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@dstansby
Created May 17, 2023 12:11
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "271125e7",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"from matplotlib.patches import Rectangle\n",
"import mpl_toolkits.mplot3d.art3d as art3d\n",
"import matplotlib.animation as animation\n",
"import numpy as np\n",
"from skimage.data import binary_blobs\n",
"from skimage.filters import gaussian\n",
"from collections import defaultdict"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "54afb0e5",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure()\n",
"ax1 = fig.add_subplot(1, 2, 1, projection='3d')\n",
"ax2 = fig.add_subplot(1, 2, 2, projection='3d')\n",
"ax1.set_title(\"Input planes\")\n",
"ax2.set_title(\"Output planes\")\n",
"\n",
"rects = defaultdict(list)\n",
"for z in np.linspace(0, 1, 10):\n",
" for ax in [ax1, ax2]:\n",
" p = Rectangle((0, 0), 1, 1, facecolor='white', edgecolor='black', alpha=0.7)\n",
" ax.add_patch(p)\n",
" rects[ax].append(p)\n",
" art3d.pathpatch_2d_to_3d(p, z=z, zdir=\"z\")\n",
"\n",
"for ax in [ax1, ax2]:\n",
" ax.axis('off')\n",
"\n",
"def update(frame):\n",
" for ax in [ax1, ax2]:\n",
" for rect in rects[ax]:\n",
" rect.set_facecolor('white')\n",
" rects[ax1][frame].set_facecolor('tab:blue')\n",
" rects[ax2][frame].set_facecolor('tab:red')\n",
" \n",
"ani = animation.FuncAnimation(fig=fig, func=update, frames=10)\n",
"with open('2d_planes.html', 'w') as f:\n",
" f.write(ani.to_jshtml(fps=3, default_mode='once'))"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "6a5736db",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.image.AxesImage at 0x13e9834f0>"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n = 20\n",
"blobs = gaussian(binary_blobs(length=n, n_dim=2, volume_fraction=0.3))\n",
"blobs = (3 * blobs + np.random.rand(*blobs.shape)) / 4\n",
"plt.imshow(blobs, cmap='gray')"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "0266bf60",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1280x960 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axs = plt.subplots(ncols=2, dpi=200)\n",
"for ax in axs:\n",
" ax.set_aspect('equal')\n",
" ax.axis('off')\n",
" ax.set_xlim(0, n)\n",
" ax.set_ylim(0, n)\n",
"\n",
" \n",
" for x in range(n + 1):\n",
" ax.axhline(x, color='k', linewidth=0.3)\n",
"\n",
" for y in range(n + 1):\n",
" ax.axvline(y, color='k', linewidth=0.3)\n",
"\n",
"\n",
"\n",
"\n",
"ax = axs[0]\n",
"# Make blobos\n",
"ax.imshow(blobs, cmap='gray', alpha=0.6, extent=((0, n, 0, n)))\n",
"\n",
"x, y = np.indices((n, n))\n",
"im = np.log(np.exp(-(x - 1)**2 - (y- 1)**2))\n",
"cmap = plt.get_cmap('Reds')\n",
"cmap.set_under('none')\n",
"im = ax.imshow(im, extent=((0, n, 0, n)), vmin=-6, vmax=0, cmap=cmap, alpha=0.6)\n",
"\n",
"data = np.zeros((n, n))\n",
"im2 = axs[1].imshow(data, extent=(0, n, 0, n), vmin=0, vmax=1, cmap='gray_r')\n",
"\n",
"def update(frame):\n",
" x0 = frame // n\n",
" y0 = frame % n\n",
" kernel = np.exp(-(x - x0)**2 - (y - y0)**2)\n",
" im.set_data(np.log(kernel))\n",
" if np.sum(kernel * blobs) > 1.5:\n",
" data[x0, y0] = 1\n",
" im2.set_data(data)\n",
" \n",
" \n",
"ani = animation.FuncAnimation(fig=fig, func=update, frames=n**2)\n",
"\n",
"with open('2d_ball.html', 'w') as f:\n",
" f.write(ani.to_jshtml(fps=14, default_mode='once'))"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "9edda071",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure()\n",
"ax1 = fig.add_subplot(1, 2, 1, projection='3d')\n",
"ax2 = fig.add_subplot(1, 2, 2, projection='3d')\n",
"ax1.set_title(\"Input planes\")\n",
"ax2.set_title(\"Output planes\")\n",
"\n",
"rects = defaultdict(list)\n",
"for z in np.linspace(0, 1, 10):\n",
" for ax in [ax1, ax2]:\n",
" p = Rectangle((0, 0), 1, 1, facecolor='white', edgecolor='black', alpha=0.7)\n",
" ax.add_patch(p)\n",
" rects[ax].append(p)\n",
" art3d.pathpatch_2d_to_3d(p, z=z, zdir=\"z\")\n",
"\n",
"for ax in [ax1, ax2]:\n",
" ax.axis('off')\n",
"\n",
"z = 3\n",
"def update(frame):\n",
" for ax in [ax1, ax2]:\n",
" for rect in rects[ax]:\n",
" rect.set_facecolor('white')\n",
" for rect in rects[ax1][frame:frame+z]:\n",
" rect.set_facecolor('tab:blue')\n",
" rects[ax2][frame+z//2].set_facecolor('tab:red')\n",
" \n",
"ani = animation.FuncAnimation(fig=fig, func=update, frames=10 - z + 1)\n",
"with open('2d_ball_planes.html', 'w') as f:\n",
" f.write(ani.to_jshtml(fps=3, default_mode='once'))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d05e855a",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.10.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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