{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0",
   "metadata": {},
   "source": [
    "# Tutorial 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from tikzpics import TikzFigure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_grid(tikz, x0, y0, L, N, options, layer=1):\n",
    "    x1 = x0 + L\n",
    "    y1 = y0 + L\n",
    "    delta = L / N\n",
    "    node_positions = []\n",
    "\n",
    "    for i in range(N + 1):\n",
    "\n",
    "        # Horizontal line\n",
    "        y = y0 + i * delta\n",
    "        node_positions = [[x0, y], [x1, y]]\n",
    "        tikz.draw(node_positions, options=options, layer=layer)\n",
    "\n",
    "        # Vertical line\n",
    "        x = x0 + i * delta\n",
    "        node_positions = [[x, y0], [x, y1]]\n",
    "        tikz.draw(node_positions, options=options, layer=layer)\n",
    "\n",
    "\n",
    "def add_square(tikz, x0, y0, L, options, layer=1):\n",
    "    node_positions = [\n",
    "        [x0, y0],\n",
    "        [x0 + L, y0],\n",
    "        [x0 + L, y0 + L],\n",
    "        [x0, y0 + L],\n",
    "        [x0, y0],\n",
    "    ]\n",
    "    tikz.draw(node_positions, options=options, layer=layer)\n",
    "\n",
    "\n",
    "def draw_grid(tikz):\n",
    "\n",
    "    # Add backgrounds\n",
    "    add_square(\n",
    "        tikz=tikz,\n",
    "        x0=0,\n",
    "        y0=0,\n",
    "        L=8,\n",
    "        options=[\"draw\", \"line width=0\", \"fill=yellow!10!white\"],\n",
    "        layer=0,\n",
    "    )\n",
    "\n",
    "    add_square(\n",
    "        tikz=tikz,\n",
    "        x0=4,\n",
    "        y0=2,\n",
    "        L=4,\n",
    "        options=[\"draw\", \"line width=0\", \"fill=blue!10!white\"],\n",
    "        layer=1,\n",
    "    )\n",
    "\n",
    "    add_square(\n",
    "        tikz=tikz,\n",
    "        x0=5,\n",
    "        y0=3,\n",
    "        L=1,\n",
    "        options=[\"draw\", \"line width=0\", \"fill=red!10!white\"],\n",
    "        layer=2,\n",
    "    )\n",
    "\n",
    "    # Level A\n",
    "    add_grid(\n",
    "        tikz,\n",
    "        x0=0,\n",
    "        y0=0,\n",
    "        L=8,\n",
    "        N=4,\n",
    "        options=[\"draw\", \"line width=2\", \"color=black\"],\n",
    "        layer=3,\n",
    "    )\n",
    "\n",
    "    # Level B\n",
    "    add_grid(\n",
    "        tikz,\n",
    "        x0=4,\n",
    "        y0=2,\n",
    "        L=4,\n",
    "        N=4,\n",
    "        options=[\"draw\", \"line width=2\", \"color=blue\"],\n",
    "        layer=4,\n",
    "    )\n",
    "\n",
    "    # Level C\n",
    "    add_grid(\n",
    "        tikz,\n",
    "        x0=5,\n",
    "        y0=3,\n",
    "        L=1.0,\n",
    "        N=2,\n",
    "        options=[\"draw\", \"line width=2\", \"color=red\"],\n",
    "        layer=5,\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4",
   "metadata": {},
   "outputs": [],
   "source": [
    "tikz = TikzFigure(figure_setup=\">={{Triangle[scale=1]}}\")\n",
    "\n",
    "# Draw grid\n",
    "draw_grid(tikz=tikz)\n",
    "\n",
    "z_path = [\n",
    "    [1, 7],\n",
    "    [3, 7],\n",
    "    [1, 5],\n",
    "    [3, 5],\n",
    "    [5, 7],\n",
    "    [7, 7],\n",
    "    [4.5, 5.5],\n",
    "    [5.5, 5.5],\n",
    "    [4.5, 4.5],\n",
    "    [5.5, 4.5],\n",
    "    [6.5, 5.5],\n",
    "    [7.5, 5.5],\n",
    "    [6.5, 4.5],\n",
    "    [7.5, 4.5],\n",
    "    [1, 3],\n",
    "    [3, 3],\n",
    "    [1, 1],\n",
    "    [3, 1],\n",
    "    [4.5, 3.5],\n",
    "    [5.25, 3.75],\n",
    "    [5.75, 3.75],\n",
    "    [5.25, 3.25],\n",
    "    [5.75, 3.25],\n",
    "    [4.5, 2.5],\n",
    "    [5.5, 2.5],\n",
    "    [6.5, 3.5],\n",
    "    [7.5, 3.5],\n",
    "    [6.5, 2.5],\n",
    "    [7.5, 2.5],\n",
    "    [5, 1],\n",
    "    [7, 1],\n",
    "]\n",
    "for i in range(len(z_path) - 1):\n",
    "    path = [z_path[i], z_path[i + 1]]\n",
    "    options = [\"->\", \"draw\", \"line width=1\", \"color=black\"]\n",
    "    tikz.draw(path, options=options, layer=5, center=True)\n",
    "\n",
    "tikz.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5",
   "metadata": {},
   "outputs": [],
   "source": [
    "tikz = TikzFigure(figure_setup=\">={{Triangle[scale=1]}}\")\n",
    "\n",
    "# Draw grid\n",
    "draw_grid(tikz=tikz)\n",
    "\n",
    "hilbert_path = [\n",
    "    [1, 1],\n",
    "    [3, 1],\n",
    "    [3, 3],\n",
    "    [1, 3],\n",
    "    [1, 7],\n",
    "    [3, 7],\n",
    "    [3, 5],\n",
    "    [4.5, 4.5],\n",
    "    [5.5, 4.5],\n",
    "    [5.5, 5.5],\n",
    "    [4.5, 5.5],\n",
    "    [5, 7],\n",
    "    [7, 7],\n",
    "    [7.5, 5.5],\n",
    "    [6.5, 5.5],\n",
    "    [6.5, 4.5],\n",
    "    [7.5, 4.5],\n",
    "    [7.5, 2.5],\n",
    "    [6.5, 2.5],\n",
    "    [6.5, 3.5],\n",
    "    [5.75, 3.75],\n",
    "    [5.75, 3.25],\n",
    "    [5.25, 3.25],\n",
    "    [5.25, 3.75],\n",
    "    [4.5, 3.5],\n",
    "    [4.5, 2.5],\n",
    "    [5.5, 2.5],\n",
    "    [5, 1],\n",
    "    [7, 1],\n",
    "]\n",
    "for i in range(len(hilbert_path) - 1):\n",
    "    path = [hilbert_path[i], hilbert_path[i + 1]]\n",
    "    options = [\"->\", \"draw\", \"line width=1\", \"color=black\"]\n",
    "    tikz.draw(path, options=options, layer=5, center=True)\n",
    "\n",
    "tikz.show()"
   ]
  }
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