, Ix, Iy, Iz],
+            [props.surface_area, props.characteristic_length, sbx, sby, sbz, I3, I2, I1],
         )
     end
 end
 ```
 
+:::{.column-body-outset}
+
 ```{julia}
+#| echo: false
+
 describe(df)
 ```
 
+:::
+
+```{julia}
+S = cov(Matrix(df))
+
+eig_vals = eigvals(S);
+
+# sorting eigenvalues from largest to smallest
+sort_index = sortperm(eig_vals; rev=true)
+
+lambda = eig_vals[sort_index]
+names_sorted = names(df)[sort_index]
+
+lambda_ratio = cumsum(lambda) ./ sum(lambda)
+
+plot(lambda_ratio, marker=:x)
+xticks!(sort_index,names(df), xrotation = 15)
+```
+
 ## Gathering Data
 
 To get started on the project before any scans of the actual debris are made available, I opted to
@@ -165,7 +239,7 @@ eig_vals = eig(S);
 lambda_ratio = cumsum(lambda) ./ sum(lambda)
 ```
 
-Then plotting `lambda_ratio`, which is the `cumsum`/`sum` produces the following plot:
+Then plotting `lambda_ratio`, which is the `cumsum ./ sum` produces the following plot:
 
 ![PCA Plot](Figures/pca.png)
 
diff --git a/report.tex b/report.tex
deleted file mode 100644
index f7eddfe..0000000
--- a/report.tex
+++ /dev/null
@@ -1,460 +0,0 @@
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-
-\title{Characterization of Space Debris using Machine Learning Methods}
-\usepackage{etoolbox}
-\makeatletter
-\providecommand{\subtitle}[1]{% add subtitle to \maketitle
-  \apptocmd{\@title}{\par {\large #1 \par}}{}{}
-}
-\makeatother
-\subtitle{Advanced processing of 3D meshes using Julia, and data science
-in Matlab.}
-\author{Anson Biggs}
-\date{4/30/2022}
-
-\begin{document}
-\maketitle
-
-\ifdefined\Shaded\renewenvironment{Shaded}{\begin{tcolorbox}[interior hidden, borderline west={3pt}{0pt}{shadecolor}, boxrule=0pt, enhanced, breakable, sharp corners, frame hidden]}{\end{tcolorbox}}\fi
-
-\hypertarget{gathering-data}{%
-\subsection{Gathering Data}\label{gathering-data}}
-
-To get started on the project before any scans of the actual debris are
-made available, I opted to find 3D models online and process them as if
-they were data collected by my team. GrabCAD is an excellent source of
-high-quality 3D models, and all the models have, at worst, a
-non-commercial license making them suitable for this study. The current
-dataset uses three separate satellite assemblies found on GrabCAD, below
-is an example of one of the satellites that was used.
-
-\begin{figure}
-
-{\centering \includegraphics{Figures/assembly.jpg}
-
-}
-
-\caption{Example CubeSat Used for Analysis}
-
-\end{figure}
-
-\hypertarget{data-preparation}{%
-\subsection{Data Preparation}\label{data-preparation}}
-
-The models were processed in Blender, which quickly converted the
-assemblies to \texttt{stl} files, giving 108 unique parts to be
-processed. Since the expected final size of the dataset is expected to
-be in the magnitude of the thousands, an algorithm capable of getting
-the required properties of each part is the only feasible solution. From
-the analysis performed in
-\href{https://gitlab.com/orbital-debris-research/directed-study/report-1/-/blob/main/README.md}{Report
-1}, we know that the essential debris property is the moments of inertia
-which helped narrow down potential algorithms. Unfortunately, this is
-one of the more complicated things to calculate from a mesh, but thanks
-to a paper from (Eberly
-2002)\marginpar{\begin{footnotesize}\leavevmode\vadjust pre{\protect\hypertarget{ref-eberlyPolyhedralMassProperties2002}{}}%
-Eberly, David. 2002. {``Polyhedral {Mass Properties} ({Revisited}).''}
-\url{https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf}.\vspace{2mm}\par\end{footnotesize}}
-titled
-\href{https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf}{Polyhedral
-Mass Properties}, his algorithm was implemented in the Julia programming
-language. The current implementation of the algorithm calculates a
-moment of inertia tensor, volume, center of gravity, characteristic
-length, and surface body dimensions in a few milliseconds per part. The
-library can be found
-\href{https://gitlab.com/MisterBiggs/stl-process}{here.} The
-characteristic length is a value that is heavily used by the NASA
-DebriSat project (Murray et al.
-2019)\marginpar{\begin{footnotesize}\leavevmode\vadjust pre{\protect\hypertarget{ref-DebriSat2019}{}}%
-Murray, James, Heather Cowardin, J-C Liou, Marlon Sorge, Norman
-Fitz-Coy, and Tom Huynh. 2019. {``Analysis of the DebriSat Fragments and
-Comparison to the NASA Standard Satellite Breakup Model.''} In
-\emph{International Orbital Debris Conference (IOC)}. JSC-E-DAA-TN73918.
-\url{https://ntrs.nasa.gov/citations/20190034081}.\vspace{2mm}\par\end{footnotesize}}
-that is doing very similar work to this project. The characteristic
-length takes the maximum orthogonal dimension of a body, sums the
-dimensions then divides by 3 to produce a single scalar value that can
-be used to get an idea of thesize of a 3D object.
-
-\begin{figure}
-
-{\centering \includegraphics{Figures/current_process.pdf}
-
-}
-
-\caption{Current mesh processing pipeline}
-
-\end{figure}
-
-The algorithm's speed is critical not only for the eventual large number
-of debris pieces that have to be processed, but many of the data science
-algorithms we plan on performing on the compiled data need the data to
-be normalized. For the current dataset and properties, it makes the most
-sense to normalize the dataset based on volume. Volume was chosen for
-multiple reasons, namely because it was easy to implement an efficient
-algorithm to calculate volume, and currently, volume produces the least
-amount of variation out of the current set of properties calculated.
-Unfortunately, scaling a model to a specific volume is an iterative
-process, but can be done very efficiently using derivative-free
-numerical root-finding algorithms. The current implementation can scale
-and process all the properties using only 30\% more time than getting
-the properties without first scaling.
-
-\begin{Shaded}
-\begin{Highlighting}[]
-\NormalTok{ Row │ variable               mean      min        median     max}
-\NormalTok{─────┼───────────────────────────────────────────────────────────────────}
-\NormalTok{   1 │ surface\_area           25.2002   5.60865     13.3338     159.406}
-\NormalTok{   2 │ characteristic\_length  79.5481   0.158521    1.55816     1582.23}
-\NormalTok{   3 │ sbx                     1.40222  0.0417367   0.967078    10.0663}
-\NormalTok{   4 │ sby                     3.3367   0.0125824   2.68461     9.68361}
-\NormalTok{   5 │ sbz                     3.91184  0.29006     1.8185      14.7434}
-\NormalTok{   6 │ Ix                      1.58725  0.0311782   0.23401     11.1335}
-\NormalTok{   7 │ Iy                      3.74345  0.178598    1.01592     24.6735}
-\NormalTok{   8 │ Iz                      5.20207  0.178686    1.742       32.0083}
-\end{Highlighting}
-\end{Shaded}
-
-Above is a summary of the current 108 part with scaling. Since all the
-volumes are the same it is left out of the dataset, the center of
-gravity is also left out of the dataset since it currently is just an
-artifact of the \texttt{stl} file format. There are many ways to
-determine the `center' of a 3D mesh, but since only one is being
-implemented at the moment comparisons to other properties doesn't make
-sense. The other notable part of the data is the model is rotated so
-that the magnitudes of \texttt{Iz}, \texttt{Iy}, and \texttt{Ix} are in
-descending order. This makes sure that the rotation of a model doesn't
-matter for characterization. The dataset is available for download here:
-
-\begin{itemize}
-\tightlist
-\item
-  \href{https://gitlab.com/orbital-debris-research/directed-study/report-3/-/blob/main/scaled_dataset.csv}{scaled\_dataset.csv}
-\end{itemize}
-
-\hypertarget{characterization}{%
-\subsection{Characterization}\label{characterization}}
-
-The first step toward characterization is to perform a principal
-component analysis to determine what properties of the data capture the
-most variation. \texttt{PCA} also requires that the data is scaled, so
-as discussed above the dataset that is scaled by \texttt{volume} will be
-used. \texttt{PCA} is implemented manually instead of the Matlab
-built-in function as shown below:
-
-\begin{Shaded}
-\begin{Highlighting}[]
-\CommentTok{\% covaraince matrix of data points}
-\VariableTok{S}\OperatorTok{=}\VariableTok{cov}\NormalTok{(}\VariableTok{scaled\_data}\NormalTok{)}\OperatorTok{;}
-
-\CommentTok{\% eigenvalues of S}
-\VariableTok{eig\_vals} \OperatorTok{=} \VariableTok{eig}\NormalTok{(}\VariableTok{S}\NormalTok{)}\OperatorTok{;}
-
-\CommentTok{\% sorting eigenvalues from largest to smallest}
-\NormalTok{[}\VariableTok{lambda}\OperatorTok{,} \VariableTok{sort\_index}\NormalTok{] }\OperatorTok{=} \VariableTok{sort}\NormalTok{(}\VariableTok{eig\_vals}\OperatorTok{,}\SpecialStringTok{\textquotesingle{}descend\textquotesingle{}}\NormalTok{)}\OperatorTok{;}
-
-
-\VariableTok{lambda\_ratio} \OperatorTok{=} \VariableTok{cumsum}\NormalTok{(}\VariableTok{lambda}\NormalTok{) }\OperatorTok{./} \VariableTok{sum}\NormalTok{(}\VariableTok{lambda}\NormalTok{)}
-\end{Highlighting}
-\end{Shaded}
-
-Then plotting \texttt{lambda\_ratio}, which is the
-\texttt{cumsum}/\texttt{sum} produces the following plot:
-
-\begin{figure}
-
-{\centering \includegraphics{Figures/pca.png}
-
-}
-
-\caption{PCA Plot}
-
-\end{figure}
-
-The current dataset can be described incredibly well just by looking at
-\texttt{Iz}, which again the models are rotated so that \texttt{Iz} is
-the largest moment of inertia. Then including \texttt{Iy} and
-\texttt{Iz} means that a 3D plot of the principle moments of inertia
-almost capture all the variation in the data.
-
-The next step for characterization is to get only the inertia's from the
-dataset. Since the current dataset is so small, the scaled dataset will
-be used for rest of the characterization process. Once more parts are
-added to the database it will make sense to start looking at the raw
-dataset. Now we can proceed to cluster the data using the k-means method
-of clustering. To properly use k-means a value of k, which is the number
-of clusters, needs to be determined. This can be done by creating an
-elbow plot using the following code:
-
-\begin{Shaded}
-\begin{Highlighting}[]
-\KeywordTok{for} \VariableTok{ii}\OperatorTok{=}\FloatTok{1}\OperatorTok{:}\FloatTok{20}
-\NormalTok{    [}\VariableTok{idx}\OperatorTok{,\textasciitilde{},}\VariableTok{sumd}\NormalTok{] }\OperatorTok{=} \VariableTok{kmeans}\NormalTok{(}\VariableTok{inertia}\OperatorTok{,}\VariableTok{ii}\NormalTok{)}\OperatorTok{;}
-    \VariableTok{J}\NormalTok{(}\VariableTok{ii}\NormalTok{)}\OperatorTok{=}\VariableTok{norm}\NormalTok{(}\VariableTok{sumd}\NormalTok{)}\OperatorTok{;}
-\KeywordTok{end}
-\end{Highlighting}
-\end{Shaded}
-
-Which produces the following plot:
-
-\begin{figure}
-
-{\centering \includegraphics{Figures/kmeans.png}
-
-}
-
-\caption{Elbow method to determine the required number of clusters.}
-
-\end{figure}
-
-As can be seen in the above elbow plot, at 6 clusters there is an
-``elbow'' which is where there is a large drop in the sum distance to
-the centroid of each cluster which means that it is the optimal number
-of clusters. The inertia's can then be plotted using 6 k-means clusters
-produces the following plot:
-
-\begin{figure}
-
-{\centering \includegraphics{Figures/inertia3d.png}
-
-}
-
-\caption{Moments of Inertia plotted with 6 clusters.}
-
-\end{figure}
-
-From this plot it is immediately clear that there are clusters of
-outliers. These are due to the different shapes and the extreme values
-are slender rods or flat plates while the clusters closer to the center
-more closely resemble a sphere. As the dataset grows it should become
-more apparent what kind of clusters actually make up a satellite, and
-eventually space debris in general.
-
-\hypertarget{next-steps}{%
-\subsection{Next Steps}\label{next-steps}}
-
-The current dataset needs to be grown in both the amount of data and the
-variety of data. The most glaring issue with the current dataset is the
-lack of any debris since the parts are straight from satellite
-assemblies. Getting accurate properties from the current scans we have
-is an entire research project in itself, so hopefully, getting pieces
-that are easier to scan can help bring the project back on track. The
-other and harder-to-fix issue is finding/deriving more data properties.
-Properties such as cross-sectional or aerodynamic drag would be very
-insightful but are likely to be difficult to implement in code and
-significantly more resource intensive than the current properties the
-code can derive.
-
-
-
-
-\end{document}