Spacing_with_countershapes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "YvDl6oFTtlPj"
   },
   "source": [
    "# Spacing with Countershapes\n",
    "\n",
    "This is an experimental contribution to research into automated font spacing.\n",
    "The aim is not just to provide sidebearing values (e.g. spacing a glyph against\n",
    "\"H\" or \"n\", which is what we often refer to as \"spacing\") but also to be able\n",
    "to determine the optimal spacing value between an arbitrary pair of glyphs.\n",
    "(what we often refer to as \"kerning\")\n",
    "\n",
    "As mentioned, it is an experimental contribution. Please don't expect to be able\n",
    "to use it to fully space and kern your fonts yet. At this stage, its purpose is\n",
    "to help develop our understanding of problems in spacing and autospacing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "XxEoU6P_tehi"
   },
   "outputs": [],
   "source": [
    "#%matplotlib notebook\n",
    "from CounterSpace import CounterSpace\n",
    "import matplotlib.pyplot as plt\n",
    "CounterSpace.get_sample_font(\"OpenSans-Regular.ttf\")\n",
    "c = CounterSpace(\"OpenSans-Regular.ttf\",serif_smoothing=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The basic conceit of CounterSpace is that well-spaced fonts have equal areas of \"influence\" in the counters between two glyphs. The problem is defining what we mean by influence.\n",
    "\n",
    "For previous equal-area spacers such as [HTLetterSpacer](https://github.com/huertatipografica/HTLetterspacer), the area of influence is just the whitespace area between two glyphs. (There are several refinements HTLetterSpacer makes to this statement, but go with it for now, please.)\n",
    "\n",
    "We can emulate this approach in CounterSpace. Here are the whitespace counters between \"HH\", and \"OO\", together with their respective areas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "dgx56w9OoE0x"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '4179.884095252702')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c.options = { \"h_center\": 1000, \"w_center\": 1000, \"h_top\":1, \"w_top\": 1, \"h_bottom\":1, \"w_bottom\": 1, \"top_strength\":0.1, \"bottom_strength\":0.1, \"center_strength\":1 }\n",
    "fig, ax = plt.subplots(1,2,figsize = (20,20))\n",
    "hh = c.pair_area(\"H\",\"H\",c.options)\n",
    "oo = c.pair_area(\"O\",\"O\",c.options)\n",
    "ax[0].imshow(hh)\n",
    "ax[0].set_title(hh.sum(),fontsize=20)\n",
    "ax[1].imshow(oo)\n",
    "ax[1].set_title(oo.sum(),fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "7gN-Uo_L8URB"
   },
   "source": [
    "Oh, well. The areas aren't actually the same between our two reference pairs. HTLetterSpacer deals with this by having a parameter which determines how \"deep\" to descend into the counters. This cuts off the long tails around the corners of \"OO\"'s counter, reducing its area to the same as that of \"HH\". (That was one of the refinements I mentioned. We will deal with another one later.)\n",
    "\n",
    "CounterSpace deals with the problem a different way. Our intuition is that the eye perceives the space in the center of a counter more strongly than around the edges. In other words, rather than our counterspace being a solid block as in the diagrams above, it's more like a light radiating outwards from the center. I don't believe it's literally a light source, but that gives us a useful metaphor to model what correct spacing looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "snRhxiHuoE0-"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '2713.8562108570372')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x1440 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c.options = { \"h_center\": 45, \"w_center\": 45, \"h_top\":1, \"w_top\": 1, \"h_bottom\":1, \"w_bottom\": 1, \"top_strength\":0.1, \"bottom_strength\":0.1, \"center_strength\":1 }\n",
    "fig, ax = plt.subplots(1,2,figsize = (20,20))\n",
    "hh = c.pair_area(\"H\",\"H\",c.options)\n",
    "oo = c.pair_area(\"O\",\"O\",c.options)\n",
    "ax[0].imshow(hh)\n",
    "ax[0].set_title(hh.sum(),fontsize=20)\n",
    "ax[1].imshow(oo)\n",
    "ax[1].set_title(oo.sum(),fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that's better. The total intensity of light is extremely similar between our two reference values. We can now take an arbitrary pair of glyphs, and change the distance between them until the intensity matches our expected total. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VO distance should be set to 36 units\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize = (20,20))\n",
    "VO = c.pair_area(\"V\",\"O\",c.options)\n",
    "distance = 3\n",
    "VO_corrected = c.pair_area(\"V\",\"O\",c.options,dist=distance)\n",
    "ax[0].imshow(VO)\n",
    "ax[0].set_title(VO.sum(),fontsize=20)\n",
    "ax[1].imshow(VO_corrected)\n",
    "ax[1].set_title(VO_corrected.sum(),fontsize=20)\n",
    "distance_in_font_units = (distance/c.font.scale_factor)\n",
    "print(\"VO distance should be set to %i units\" % distance_in_font_units)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "h1dvl3VS8fqZ"
   },
   "source": [
    "Note that the distance here refers to the ink-to-ink distance between the right edge of \"V\" and the left edge of \"O\" - essentially, the \"total sidebearing\" of the pair. To go from this to a kerning value, sum the actual right sidebearing and left sidebearing, and subtract from our desired difference:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-85\n"
     ]
    }
   ],
   "source": [
    "rofV = c.font.glyph(\"V\").rsb\n",
    "lofO = c.font.glyph(\"O\").lsb\n",
    "natural_ink_to_ink = (rofV + lofO) / c.font.scale_factor\n",
    "kern_required = int(distance_in_font_units - natural_ink_to_ink)\n",
    "print(kern_required)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What you should notice about this is that it is clearly wrong. The diagram on the left above (which sets the pair at the distance provided by the font, *including* the font's kerning adjustment of -20 units) is correctly spaced, and the one on the right is way too tight, even though the light intensity is equal to the reference pairs.\n",
    "\n",
    "What's gone wrong? Well, it could be a number of things. One is that we set the intensity of our light source to be a circular light of 50 units across. Maybe an oval-shaped light would be better:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 208
    },
    "colab_type": "code",
    "id": "swj32VZx8c4L",
    "outputId": "2456145a-3e8b-4a5e-e8bf-d8461299894d",
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '2796.924826288794')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x1440 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c.options = { \"h_center\": 75, \"w_center\": 15, \"h_top\":1, \"w_top\": 1, \"h_bottom\":1, \"w_bottom\": 1, \"top_strength\":0.1, \"bottom_strength\":0.1, \"center_strength\":1 }\n",
    "fig, ax = plt.subplots(1,3,figsize = (20,20))\n",
    "hh = c.pair_area(\"H\",\"H\",c.options)\n",
    "oo = c.pair_area(\"O\",\"O\",c.options)\n",
    "ov = c.pair_area(\"O\",\"V\",c.options)\n",
    "ax[0].imshow(hh)\n",
    "ax[0].set_title(hh.sum(),fontsize=20)\n",
    "ax[1].imshow(oo)\n",
    "ax[1].set_title(oo.sum(),fontsize=20)\n",
    "ax[2].imshow(ov)\n",
    "ax[2].set_title(ov.sum(),fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "THzbIDiz83NA"
   },
   "source": [
    "Well, that looks like it might be a slightly better set of parameters. The influence isn't exactly equal, but it's more consistent across correctly-spaced pairs than we had before.\n",
    "\n",
    "One thing I want you to hold in your head at this stage is that I have manually searched for a set of parameters of lightsource width, height and intensity, so that the three pairs I am interested in (\"HH\", \"OO\", \"OV\") will ideally have equal total influence. But there's no reason why I should have to do this manually. What we will do later is say to the computer, \"I declare that the following set of pairs are correctly spaced. Now search for the set of parameters which equalizes the influence between these pairs,* and we'll see how that works for other glyphs.\" This is something we can easily use an optimizer to do, and provides us with a nice interface to the type designer. \"I've done these, you fill in the rest.\" \"No, you got that one wrong. I'll space it manually, then declare that it is correct, and you can try again.\"\n",
    "\n",
    "<small>*: Technically, which minimizes the square of the differences between the total influence of each of these pairs. This means we have a mean-square-error input to an optimizer, which computationally is a solved problem.</small>\n",
    "\n",
    "CounterSpace also brings in another intuition, which provides us with more knobs to twiddle. This is taken from an idea found in Jost Hochuli's *Detail in Typography*. He introduces the metaphor of light flowing from below and above the counterspace:\n",
    "\n",
    "![hochuli's light idea](https://pbs.twimg.com/media/D-PInV6W4AATKHW?format=jpg)\n",
    "\n",
    "Now Hochuli's idea is [disputed](https://twitter.com/justvanrossum/status/1145369505855672321), and it also doesn't tell us how much \"stronger\" this conceptual \"top light\" is from \"bottom light\". It also doesn't tell us how the top and and bottom ideas interact with our \"center light\" intution. But that doesn't actually matter. We can model three light sources, and combine them in arbitrary ways:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "rTe9oNjHoE1E"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11c9ce210>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c.options = { \"h_center\": 50, \"w_center\": 50, \"h_top\":40, \"w_top\": 40, \"h_bottom\":40, \"w_bottom\": 40, \"top_strength\":5, \"bottom_strength\":0, \"center_strength\":0.1 }\n",
    "fig, ax = plt.subplots(1,3,figsize = (20,20))\n",
    "hh = c.pair_area(\"V\",\"O\",c.options)\n",
    "c.options = { \"h_center\": 50, \"w_center\": 50, \"h_top\":40, \"w_top\": 40, \"h_bottom\":40, \"w_bottom\": 40, \"top_strength\":0, \"bottom_strength\":5, \"center_strength\":0.1 }\n",
    "hh2 = c.pair_area(\"V\",\"O\",c.options)\n",
    "c.options = { \"h_center\": 10, \"w_center\": 10, \"h_top\":40, \"w_top\": 40, \"h_bottom\":40, \"w_bottom\": 40, \"top_strength\":8, \"bottom_strength\":5, \"center_strength\":3 }\n",
    "hh3 = c.pair_area(\"V\",\"O\",c.options)\n",
    "ax[0].imshow(hh)\n",
    "ax[1].imshow(hh2)\n",
    "ax[2].imshow(hh3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "K04P4160qDUg"
   },
   "source": [
    "I've deliberately emphasised the effect in the parameters chosen above, but how strong should the influence of these lights be? Again, I don't care - now that we have our model, we can ask the computer to tell us the best parameters which equalize area. (This next cell takes quite a while to run.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 286
    },
    "colab_type": "code",
    "id": "xiW1tLSUoE1N",
    "outputId": "8860d54b-d429-4e4d-bb85-ee3632dc6dda"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'w_top': 15.419977486850728, 'w_bottom': 20.208110931511285, 'h_top': 16.24043686617071, 'h_bottom': 12.505802989022957, 'h_center': 50.0, 'w_center': 14.644407849180935, 'top_strength': 0.5021840542221542, 'bottom_strength': 0.8038162014633223, 'center_strength': 2.0323006307316973}\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '5028.96319824444')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x1440 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c.key_pairs = [\"HH\",\"OO\",\"VO\"]\n",
    "print(c.determine_parameters())\n",
    "fig, ax = plt.subplots(1,3,figsize = (20,20))\n",
    "hh = c.pair_area(\"H\",\"H\",c.options)\n",
    "oo = c.pair_area(\"O\",\"O\",c.options)\n",
    "ov = c.pair_area(\"O\",\"V\",c.options)\n",
    "ax[0].imshow(hh)\n",
    "ax[0].set_title(hh.sum(),fontsize=20)\n",
    "ax[1].imshow(oo)\n",
    "ax[1].set_title(oo.sum(),fontsize=20)\n",
    "ax[2].imshow(ov)\n",
    "ax[2].set_title(ov.sum(),fontsize=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TCkCTxvw9aET"
   },
   "source": [
    "Eyeballing the diagrams above, it seems like top light and bottom light didn't contribute much in the case of this font. But the options are there for the computer to twiddle in case they do help.\n",
    "\n",
    "CounterSpace brings two final refinements. One, also from HTLetterSpacer, is the idea of diagonizing the counters. The reason you have to do this is that some glyphs have insanely big counters, and that's OK. Not *all* of the counter should be considered as taking part in the spacing process.\n",
    "\n",
    "Consider:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 153
    },
    "colab_type": "code",
    "id": "-Mw-HyT3s1AG",
    "outputId": "5fa06028-dba1-4ff7-89b4-0924ce47a33d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11df7ba50>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(c.font.set_string(\"LTHH\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "1UZbSd5z9iv5"
   },
   "source": [
    "What's going to happen if we strictly enforce the principle that the total influence of \"LT\" should be equal to that of \"HH\"?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 367
    },
    "colab_type": "code",
    "id": "BlbQ5jO4oE1c",
    "outputId": "88f8b3ab-f569-48f9-ddfb-7da72359e03a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11b8aad10>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(c.font.set_string(\"LTHH\",{(\"L\",\"T\"):-55})>0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "BbZ9UbXC-F82"
   },
   "source": [
    "Yeah, oops. So instead, we look for glyphs which have deep \"holes\" in their outlines, and attempt to smoothly fill in those discontinuities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 506
    },
    "colab_type": "code",
    "id": "oqgQy6bjH-Px",
    "outputId": "db2cd99c-1d2d-44fd-a5cc-c4848e941631"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,5,figsize = (10,10))\n",
    "for ix,s in enumerate(\"LTFCR\"):\n",
    "    l = c.font.glyph(s).as_matrix()\n",
    "    conc = 1-l.right_face()\n",
    "    ax[ix].imshow(l.reduce_concavity(conc).with_padding_to_constant_box_width(150))\n",
    "    ax[ix].set_title(s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two final refinements, which we will demonstrate together. The first is a small one to do with serifs. We apply a blur kernel to the outlines to remove the influence of serifs, which should not contribute to spacing decisions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'H (serif smoothing = 5)')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2,figsize = (10,10))\n",
    "CounterSpace.get_sample_font(\"PTSerif-Italic.ttf\")\n",
    "c = CounterSpace(\"PTSerif-Italic.ttf\",serif_smoothing=0)\n",
    "ax[0].imshow(c.lshifted_counter(\"H\",0,50,200))\n",
    "ax[0].set_title(\"H (no serif smoothing)\")\n",
    "c = CounterSpace(\"PTSerif-Italic.ttf\",serif_smoothing=5)\n",
    "ax[1].imshow(c.lshifted_counter(\"H\",0,50,200))\n",
    "ax[1].set_title(\"H (serif smoothing = 5)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second refinement happens automatically when you use an italic font: the light from the top and bottom is automatically angled to match:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x11c942c90>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "c.options = { \"h_center\": 50, \"w_center\": 50, \"h_top\":70, \"w_top\": 10, \"h_bottom\":40, \"w_bottom\": 10, \"top_strength\":2, \"bottom_strength\":3, \"center_strength\":0 }\n",
    "plt.imshow(c.pair_area(\"H\",\"H\",c.options))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So now we have all the pieces required to space our font. Let us run the solver again, and use it to fill a dictionary with spacing values for pairs in a string. (The next cells take quite a long time.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "c = CounterSpace(\"PTSerif-Italic.ttf\",serif_smoothing=5)\n",
    "c.key_pairs = [\"HH\",\"OO\"]\n",
    "c.bare_minimum = 15\n",
    "c.determine_parameters()\n",
    "\n",
    "from itertools import tee\n",
    "def pairwise(iterable):\n",
    "  a, b = tee(iterable)\n",
    "  next(b, None)\n",
    "  return zip(a, b)\n",
    "\n",
    "pdd = {} # Pair distance dictionary\n",
    "def space_string(s):\n",
    "  for l,r in pairwise(s):\n",
    "    if not (l,r) in pdd: pdd[(l,r)] = int(c.space(l,r) * c.font.scale_factor)\n",
    "  return c.font.set_string(s,pair_distance_dict = pdd) > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1268c0710>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(2,1,figsize = (10,10))\n",
    "ax[0].imshow(space_string(\"ATAVISTIC\"))\n",
    "ax[1].imshow(space_string(\"hamburgefonsiv\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Well, not bad, I think. Where are the problems?\n",
    "\n",
    "We brought in the idea of discontinuity smoothing because some deep countershapes (LT) had too much influence, and so their counters needed to be reduced. But the discontinuity smoothing process is hard to get right, and some counters (such as XX) now don't get enough influence (and so end up being spaced too wide, to compensate).\n",
    "\n",
    "In the below, blue is the real metrics from the font, red is autospaced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "fig, ax = plt.subplots(3,3,figsize=(15,3))\n",
    "fig.subplots_adjust(wspace=0, hspace=0)\n",
    "from matplotlib import colors\n",
    "import numpy as np\n",
    "cmap1 = colors.ListedColormap(['white', 'red'])\n",
    "cmap2 = colors.ListedColormap(['white', 'blue'])\n",
    "def comparison(s,axix):\n",
    "    real = c.font.set_string(s)\n",
    "    autospaced = space_string(s)\n",
    "    diff1 = max(autospaced.shape[1]-real.shape[1],0)/2\n",
    "    real = real.with_padding(math.floor(diff1),math.ceil(diff1)) > 0\n",
    "    autospaced._glyph = None\n",
    "    diff2 = max(real.shape[1]-autospaced.shape[1],0)/2\n",
    "    autospaced = autospaced.with_padding(math.floor(diff2),math.ceil(diff2)) > 0\n",
    "#     return real\n",
    "    ax[0][axix].imshow(real,cmap=cmap2)\n",
    "    ax[1][axix].imshow(autospaced,cmap=cmap1)\n",
    "    ax[2][axix].imshow(real,alpha=0.5,cmap=cmap2)\n",
    "    ax[2][axix].imshow(autospaced,alpha=0.5,cmap=cmap1)\n",
    "\n",
    "for a in ax:\n",
    "    for b in a:\n",
    "        b.set_yticklabels([])\n",
    "\n",
    "comparison(\"hamburgefontsiv\",0)\n",
    "comparison(\"ATAVISTIC\",1)\n",
    "comparison(\"LVOVFAXX\",2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ideally, discontinuity smoothing operation should be improved, and also the degree of smoothing should be customisable.\n",
    "\n",
    "Hopefully this has been enough to demonstrate the concept of CounterSpace, its strengths and its weaknesses, and provide some stimulus to the further development of automated spacing and kerning tools."
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Spacing with countershapes.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}