From 49c4d79ea2a1884316204fd1becd61bca2b1e9ac Mon Sep 17 00:00:00 2001
From: Bas Nijholt <basnijholt@gmail.com>
Date: Tue, 17 Sep 2019 15:17:58 +0200
Subject: [PATCH] add one more subplot

---
 figures.ipynb         |  10 +++++-----
 figures/line_loss.pdf | Bin 39558 -> 41700 bytes
 paper.md              |   6 ++++--
 3 files changed, 9 insertions(+), 7 deletions(-)

diff --git a/figures.ipynb b/figures.ipynb
index d8677f6..2f8ff0d 100644
--- a/figures.ipynb
+++ b/figures.ipynb
@@ -487,7 +487,7 @@
    "source": [
     "from matplotlib.patches import Polygon\n",
     "\n",
-    "fig, axs = plt.subplots(4, 1, figsize=(fig_width, 1.5 * fig_height))\n",
+    "fig, axs = plt.subplots(5, 1, figsize=(fig_width, 1.5 * fig_height))\n",
     "f = lambda x: np.sin(x)**2\n",
     "xs = np.array([0, 1.3, 3,  5, 7, 8])\n",
     "ys = f(xs)\n",
@@ -505,11 +505,11 @@
     "    \n",
     "for i, ax in enumerate(axs):\n",
     "    ax.axis(\"off\")\n",
-    "    ax.set_ylim(-2, 2)\n",
-    "    label = \"abcd\"[i]\n",
+    "    ax.set_ylim(-1.5, 1.5)\n",
+    "    label = \"abcde\"[i]\n",
     "    ax.text(\n",
     "        0.5,\n",
-    "        0.8,\n",
+    "        0.9,\n",
     "        f\"$\\mathrm{{({label})}}$\",\n",
     "        transform=ax.transAxes,\n",
     "        horizontalalignment=\"center\",\n",
@@ -533,7 +533,7 @@
     "\n",
     "plot_tri(xs, axs[1])\n",
     "\n",
-    "for i in [2, 3]:\n",
+    "for i in [2, 3, 4]:\n",
     "    ax = axs[i]\n",
     "    learner = adaptive.Learner1D(\n",
     "        f,\n",
diff --git a/figures/line_loss.pdf b/figures/line_loss.pdf
index beb35e7af8f044f2290e39494801229d3094afdf..02ec22e142dc458c06fd4727c997ec8a0b7c13c9 100644
GIT binary patch
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diff --git a/paper.md b/paper.md
index e224005..643db28 100755
--- a/paper.md
+++ b/paper.md
@@ -198,13 +198,15 @@ By adding the two loss functions, we can combine the 3D area loss to exploit int
 ## Line simplification loss
 
 #### The line simplification loss is based on an inverse Visvalingam’s algorithm.
-Inspired by a method commonly employed in digital cartography for coastline simplification, Visvalingam's algorithm, we construct a loss function that does its reverse. [@visvalingam1990douglas]
+Inspired by a method commonly employed in digital cartography for coastline simplification, Visvalingam's algorithm, we construct a loss function that does its reverse.[@visvalingam1990douglas]
+Here, at each point (ignoring the boundary points), we compute the effective area associated with its triangle, see Fig. @fig:line_loss(b).
+The loss then becomes the average area of two adjacent traingles.
 
 ![Line loss visualization.
 We start with 6 points (a) on the function (grey).
 Ignoring the endpoints, the effective area of each point is determined by its associated triangle (b).
 The loss of each interval can be computed by taking the average area of the adjacent triangles.
-Subplots (c) and (d) show the the subsequent time steps.](figures/line_loss.pdf){#fig:line_loss}
+Subplots (c), (d), and (e) show the subsequent time steps following (b).](figures/line_loss.pdf){#fig:line_loss}
 
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