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stwind/cotangent_formula.ipynb

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cotangent_formula.ipynb
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"provenance": [],
"collapsed_sections": [
"kWpTRCN_SI-4",
"fjfI-a3zSN-1"
],
"machine_shape": "hm",
"authorship_tag": "ABX9TyNieGHOupr/3qa1T+GaaeBf",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/stwind/ead990e7084b0da6ba0c4a458239760c/cotangent_formula.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"source": [
"## Setup"
],
"metadata": {
"id": "Gqv4ujUnSIFH"
}
},
{
"cell_type": "markdown",
"source": [
"### Dependencies"
],
"metadata": {
"id": "kWpTRCN_SI-4"
}
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 0
},
"id": "gBOK3NnzSFKE",
"outputId": "e697300f-23e4-47fb-89d5-d5d48dae1194"
},
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m62.1/62.1 kB\u001b[0m \u001b[31m939.7 kB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
"\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m16.9/16.9 MB\u001b[0m \u001b[31m116.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
"\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m8.6/8.6 MB\u001b[0m \u001b[31m119.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
"\u001b[?25h\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
"numba 0.60.0 requires numpy<2.1,>=1.22, but you have numpy 2.3.2 which is incompatible.\n",
"tensorflow 2.18.0 requires numpy<2.1.0,>=1.26.0, but you have numpy 2.3.2 which is incompatible.\n",
"opencv-python 4.12.0.88 requires numpy<2.3.0,>=2; python_version >= \"3.9\", but you have numpy 2.3.2 which is incompatible.\n",
"cupy-cuda12x 13.3.0 requires numpy<2.3,>=1.22, but you have numpy 2.3.2 which is incompatible.\n",
"opencv-python-headless 4.12.0.88 requires numpy<2.3.0,>=2; python_version >= \"3.9\", but you have numpy 2.3.2 which is incompatible.\n",
"opencv-contrib-python 4.12.0.88 requires numpy<2.3.0,>=2; python_version >= \"3.9\", but you have numpy 2.3.2 which is incompatible.\u001b[0m\u001b[31m\n",
"\u001b[0m"
]
}
],
"source": [
"!pip install --no-cache-dir -Uq numpy matplotlib pillow scipy einops ffmpeg-python"
]
},
{
"cell_type": "markdown",
"source": [
"#### Texlive"
],
"metadata": {
"id": "i6urytS1SXWx"
}
},
{
"cell_type": "code",
"source": [
"# https://tug.org/texlive/quickinstall.html\n",
"!wget -qc --show-progress https://mirror.ctan.org/systems/texlive/tlnet/install-tl-unx.tar.gz && tar -xzf install-tl-unx.tar.gz\n",
"# https://tug.org/texlive/doc/install-tl.html\n",
"!cd install-tl-2* && perl ./install-tl -no-gui -no-interaction -scheme scheme-minimal -no-doc-install -no-src-install -q"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 0
},
"id": "vfLeO5ENSZC3",
"outputId": "92158a70-474a-4ca0-cde7-636638471185"
},
"execution_count": 2,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"\rinstall-tl-unx.tar. 0%[ ] 0 --.-KB/s \rinstall-tl-unx.tar. 100%[===================>] 5.54M --.-KB/s in 0.05s \n",
"mktexlsr: Updating /usr/local/texlive/2025/texmf-dist/ls-R... \n",
"mktexlsr: Done.\n",
"mktexlsr: Updating /usr/local/texlive/2025/texmf-config/ls-R... \n",
"mktexlsr: Updating /usr/local/texlive/2025/texmf-dist/ls-R... \n",
"mktexlsr: Updating /usr/local/texlive/2025/texmf-var/ls-R... \n",
"mktexlsr: Done.\n",
"[01:38:01] mktexlsr: Updating /usr/local/texlive/2025/texmf-config/ls-R... \n",
"mktexlsr: Updating /usr/local/texlive/2025/texmf-var/ls-R... \n",
"mktexlsr: Done.\n",
"[01:38:01] \n",
"./install-tl: errors in installation reported above\n",
"\n",
"Logfile: /usr/local/texlive/2025/install-tl.log\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"!/usr/local/texlive/2025/bin/x86_64-linux/tlmgr install cm-super collection-latexextra dvipng dvisvgm kastrup newtx pxfonts tex-gyre-pagella newpx"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 0
},
"id": "fNTWANmlSaYC",
"outputId": "d9f62d2c-aabd-4494-f1de-12b184304966"
},
"execution_count": 3,
"outputs": [
{
"metadata": {
"tags": null
},
"name": "stdout",
"output_type": "stream",
"text": [
"tlmgr: package repository https://tw.mirrors.cicku.me/ctan/systems/texlive/tlnet (verified)\n",
"tlmgr install: package tex-gyre-pagella not present in repository.\n",
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"[203/2093, 02:18/01:52:35] install: callouts [2k]\n",
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"[205/2093, 02:20/01:54:07] install: calrsfs [1k]\n",
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"[207/2093, 02:21/01:54:45] install: calxxxx-yyyy [7k]\n",
"[208/2093, 02:22/01:55:21] install: cancel [3k]\n",
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"[210/2093, 02:23/01:55:59] install: capt-of [2k]\n",
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"[215/2093, 02:26/01:56:08] install: carlisle [9k]\n",
"[216/2093, 02:27/01:56:40] install: cases [4k]\n",
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"[219/2093, 02:30/01:58:38] install: catchfilebetweentags [2k]\n",
"[220/2093, 02:31/01:59:22] install: catechis [2k]\n",
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"[222/2093, 02:32/01:58:53] install: catppuccinpalette [4k]\n",
"[223/2093, 02:33/01:59:33] install: cbcoptic [99k]\n",
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"[226/2093, 02:35/01:57:45] install: cd [5k]\n",
"[227/2093, 02:36/01:58:23] install: cd-cover [4k]\n",
"[228/2093, 02:36/01:58:15] install: cdcmd [4k]\n",
"[229/2093, 02:37/01:58:54] install: cdpbundl [19k]\n",
"[230/2093, 02:38/01:59:05] install: cellprops [7k]\n",
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"[234/2093, 02:40/02:00:05] install: centeredline [2k]\n",
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"[242/2093, 02:47/02:04:24] install: chapterfolder [2k]\n",
"[243/2093, 02:47/02:04:21] install: cheatsheet [3k]\n",
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"[248/2093, 02:51/02:05:59] install: childdoc [2k]\n",
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"[250/2093, 02:52/02:06:39] install: chletter [4k]\n",
"[251/2093, 02:53/02:07:16] install: chngcntr [3k]\n",
"[252/2093, 02:54/02:07:56] install: chronology [2k]\n",
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"[254/2093, 02:55/02:07:24] install: circ [24k]\n",
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"[256/2093, 02:57/02:08:03] install: circledtext [7k]\n",
"[257/2093, 02:57/02:07:50] install: circuit-macros [2k]\n",
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"[261/2093, 03:00/02:02:50] install: cite [20k]\n",
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"[268/2093, 03:05/02:04:23] install: clicks [2k]\n",
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"[270/2093, 03:06/02:04:59] install: clistmap [6k]\n",
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"[272/2093, 03:08/02:06:05] install: clrdblpg [2k]\n",
"[273/2093, 03:09/02:06:43] install: clrstrip [2k]\n",
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"[275/2093, 03:16/08:21] install: cmap [6k]\n",
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"[278/2093, 03:18/08:26] install: cmsd [2k]\n",
"[279/2093, 03:19/08:29] install: cnltx [35k]\n",
"[280/2093, 03:19/08:29] install: cntformats [3k]\n",
"[281/2093, 03:20/08:31] install: cntperchap [4k]\n",
"[282/2093, 03:20/08:31] install: codebox [4k]\n",
"[283/2093, 03:21/08:34] install: codedescribe [14k]\n",
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"[285/2093, 03:22/08:36] install: codehigh [7k]\n",
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"[287/2093, 03:23/08:39] install: codesection [3k]\n",
"[288/2093, 03:24/08:41] install: coffeestains [85k]\n",
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"[290/2093, 03:26/08:46] install: collectbox [3k]\n",
"[291/2093, 03:27/08:48] install: colophon [2k]\n",
"[292/2093, 03:27/08:48] install: color-edits [2k]\n",
"[293/2093, 03:28/08:51] install: colorblind [4k]\n",
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"[295/2093, 03:29/08:53] install: coloredbelts [25k]\n",
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"[303/2093, 03:34/09:05] install: colorwav [2k]\n",
"[304/2093, 03:35/09:08] install: colorweb [3k]\n",
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"[306/2093, 03:36/09:10] install: combelow [2k]\n",
"[307/2093, 03:37/09:13] install: combine [11k]\n",
"[308/2093, 03:38/09:15] install: combinedgraphics [4k]\n",
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"[310/2093, 03:39/09:18] install: commado [3k]\n",
"[311/2093, 03:40/09:21] install: commalists-tools [2k]\n",
"[312/2093, 03:41/09:23] install: commedit [4k]\n",
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"[314/2093, 03:42/09:26] install: commonunicode [6k]\n",
"[315/2093, 03:42/09:26] install: competences [3k]\n",
"[316/2093, 03:43/09:28] install: concepts [7k]\n",
"[317/2093, 03:44/09:31] install: concprog [5k]\n",
"[318/2093, 03:44/09:30] install: conditext [7k]\n",
"[319/2093, 03:45/09:33] install: constants [3k]\n",
"[320/2093, 03:46/09:36] install: continue [3k]\n",
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"[323/2093, 03:48/09:41] install: conv-xkv [3k]\n",
"[324/2093, 03:48/09:41] install: cooking [2k]\n",
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"[333/2093, 03:54/09:55] install: coordsys [5k]\n",
"[334/2093, 03:54/09:55] install: copyedit [4k]\n",
"[335/2093, 03:55/09:58] install: copyrightbox [2k]\n",
"[336/2093, 03:55/09:58] install: coseoul [1k]\n",
"[337/2093, 03:56/10:00] install: count1to [2k]\n",
"[338/2093, 03:57/10:03] install: counterz [3k]\n",
"[339/2093, 03:57/10:03] install: counttexruns [1k]\n",
"[340/2093, 03:58/10:05] install: courseoutline [4k]\n",
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"[343/2093, 04:00/10:10] install: cprotect [3k]\n",
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"[345/2093, 04:01/10:13] install: crbox [2k]\n",
"[346/2093, 04:02/10:15] install: create-theorem [16k]\n",
"[347/2093, 04:03/10:18] install: creationboites [3k]\n",
"[348/2093, 04:03/10:18] install: crefthe [5k]\n",
"[349/2093, 04:04/10:20] install: crop [5k]\n",
"[350/2093, 04:04/10:20] install: crossreference [2k]\n",
"[351/2093, 04:05/10:23] install: crossreftools [4k]\n",
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"[353/2093, 04:06/10:25] install: csquotes [18k]\n",
"[354/2093, 04:07/10:28] install: css-colors [3k]\n",
"[355/2093, 04:08/10:30] install: csvmerge [3k]\n",
"[356/2093, 04:09/10:33] install: csvsimple [12k]\n",
"[357/2093, 04:09/10:33] install: ctable [4k]\n",
"[358/2093, 04:10/10:35] install: cuisine [3k]\n",
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"[360/2093, 04:11/10:38] install: currfile [4k]\n",
"[361/2093, 04:11/10:38] install: curriculum-vitae [2k]\n",
"[362/2093, 04:12/10:40] install: currvita [3k]\n",
"[363/2093, 04:13/10:43] install: curve [7k]\n",
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"[365/2093, 04:14/10:45] install: curves [6k]\n",
"[366/2093, 04:14/10:45] install: customenvs [222k]\n",
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"[368/2093, 04:15/10:45] install: cv [1k]\n",
"[369/2093, 04:16/10:48] install: cv4tw [6k]\n",
"[370/2093, 04:17/10:50] install: cweb-latex [36k]\n",
"[371/2093, 04:18/10:53] install: cyber [4k]\n",
"[372/2093, 04:18/10:53] install: cybercic [3k]\n",
"[373/2093, 04:19/10:55] install: darkmode [2k]\n",
"[374/2093, 04:20/10:58] install: dashbox [2k]\n",
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"[378/2093, 04:22/11:03] install: dataref [8k]\n",
"[379/2093, 04:23/11:05] install: datatool [160k]\n",
"[380/2093, 04:24/11:06] install: datatool-english [8k]\n",
"[381/2093, 04:25/11:08] install: datatool-regions [7k]\n",
"[382/2093, 04:25/11:08] install: datax [2k]\n",
"[383/2093, 04:26/11:11] install: dateiliste [5k]\n",
"[384/2093, 04:26/11:11] install: datenumber [4k]\n",
"[385/2093, 04:27/11:13] install: datestamp [2k]\n",
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"[392/2093, 04:31/11:23] install: datetime2-catalan [3k]\n",
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"[394/2093, 04:33/11:28] install: datetime2-czech [3k]\n",
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"[396/2093, 04:34/11:31] install: datetime2-dutch [3k]\n",
"[397/2093, 04:35/11:33] install: datetime2-en-fulltext [3k]\n",
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"[399/2093, 04:36/11:35] install: datetime2-esperanto [3k]\n",
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"[404/2093, 04:39/11:43] install: datetime2-german [4k]\n",
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"[408/2093, 04:41/11:48] install: datetime2-irish [3k]\n",
"[409/2093, 04:42/11:50] install: datetime2-it-fulltext [4k]\n",
"[410/2093, 04:43/11:53] install: datetime2-italian [3k]\n",
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"[412/2093, 04:45/11:58] install: datetime2-lsorbian [3k]\n",
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"[417/2093, 04:47/12:03] install: datetime2-romanian [3k]\n",
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"[427/2093, 04:53/12:18] install: datetime2-ukrainian [4k]\n",
"[428/2093, 04:53/12:17] install: datetime2-usorbian [3k]\n",
"[429/2093, 04:54/12:20] install: datetime2-welsh [3k]\n",
"[430/2093, 04:55/12:22] install: dblfloatfix [3k]\n",
"[431/2093, 04:55/12:22] install: dbshow [7k]\n",
"[432/2093, 04:56/12:25] install: dcpic [14k]\n",
"[433/2093, 04:56/12:25] install: debate [2k]\n",
"[434/2093, 04:57/12:27] install: decimal [2k]\n",
"[435/2093, 04:57/12:27] install: decimalcomma [2k]\n",
"[436/2093, 04:58/12:30] install: decorule [2k]\n",
"[437/2093, 04:59/12:32] install: defoldfonts [2k]\n",
"[438/2093, 05:00/12:35] install: delimtxt [2k]\n",
"[439/2093, 05:01/12:37] install: democodetools [8k]\n",
"[440/2093, 05:01/12:37] install: denisbdoc [16k]\n",
"[441/2093, 05:02/12:39] install: diabetes-logbook [7k]\n",
"[442/2093, 05:03/12:42] install: diagbox [4k]\n",
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"[444/2093, 05:04/12:44] install: diagnose [1k]\n",
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"[447/2093, 05:06/12:49] install: didactic [5k]\n",
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"[452/2093, 05:10/12:59] install: dirtytalk [2k]\n",
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"[455/2093, 05:12/13:03] install: dnaseq [2k]\n",
"[456/2093, 05:13/13:06] install: doc-pictex [1k]\n",
"[457/2093, 05:14/13:08] install: doclicense [232k]\n",
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"[460/2093, 05:16/13:11] install: docshots [3k]\n",
"[461/2093, 05:17/13:13] install: doctools [6k]\n",
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"[463/2093, 05:19/13:18] install: docutils [3k]\n",
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"[471/2093, 05:23/13:28] install: download [2k]\n",
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"[473/2093, 05:25/13:33] install: dpcircling [3k]\n",
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"[648/2093, 07:27/17:00] install: fig4latex.x86_64-linux [1k]\n",
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"[1451/2093, 16:42/19:01] install: practicalreports [2k]\n",
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"[1490/2093, 17:10/19:26] install: pynotebook [4k]\n",
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"[1553/2093, 17:54/20:00] install: romanbar [3k]\n",
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"[1940/2093, 22:24/23:13] install: uassign [2k]\n",
"[1941/2093, 22:25/23:14] install: ucharcat [2k]\n",
"[1942/2093, 22:26/23:16] install: ucs [302k]\n",
"[1943/2093, 22:27/23:14] install: uebungsblatt [4k]\n",
"[1944/2093, 22:27/23:14] install: ulem [7k]\n",
"[1945/2093, 22:27/23:14] install: ullrcorners [2k]\n",
"[1946/2093, 22:28/23:15] install: umoline [3k]\n",
"[1947/2093, 22:29/23:16] install: underlin [2k]\n",
"[1948/2093, 22:30/23:17] install: underoverlap [4k]\n",
"[1949/2093, 22:30/23:17] install: underscore [5k]\n",
"[1950/2093, 22:31/23:18] install: undolabl [3k]\n",
"[1951/2093, 22:32/23:19] install: uni-titlepage [11k]\n",
"[1952/2093, 22:33/23:20] install: unicode-math [42k]\n",
"[1953/2093, 22:33/23:20] install: unicode-math-input [17k]\n",
"[1954/2093, 22:34/23:20] install: unicodefonttable [8k]\n",
"[1955/2093, 22:35/23:21] install: unifront [3k]\n",
"[1956/2093, 22:35/23:21] install: uniquecounter [3k]\n",
"[1957/2093, 22:36/23:22] install: unisc [3k]\n",
"[1958/2093, 22:37/23:23] install: unitconv [2k]\n",
"[1959/2093, 22:37/23:23] install: units [2k]\n",
"[1960/2093, 22:38/23:24] install: unravel [30k]\n",
"[1961/2093, 22:39/23:25] install: updatemarks [6k]\n",
"[1962/2093, 22:39/23:25] install: upmethodology [32k]\n",
"[1963/2093, 22:40/23:26] install: upquote [2k]\n",
"[1964/2093, 22:41/23:27] install: uri [4k]\n",
"[1965/2093, 22:41/23:27] install: url [6k]\n",
"[1966/2093, 22:42/23:28] install: useclass [2k]\n",
"[1967/2093, 22:43/23:29] install: ushort [2k]\n",
"[1968/2093, 22:43/23:29] install: uspace [2k]\n",
"[1969/2093, 22:44/23:30] install: utf8add [5k]\n",
"[1970/2093, 22:45/23:31] install: utfsym [1846k]\n",
"[1971/2093, 22:46/23:17] install: uwmslide [4k]\n",
"[1972/2093, 22:46/23:17] install: variablelm [4k]\n",
"[1973/2093, 22:47/23:18] install: varindex [7k]\n",
"[1974/2093, 22:48/23:18] install: varsfromjobname [2k]\n",
"[1975/2093, 22:48/23:18] install: varwidth [5k]\n",
"[1976/2093, 22:49/23:19] install: vcell [2k]\n",
"[1977/2093, 22:50/23:20] install: vdmlisting [3k]\n",
"[1978/2093, 22:50/23:20] install: vectorlogos [334k]\n",
"[1979/2093, 22:51/23:19] install: venndiagram [5k]\n",
"[1980/2093, 22:52/23:20] install: verbasef [5k]\n",
"[1981/2093, 22:53/23:21] install: verbatimbox [4k]\n",
"[1982/2093, 22:54/23:22] install: verbatimcopy [3k]\n",
"[1983/2093, 22:54/23:22] install: verbdef [2k]\n",
"[1984/2093, 22:55/23:23] install: verbments [3k]\n",
"[1985/2093, 22:55/23:23] install: verifiche [6k]\n",
"[1986/2093, 22:56/23:24] install: verifycommand [3k]\n",
"[1987/2093, 22:57/23:25] install: version [3k]\n",
"[1988/2093, 22:58/23:26] install: versions [6k]\n",
"[1989/2093, 22:58/23:26] install: versonotes [3k]\n",
"[1990/2093, 22:59/23:27] install: vertbars [2k]\n",
"[1991/2093, 22:59/23:27] install: vgrid [2k]\n",
"[1992/2093, 23:00/23:28] install: vhistory [9k]\n",
"[1993/2093, 23:00/23:28] install: visualpstricks [1k]\n",
"[1994/2093, 23:01/23:29] install: vmargin [3k]\n",
"[1995/2093, 23:02/23:30] install: volumes [3k]\n",
"[1996/2093, 23:03/23:31] install: vpe.x86_64-linux [1k]\n",
"[1997/2093, 23:04/23:32] install: vpe [8k]\n",
"[1998/2093, 23:04/23:31] install: vruler [6k]\n",
"[1999/2093, 23:05/23:32] install: vtable [4k]\n",
"[2000/2093, 23:06/23:33] install: vwcol [4k]\n",
"[2001/2093, 23:06/23:33] install: wallcalendar [26k]\n",
"[2002/2093, 23:07/23:34] install: wallpaper [2k]\n",
"[2003/2093, 23:08/23:35] install: warning [2k]\n",
"[2004/2093, 23:09/23:36] install: warpcol [2k]\n",
"[2005/2093, 23:09/23:36] install: was [2k]\n",
"[2006/2093, 23:10/23:37] install: webquiz.x86_64-linux [1k]\n",
"[2007/2093, 23:11/23:38] install: webquiz [47k]\n",
"[2008/2093, 23:11/23:38] install: whatsnote [6k]\n",
"[2009/2093, 23:12/23:39] install: wheelchart [18k]\n",
"[2010/2093, 23:13/23:40] install: widetable [2k]\n",
"[2011/2093, 23:13/23:40] install: widows-and-orphans [3k]\n",
"[2012/2093, 23:14/23:41] install: williams [3k]\n",
"[2013/2093, 23:15/23:42] install: willowtreebook [7k]\n",
"[2014/2093, 23:15/23:42] install: withargs [6k]\n",
"[2015/2093, 23:16/23:43] install: wordcloud [7k]\n",
"[2016/2093, 23:17/23:44] install: wordcount.x86_64-linux [1k]\n",
"[2017/2093, 23:17/23:44] install: wordcount [5k]\n",
"[2018/2093, 23:18/23:45] install: wordlike [2k]\n",
"[2019/2093, 23:19/23:46] install: worksheet [4k]\n",
"[2020/2093, 23:20/23:47] install: worldflags [2027k]\n",
"[2021/2093, 23:22/23:32] install: wrapfig [10k]\n",
"[2022/2093, 23:23/23:33] install: wrapfig2 [7k]\n",
"[2023/2093, 23:24/23:34] install: wrapstuff [12k]\n",
"[2024/2093, 23:24/23:33] install: writeongrid [6k]\n",
"[2025/2093, 23:25/23:34] install: wtref [3k]\n",
"[2026/2093, 23:25/23:34] install: xargs [4k]\n",
"[2027/2093, 23:26/23:35] install: xassoccnt [20k]\n",
"[2028/2093, 23:27/23:36] install: xbmks [5k]\n",
"[2029/2093, 23:27/23:36] install: xcntperchap [4k]\n",
"[2030/2093, 23:28/23:37] install: xcolor [18k]\n",
"[2031/2093, 23:29/23:38] install: xcolor-material [5k]\n",
"[2032/2093, 23:29/23:38] install: xcolor-solarized [2k]\n",
"[2033/2093, 23:30/23:39] install: xcomment [3k]\n",
"[2034/2093, 23:31/23:40] install: xcookybooky [7k]\n",
"[2035/2093, 23:31/23:40] install: xcpdftips [4k]\n",
"[2036/2093, 23:32/23:41] install: xdoc [12k]\n",
"[2037/2093, 23:33/23:42] install: xellipsis [2k]\n",
"[2038/2093, 23:33/23:42] install: xfakebold [2k]\n",
"[2039/2093, 23:34/23:43] install: xfor [2k]\n",
"[2040/2093, 23:35/23:44] install: xfrac [4k]\n",
"[2041/2093, 23:36/23:45] install: xhfill [2k]\n",
"[2042/2093, 23:37/23:46] install: xifthen [3k]\n",
"[2043/2093, 23:37/23:46] install: ximera [15k]\n",
"[2044/2093, 23:38/23:47] install: xint [80k]\n",
"[2045/2093, 23:39/23:47] install: xint-regression [4k]\n",
"[2046/2093, 23:39/23:47] install: xistercian [5k]\n",
"[2047/2093, 23:40/23:48] install: xkcdcolors [9k]\n",
"[2048/2093, 23:41/23:49] install: xkeymask [2k]\n",
"[2049/2093, 23:42/23:50] install: xkeyval [9k]\n",
"[2050/2093, 23:42/23:50] install: xltabular [3k]\n",
"[2051/2093, 23:43/23:51] install: xltxtra [3k]\n",
"[2052/2093, 23:44/23:52] install: xmpincl [2k]\n",
"[2053/2093, 23:45/23:53] install: xnewcommand [1k]\n",
"[2054/2093, 23:45/23:53] install: xoptarg [2k]\n",
"[2055/2093, 23:46/23:54] install: xpatch [2k]\n",
"[2056/2093, 23:47/23:55] install: xpeek [2k]\n",
"[2057/2093, 23:48/23:56] install: xpicture [9k]\n",
"[2058/2093, 23:49/23:57] install: xprintlen [2k]\n",
"[2059/2093, 23:49/23:57] install: xpunctuate [2k]\n",
"[2060/2093, 23:50/23:58] install: xreview [2k]\n",
"[2061/2093, 23:51/23:59] install: xsavebox [5k]\n",
"[2062/2093, 23:51/23:59] install: xsim [32k]\n",
"[2063/2093, 23:52/23:59] install: xsipa [5k]\n",
"[2064/2093, 23:52/23:59] install: xstring [12k]\n",
"[2065/2093, 23:53/24:00] install: xtab [5k]\n",
"[2066/2093, 23:54/24:01] install: xunicode [26k]\n",
"[2067/2093, 23:55/24:02] install: xurl [2k]\n",
"[2068/2093, 23:56/24:03] install: xwatermark [17k]\n",
"[2069/2093, 23:57/24:04] install: xypic [694k]\n",
"[2070/2093, 23:58/23:59] install: xytree [4k]\n",
"[2071/2093, 23:59/24:00] install: yafoot [4k]\n",
"[2072/2093, 23:59/24:00] install: yagusylo [6k]\n",
"[2073/2093, 24:00/24:01] install: yaletter [4k]\n",
"[2074/2093, 24:00/24:01] install: ycbook [5k]\n",
"[2075/2093, 24:01/24:02] install: ydoc [10k]\n",
"[2076/2093, 24:02/24:03] install: yplan.x86_64-linux [1k]\n",
"[2077/2093, 24:02/24:03] install: yplan [7k]\n",
"[2078/2093, 24:03/24:04] install: zapfding [46k]\n",
"[2079/2093, 24:04/24:04] install: zebra-goodies [3k]\n",
"[2080/2093, 24:04/24:04] install: zed-csp [8k]\n",
"[2081/2093, 24:05/24:05] install: zennote [2k]\n",
"[2082/2093, 24:06/24:06] install: ziffer [2k]\n",
"[2083/2093, 24:07/24:07] install: zref [15k]\n",
"[2084/2093, 24:08/24:08] install: zref-check [6k]\n",
"[2085/2093, 24:09/24:09] install: zref-clever [26k]\n",
"[2086/2093, 24:10/24:10] install: zref-vario [5k]\n",
"[2087/2093, 24:11/24:11] install: zugferd [13k]\n",
"[2088/2093, 24:12/24:12] install: zwgetfdate [2k]\n",
"[2089/2093, 24:13/24:13] install: zwpagelayout [9k]\n",
"[2090/2093, 24:13/24:13] install: collection-latex [1k]\n",
"[2091/2093, 24:14/24:14] install: collection-latexextra [8k]\n",
"[2092/2093, 24:15/24:15] install: collection-latexrecommended [1k]\n",
"[2093/2093, 24:16/24:16] install: collection-pictures [2k]\n",
"tlmgr: action install returned an error; continuing.\n",
"running mktexlsr ...\n",
"done running mktexlsr.\n",
"running updmap-sys ...\n",
"done running updmap-sys.\n",
"regenerating language.dat\n",
"regenerating language.def\n",
"regenerating language.dat.lua\n",
"regenerating fmtutil.cnf in /usr/local/texlive/2025/texmf-dist\n",
"running fmtutil-sys --byfmt latex-dev --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: latex-dev.fmt/pdftex\n",
"running fmtutil-sys --byfmt mptopdf --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: mptopdf.fmt/pdftex\n",
"running fmtutil-sys --byfmt dvilualatex-dev --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: dvilualatex-dev.fmt/luatex\n",
"running fmtutil-sys --byfmt pdflatex-dev --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: pdflatex-dev.fmt/pdftex\n",
"running fmtutil-sys --byfmt lualatex-dev --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: lualatex-dev.fmt/luahbtex\n",
"running fmtutil-sys --byfmt pdflatex --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: pdflatex.fmt/pdftex\n",
"running fmtutil-sys --byfmt latex --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: latex.fmt/pdftex\n",
"running fmtutil-sys --byfmt lualatex --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: lualatex.fmt/luahbtex\n",
"running fmtutil-sys --byfmt dvilualatex --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: dvilualatex.fmt/luatex\n",
"running fmtutil-sys --byhyphen \"/usr/local/texlive/2025/texmf-var/tex/generic/config/language.dat\" --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: latex-dev.fmt/pdftex lualatex.fmt/luahbtex pdflatex.fmt/pdftex dvilualatex.fmt/luatex dvilualatex-dev.fmt/luatex lualatex-dev.fmt/luahbtex latex.fmt/pdftex pdflatex-dev.fmt/pdftex\n",
"running fmtutil-sys --byhyphen \"/usr/local/texlive/2025/texmf-var/tex/generic/config/language.def\" --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
" OK: luatex.fmt/luatex luahbtex.fmt/luahbtex pdftex.fmt/pdftex dviluatex.fmt/luatex pdfetex.fmt/pdftex etex.fmt/pdftex\n",
"running fmtutil-sys --byhyphen \"/usr/local/texlive/2025/texmf-var/tex/generic/config/language.dat.lua\" --no-error-if-no-engine=luametatex,luajithbtex,luajittex,mfluajit --status-file=/tmp/2EzEQH0s0C/ucz2eTQM53 ...\n",
"tlmgr: package log updated: /usr/local/texlive/2025/texmf-var/web2c/tlmgr.log\n",
"tlmgr: command log updated: /usr/local/texlive/2025/texmf-var/web2c/tlmgr-commands.log\n",
"tlmgr: An error has occurred. See above messages. Exiting.\n"
]
}
]
},
{
"cell_type": "markdown",
"source": [
"### Commons"
],
"metadata": {
"id": "fjfI-a3zSN-1"
}
},
{
"cell_type": "code",
"source": [
"%matplotlib inline\n",
"%config InlineBackend.figure_format = 'retina'\n",
"\n",
"import os\n",
"import numpy as np\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib.font_manager as fm\n",
"import locale\n",
"from fastprogress import progress_bar\n",
"from einops import rearrange, reduce, repeat, einsum\n",
"\n",
"locale.getpreferredencoding = lambda: \"UTF-8\"\n",
"\n",
"COLORS = {\n",
" \"red\": np.array([0.79215686, 0.14901961, 0.14901961]),\n",
" \"blue\": np.array([0.08683021, 0.41940383, 0.71699529]),\n",
" **{f\"gray{k:02d}\": np.array([k,k,k])*.01 for k in np.arange(5,100,5)}\n",
"}\n",
"\n",
"def mpl_theme(gray=COLORS['gray50'], stroke_width=.1, fontsize=7,\n",
" facecolor=COLORS['gray10']):\n",
" ## category20: https://github.com/d3/d3-3.x-api-reference/blob/master/Ordinal-Scales.md#category20\n",
" cat20 = mpl.cycler(color=[\"1f77b4\",\"ff7f0e\",\"2ca02c\",\"d62728\",\"9467bd\",\"8c564b\",\"e377c2\",\"7f7f7f\",\"bcbd22\",\"17becf\",\n",
" \"aec7e8\",\"ffbb78\",\"98df8a\",\"ff9896\",\"c5b0d5\",\"c49c94\",\"f7b6d2\",\"c7c7c7\", \"dbdb8d\", \"9edae5\"])\n",
" return {\n",
" \"font.size\": fontsize,\n",
" \"font.family\": \"sans-serif\",\n",
" \"text.usetex\": False,\n",
" \"text.latex.preamble\": r\"\\usepackage{newpxtext,newpxmath}\",\n",
" \"text.color\": gray,\n",
" \"mathtext.fontset\": \"cm\",\n",
"\n",
" \"figure.dpi\": 100,\n",
" \"figure.facecolor\": facecolor,\n",
" \"figure.frameon\": False,\n",
" \"figure.figsize\": (5, 3),\n",
" \"figure.titlesize\": \"large\",\n",
" \"figure.titleweight\": \"bold\",\n",
" \"figure.constrained_layout.use\": True,\n",
" \"figure.constrained_layout.w_pad\": 0.05,\n",
" \"figure.constrained_layout.h_pad\": 0.05,\n",
" \"figure.constrained_layout.wspace\": 0.03,\n",
" \"figure.constrained_layout.hspace\": 0.03,\n",
"\n",
" \"axes.labelcolor\": gray,\n",
" \"axes.labelpad\": 8,\n",
" \"axes.labelsize\": \"medium\",\n",
" \"axes.labelweight\": \"normal\",\n",
" \"axes.spines.left\": False,\n",
" \"axes.spines.bottom\": False,\n",
" \"axes.spines.top\": False,\n",
" \"axes.spines.right\": False,\n",
" \"axes.facecolor\": facecolor,\n",
" \"axes.edgecolor\": gray,\n",
" \"axes.linewidth\": stroke_width,\n",
" \"axes.axisbelow\": True,\n",
" \"axes.xmargin\": 0.02,\n",
" \"axes.ymargin\": 0.02,\n",
" \"axes.zmargin\": 0.02,\n",
" \"axes.prop_cycle\": cat20,\n",
" \"axes.titlepad\": 8,\n",
" \"axes.titlesize\": \"medium\",\n",
" \"axes.titleweight\": 500,\n",
" \"axes.grid\": True,\n",
" \"axes.grid.axis\": \"both\",\n",
"\n",
" \"axes3d.grid\": False,\n",
" \"axes3d.xaxis.panecolor\": COLORS['gray15'],\n",
" \"axes3d.yaxis.panecolor\": COLORS['gray20'],\n",
" \"axes3d.zaxis.panecolor\": COLORS['gray25'],\n",
"\n",
" \"ytick.right\": False,\n",
" \"ytick.color\": gray,\n",
" \"ytick.major.width\": stroke_width,\n",
" \"ytick.major.size\": 0,\n",
" \"ytick.minor.left\": False,\n",
" \"ytick.labelsize\": \"small\",\n",
"\n",
" \"xtick.labelsize\": \"small\",\n",
" \"xtick.minor.visible\": True,\n",
" \"xtick.minor.top\": False,\n",
" \"xtick.minor.bottom\": False,\n",
" \"xtick.color\": gray,\n",
" \"xtick.major.width\": stroke_width,\n",
" \"xtick.major.size\": 0,\n",
"\n",
" \"grid.color\": gray,\n",
" \"grid.linewidth\": stroke_width,\n",
" \"grid.linestyle\": \"-\",\n",
" \"legend.fancybox\": False,\n",
" \"legend.edgecolor\": '0.3',\n",
" \"legend.framealpha\": 0.7,\n",
" \"legend.handletextpad\": 0.8,\n",
"\n",
" \"lines.linewidth\": 0.7\n",
" }\n",
"\n",
"def mpl_add_font(fname):\n",
" if fname not in [fe.fname for fe in fm.fontManager.ttflist]:\n",
" fm.fontManager.addfont(fname)\n",
"\n",
"def setup_overpass(folder=\"fonts\"):\n",
" os.makedirs(folder, exist_ok=True)\n",
" for style in [\"Regular\", \"Italic\", \"SemiBold\", \"SemiBoldItalic\", \"Bold\", \"BoldItalic\"]:\n",
" ttf = f\"Overpass-{style}.ttf\"\n",
" !wget -qc \"https://github.com/RedHatOfficial/Overpass/raw/master/fonts/ttf/{ttf}\" -O \"{folder}/{ttf}\"\n",
" mpl_add_font(f\"{folder}/{ttf}\")\n",
" if \"Overpass\" not in mpl.rcParams['font.sans-serif']:\n",
" mpl.rcParams['font.sans-serif'].insert(0, \"Quicksand\")\n",
"\n",
"def setup_quicksand(folder=\"fonts\"):\n",
" os.makedirs(folder, exist_ok=True)\n",
" for style in [\"Bold\", \"Light\", \"Medium\", \"Regular\"]:\n",
" ttf = f\"Quicksand-{style}.ttf\"\n",
" !wget -qc \"https://github.com/andrew-paglinawan/QuicksandFamily/raw/refs/heads/master/fonts/statics/{ttf}\" -O \"{folder}/{ttf}\"\n",
" mpl_add_font(f\"{folder}/{ttf}\")\n",
" if \"Quicksand\" not in mpl.rcParams['font.sans-serif']:\n",
" mpl.rcParams['font.sans-serif'].insert(0, \"Quicksand\")\n",
"\n",
"setup_quicksand()\n",
"\n",
"plt.style.use([\"dark_background\", mpl_theme()])\n",
"\n",
"if \"/usr/local/texlive/2025/bin/x86_64-linux\" not in os.environ[\"PATH\"]:\n",
" os.environ['PATH'] = f\"{os.environ['PATH']}:/usr/local/texlive/2025/bin/x86_64-linux\""
],
"metadata": {
"id": "IXYGHK18SOly"
},
"execution_count": 1,
"outputs": []
},
{
"cell_type": "code",
"source": [
"import math\n",
"import sys\n",
"import io\n",
"import bz2\n",
"import ffmpeg\n",
"import requests\n",
"import subprocess\n",
"import cv2\n",
"import PIL\n",
"import IPython.display as ipd\n",
"import ipywidgets as widgets\n",
"from scipy import linalg\n",
"from fastprogress import progress_bar\n",
"from einops import rearrange, reduce, repeat\n",
"from base64 import b64encode\n",
"from zipfile import ZipFile\n",
"from contextlib import contextmanager\n",
"from matplotlib.patches import Circle\n",
"from mpl_toolkits.mplot3d.art3d import Line3DCollection, Poly3DCollection\n",
"\n",
"class Output(object):\n",
" def __init__(self):\n",
" self.out = widgets.Output()\n",
"\n",
" def display(self):\n",
" display(self.out)\n",
" return self\n",
"\n",
" def clear(self):\n",
" self.out.clear_output()\n",
" return self.out\n",
"\n",
" def close(self):\n",
" return self.out.close()\n",
"\n",
"def to_single_rgb(img):\n",
" img = np.asarray(img)\n",
" if len(img.shape) == 4: # take first frame from animations\n",
" return img[0,:,:,:]\n",
" if len(img.shape) == 2: # convert gray to rgb\n",
" return img[:,:,np.newaxis].repeat(3, 2)\n",
" if img.shape[-1] == 4: # drop alpha\n",
" return img[:,:,:3]\n",
" else:\n",
" return img\n",
"\n",
"def imread(url, size=None, mode=None):\n",
" if url.startswith(('http:', 'https:')):\n",
" resp = requests.get(url)\n",
" if resp.status_code != 200:\n",
" return None\n",
"\n",
" f = io.BytesIO(resp.content)\n",
" else:\n",
" f = url\n",
" img = PIL.Image.open(f)\n",
" if size is not None:\n",
" img.thumbnail((size, size), PIL.Image.Resampling.LANCZOS)\n",
" if mode is not None:\n",
" img = img.convert(mode)\n",
" return img\n",
"\n",
"def imshow(img, fmt='png', retina=True, zoom=None):\n",
" if isinstance(img, str):\n",
" display(ipd.Image(filename=img, retina=retina))\n",
" return\n",
"\n",
" if len(img.shape) == 3 and img.shape[-1] == 1:\n",
" img = img.squeeze()\n",
" if img.dtype == np.float32:\n",
" img = img * 255.0\n",
" img = np.uint8(img.clip(0, 255))\n",
" if fmt in ('jpeg', 'jpg'):\n",
" img = to_single_rgb(img)\n",
"\n",
" image = PIL.Image.fromarray(img)\n",
" height, width = img.shape[:2]\n",
" if zoom is not None:\n",
" width *= zoom\n",
" height *= zoom\n",
" retina = zoom == 1\n",
" if zoom < 1:\n",
" image.resize((int(width), int(height)))\n",
"\n",
" data = io.BytesIO()\n",
" image.save(data, fmt)\n",
" display(ipd.Image(data=data.getvalue(),width=width, height=height,retina=retina))\n",
"\n",
"def find_rectangle(n, ratio=1):\n",
" ny = int((n / ratio) ** .5)\n",
" return ny, math.ceil(n / ny)\n",
"\n",
"def make_mosaic(imgs, nx=None, ny=None, gap=0):\n",
" n, h, w = imgs.shape[:3]\n",
" has_channels = len(imgs.shape) > 3\n",
"\n",
" if nx is None and ny is None:\n",
" ny, nx = find_rectangle(n)\n",
" elif ny is None:\n",
" ny = math.ceil(n / nx)\n",
" elif nx is None:\n",
" nx = math.ceil(n / ny)\n",
"\n",
" sh, sw = h + gap, w + gap\n",
" shape = (ny * sh - gap, nx * sw - gap)\n",
" if has_channels:\n",
" shape += (imgs.shape[-1],)\n",
"\n",
" canvas = np.zeros(shape, dtype=imgs.dtype)\n",
" for i, x in enumerate(imgs):\n",
" iy, ix = divmod(i, nx)\n",
" canvas[iy * sh:iy * sh + h, ix * sw:ix * sw + w] = x\n",
" return canvas\n",
"\n",
"def ffprobe_video(path):\n",
" probe = ffmpeg.probe(path)\n",
" return next(s for s in probe['streams'] if s['codec_type'] == 'video')\n",
"\n",
"def read_frame(path, frame_no):\n",
" cap = cv2.VideoCapture(path)\n",
" cap.set(cv2.CAP_PROP_POS_FRAMES, frame_no)\n",
" ret, frame = cap.read()\n",
" if not ret:\n",
" raise RuntimeError(f\"Faild reading frame {frame_no} from {path}\")\n",
" return cv2.cvtColor(frame, cv2.COLOR_BGR2RGB)\n",
"\n",
"def read_frames(path, start=0, num=None):\n",
" cap = cv2.VideoCapture(path)\n",
" n_frames = num or int(cap.get(cv2.CAP_PROP_FRAME_COUNT))\n",
" cap.set(cv2.CAP_PROP_POS_FRAMES, start)\n",
" for i in range(n_frames):\n",
" ret, frame = cap.read()\n",
" if not ret:\n",
" raise RuntimeError(f\"Faild reading frame {i} from {path}\")\n",
" yield cv2.cvtColor(frame, cv2.COLOR_BGR2RGB)\n",
"\n",
"def read_video_frames(path):\n",
" info = ffprobe_video(path)\n",
" out, _ = ffmpeg.input(path).output('pipe:', format='rawvideo', pix_fmt='rgb24').run(capture_stdout=True)\n",
" return np.frombuffer(out, np.uint8).reshape([-1, info['height'], info['width'], 3])\n",
"\n",
"def show_video(path):\n",
" vcap = cv2.VideoCapture(path)\n",
" width = int(vcap.get(cv2.CAP_PROP_FRAME_WIDTH))\n",
" with open(path, \"r+b\") as f:\n",
" url = f\"data:video/mp4;base64,{b64encode(f.read()).decode()}\"\n",
" return ipd.HTML(f\"\"\"<video autoplay=\"autoplay\" width={width} controls loop><source src=\"{url}\"></video>\"\"\")\n",
"\n",
"def write_video(frames, size, path=\"__temp__.mp4\", fps=30,\n",
" preset=\"veryfast\", args=[]):\n",
" height, width = size\n",
" command = ['ffmpeg','-v','error','-f','rawvideo','-vcodec','rawvideo',\n",
" '-pix_fmt','rgb24','-s',f'{width}x{height}','-r', f'{fps}',\n",
" '-i', '-',\n",
" \"-movflags\", \"+faststart\", \"-preset\", preset,\n",
" \"-g\", \"30\", \"-bf\",\"2\",\"-c:v\", \"libx264\",\"-profile:v\", \"high\",\n",
" '-an', '-vcodec','h264','-pix_fmt','yuv420p', *args, '-y', path]\n",
" with subprocess.Popen(command, stdin=subprocess.PIPE, stderr=subprocess.PIPE) as proc:\n",
" with proc.stdin as stdin:\n",
" for image in frames:\n",
" data = image.tobytes()\n",
" if stdin.write(data) != len(data):\n",
" proc.wait()\n",
" stderr = proc.stderr\n",
" assert stderr is not None\n",
" s = stderr.read().decode()\n",
" raise RuntimeError(f\"Error writing '{path}': {s}\")\n",
" return path\n",
"\n",
"def read_video(path):\n",
" command = ['ffmpeg','-v','error','-nostdin','-i',path,'-vcodec','rawvideo',\n",
" '-f','image2pipe','-pix_fmt','rgb24','-vsync','vfr','-']\n",
"\n",
" info = ffprobe_video(path)\n",
" num_bytes = info['height'] * info['width'] * 3 * np.dtype(np.uint8).itemsize\n",
" with subprocess.Popen(command, stdout=subprocess.PIPE, stderr=subprocess.PIPE) as proc:\n",
" stdout = proc.stdout\n",
" assert stdout is not None\n",
" data = stdout.read(num_bytes)\n",
" while data is not None and len(data) == num_bytes:\n",
" image = np.frombuffer(data, dtype=np.uint8)\n",
" yield image.reshape(info['height'], info['width'], 3)\n",
" data = stdout.read(num_bytes)\n",
"\n",
"def sdiv(a, b, nan=0, posinf=0, neginf=0):\n",
" return np.nan_to_num(a / b, nan=nan, posinf=posinf, neginf=neginf)\n",
"\n",
"def topk(x, n):\n",
" return np.argpartition(x, -n)[-n:]\n",
"\n",
"def norm(x, a, b, **kw):\n",
" return sdiv(x - a, b - a, **kw)\n",
"\n",
"def norm_v(x, axis=None, **kw):\n",
" return norm(x, x.min(axis, keepdims=True), x.max(axis, keepdims=True), **kw)\n",
"\n",
"def normalize(x, keepdims=True, axis=-1, **kw):\n",
" return sdiv(x, np.linalg.norm(x, keepdims=keepdims, axis=axis), **kw)\n",
"\n",
"def nudge(x, v=0, eps=1e-12):\n",
" return np.where(np.isclose(np.abs(x), v, atol=eps), np.where(x - v >= 0, eps, -eps), x)\n",
"\n",
"def linspace_m(start, stop, n):\n",
" return np.linspace(start, stop, n, endpoint=False) + (stop - start) * .5 / n\n",
"\n",
"def indices_m(dims, shape, dtype=\"u4\"):\n",
" return tuple(np.meshgrid(*[np.round(linspace_m(0, d, s)).astype(dtype)\n",
" for d, s in zip(dims, shape)],\n",
" indexing='ij'))\n",
"\n",
"def rot90(v, axis=-1):\n",
" return np.stack((-v.take(1,axis),v.take(0,axis)),axis)\n",
"\n",
"def rot2d(vs, rs, axis=-1):\n",
" c, s = np.cos(rs), np.sin(rs)\n",
" x, y = vs.take(0, axis), vs.take(1, axis)\n",
" return np.stack((x * c - y * s, x * s + y * c), axis)\n",
"\n",
"def atan2(x, axis=-1):\n",
" return np.atan2(x.take(1,axis), x.take(0,axis))\n",
"\n",
"def saturate(x):\n",
" return np.clip(x, 0, 1)\n",
"\n",
"def lerp(a, b, t):\n",
" return a * (1.0 - t) + b * t\n",
"\n",
"def step(v, x):\n",
" return np.where(x < v, 0, 1)\n",
"\n",
"def window(x, a, b):\n",
" return step(a, x) * step(x, b)\n",
"\n",
"def satnorm(x, a, b):\n",
" return saturate(norm(x, a, b))\n",
"\n",
"def smoothstep(x):\n",
" return x * x * (3 - 2 * x)\n",
"\n",
"def smootherstep(x):\n",
" return x * x * x * (x * (x * 6 - 15) + 10)\n",
"\n",
"def dot(a, b, axis=-1, **kw):\n",
" return (a * b).sum(axis, **kw)\n",
"\n",
"def cross(a, b, axis=-1):\n",
" return a.take(0, axis) * b.take(1, axis) - a.take(1, axis) * b.take(0, axis)\n",
"\n",
"def cubic(a, b, c, d, t):\n",
" \"\"\"https://www.desmos.com/calculator/waof4r6avv\"\"\"\n",
" s = 1. - t\n",
" return s * s * (s * a + 3 * t * b) + t * t * (3 * s * c + t * d)\n",
"\n",
"def plt_show(pin=mpl.rcParams['savefig.pad_inches']):\n",
" with plt.rc_context({'savefig.pad_inches': pin}):\n",
" plt.show()\n",
"\n",
"def fig_image(fig=None, transparent=False, bbox_inches=None,\n",
" dpi=mpl.rcParams[\"figure.dpi\"]*2):\n",
" fig = fig or plt.gcf()\n",
"\n",
" buf = io.BytesIO()\n",
" fig.savefig(buf, format=\"png\", pad_inches=0, bbox_inches=bbox_inches,\n",
" facecolor=fig.get_facecolor(), dpi=dpi,transparent=transparent)\n",
" buf.seek(0)\n",
" data = np.frombuffer(buf.getvalue(), dtype=np.uint8)\n",
" buf.close()\n",
" plt.close(fig)\n",
"\n",
" code = cv2.COLOR_BGRA2RGBA if transparent else cv2.COLOR_BGR2RGB\n",
" return cv2.cvtColor(cv2.imdecode(data, cv2.IMREAD_UNCHANGED), code)\n",
"\n",
"def plt_savefig(name, pad_inches=mpl.rcParams['savefig.pad_inches'],\n",
" bbox_inches=0,facecolor='auto',\n",
" dpi=mpl.rcParams[\"figure.dpi\"]*2,close=True,**kw):\n",
" plt.savefig(name,\n",
" pad_inches=pad_inches,\n",
" bbox_inches=bbox_inches,\n",
" facecolor=facecolor,\n",
" dpi=dpi,**kw)\n",
" if close:\n",
" plt.close()\n",
"\n",
"class Flex(object):\n",
" def __init__(self, ratios, gap, size=None):\n",
" n, s = len(ratios), sum(ratios)\n",
" self.ratios = ratios\n",
" self.gap = gap\n",
" space = gap * n / s if size is None else gap * n / (size - gap * (n - 1))\n",
" self.h = dict(nrows=1, ncols=n, width_ratios=ratios, wspace=space)\n",
" self.v = dict(nrows=n, ncols=1, height_ratios=ratios, hspace=space)\n",
" self.size = s + gap * (n - 1) if size is None else size\n",
"\n",
"def ax_lim(mn, mx, ax=None):\n",
" ax = ax or plt.gca()\n",
" ax.set_xlim(mn[0], mx[0])\n",
" ax.set_ylim(mn[1], mx[1])\n",
" if len(mn) > 2:\n",
" ax.set_zlim(mn[2], mx[2])\n",
"\n",
"def ax_spines(sides=[\"left\",\"right\",\"bottom\",\"top\"], ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" ax.spines[sides].set(**kw)\n",
"\n",
"def ax_lines(lines, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" ax.add_collection(mpl.collections.LineCollection(lines,**kw))\n",
"\n",
"def ax_text(p, text, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" ax.text(p[0],p[1],text,**kw)\n",
"\n",
"def ax_line3d(lines, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" return ax.add_collection(Line3DCollection(lines, **kw))\n",
"\n",
"def ax_poly3d(verts, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" return ax.add_collection(Poly3DCollection(verts, **kw))\n",
"\n",
"def ax_trisurf(v, f, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" ax.plot_trisurf(v[:,0],v[:,1],v[:,2],triangles=f, **kw)\n",
"\n",
"def ax_box2(mn, mx, ax=None):\n",
" ax = ax or plt.gca()\n",
" ax.set(xlim=(mn[0],mx[0]),ylim=(mn[1],mx[1]),aspect='equal')\n",
"\n",
"def ax_box3(mn, mx, ax=None):\n",
" ax = ax or plt.gca()\n",
" ax.set(xlim=(mn[0],mx[0]),ylim=(mn[1],mx[1]),zlim=(mn[2],mx[2]),box_aspect=mx-mn)\n",
"\n",
"def ax_axis_lines(ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" ax.xaxis.line.set(**kw)\n",
" ax.yaxis.line.set(**kw)\n",
" ax.zaxis.line.set(**kw)\n",
"\n",
"def ax_scatter(pts, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" return ax.scatter(*[pts[...,i] for i in range(pts.shape[-1])], **kw)\n",
"\n",
"def ax_swatch(cols, size=32, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" ax.imshow(repeat(cols, \"n ...->h (n w) ...\",h=size,w=size), **kw)\n",
"\n",
"def ax_texts(pts, texts, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" for p, t in zip(pts, texts):\n",
" ax.text(p[0], p[1], t, **kw)\n",
"\n",
"def ax_circle(c, r, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" return ax.add_patch(Circle(c, r, **kw))\n",
"\n",
"def lowess(x, y, f=2. / 3., iter=3):\n",
" \"\"\"https://gist.github.com/agramfort/850437\n",
" lowess(x, y, f=2./3., iter=3) -> yest\n",
" Lowess smoother: Robust locally weighted regression.\n",
" The lowess function fits a nonparametric regression curve to a scatterplot.\n",
" The arrays x and y contain an equal number of elements; each pair\n",
" (x[i], y[i]) defines a data point in the scatterplot. The function returns\n",
" the estimated (smooth) values of y.\n",
" The smoothing span is given by f. A larger value for f will result in a\n",
" smoother curve. The number of robustifying iterations is given by iter. The\n",
" function will run faster with a smaller number of iterations.\n",
" \"\"\"\n",
" n = len(x)\n",
" r = int(math.ceil(f * n))\n",
" h = [np.sort(np.abs(x - x[i]))[r] for i in range(n)]\n",
" w = np.clip(np.abs((x[:, None] - x[None, :]) / h), 0.0, 1.0)\n",
" w = (1 - w ** 3) ** 3\n",
" yest = np.zeros(n)\n",
" delta = np.ones(n)\n",
" for iteration in range(iter):\n",
" for i in range(n):\n",
" weights = delta * w[:, i]\n",
" b = np.array([np.sum(weights * y), np.sum(weights * y * x)])\n",
" A = np.array([[np.sum(weights), np.sum(weights * x)],\n",
" [np.sum(weights * x), np.sum(weights * x * x)]])\n",
" beta = linalg.solve(A, b)\n",
" yest[i] = beta[0] + beta[1] * x[i]\n",
"\n",
" residuals = y - yest\n",
" s = np.median(np.abs(residuals))\n",
" delta = np.clip(residuals / (6.0 * s), -1, 1)\n",
" delta = (1 - delta ** 2) ** 2\n",
"\n",
" return yest\n",
"\n",
"def plot_metrics(metrics, groups=None, title=\"Metrics\", lowess=False):\n",
" groups = groups or [list(metrics.keys())]\n",
" n = len(groups)\n",
" ny = math.ceil(n / 2)\n",
" fig = plt.figure(figsize=(8 if n > 1 else 4, 2 * ny))\n",
"\n",
" for i, group in enumerate(groups, 1):\n",
" ax = fig.add_subplot(ny, 2 if n > 1 else 1, i)\n",
" for k in group:\n",
" x, y = np.arange(len(metrics[k])), metrics[k]\n",
" alpha = max(0.3, min(1, (1000 - len(x)) / 1000))\n",
" ax.plot(x, y, alpha=alpha, label=k, marker='.', markeredgewidth=0,lw=.5,ms=5)\n",
" if np.any(np.min(y) - y[0] > (np.max(y) - np.min(y)) * 0.01):\n",
" ax.set_ylim(np.min(y), y[0])\n",
" if lowess and len(y) >= 9:\n",
" ax.plot(x, lowess(x, y, f=0.25, iter=3), linestyle='-', alpha=0.8, label=k + \".lowess\", lw=2)\n",
" ax.legend(loc='lower left')\n",
" ax.grid(axis='x')\n",
"\n",
" fig.suptitle(title)\n",
" plt.show()\n",
"\n",
"def sph2cart(sph):\n",
" az, el, r = rearrange(sph, \"... d -> d ...\")\n",
" c = np.cos(el)\n",
" return rearrange(np.stack((c * np.cos(az), c * np.sin(az), np.sin(el)) * r), \"d ... -> ... d\")\n",
"\n",
"def cart2sph(cart, axis=-1):\n",
" x, y, z = cart.take(0,axis), cart.take(1,axis), cart.take(2,axis)\n",
" az, el = np.arctan2(y, x), np.arctan2(z, np.hypot(x, y))\n",
" r = np.sqrt(x ** 2 + y ** 2 + z ** 2)\n",
" return np.stack((az, el, r), axis)\n",
"\n",
"def iter_batch(xs, bs, drop_last=True):\n",
" n = len(xs) // bs\n",
" for i in range(n):\n",
" yield xs[i*bs:(i+1)*bs]\n",
" if not drop_last:\n",
" yield xs[n*bs:]\n",
"\n",
"def unpack_bz2(src_path):\n",
" data = bz2.BZ2File(src_path).read()\n",
" dst_path = src_path[:-4]\n",
" with open(dst_path, 'wb') as fp:\n",
" fp.write(data)\n",
" return dst_path\n",
"\n",
"def make_zip(files, target, filename=os.path.basename):\n",
" with ZipFile(target, 'w') as f:\n",
" for p in files:\n",
" f.write(p, filename(p))\n",
" return target"
],
"metadata": {
"id": "_oAgoo5MSRUW"
},
"execution_count": 2,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"## Diagram"
],
"metadata": {
"id": "xtwNyPD-SPCJ"
}
},
{
"cell_type": "code",
"source": [
"from matplotlib.patheffects import withStroke\n",
"from matplotlib.patches import PathPatch, Path\n",
"\n",
"\n",
"def ax_lim_aspect(ax=None):\n",
" ax = ax or plt.gca()\n",
" xmin, xmax = ax.get_xlim()\n",
" ymin, ymax = ax.get_ylim()\n",
" return (xmax - xmin) / (ymax - ymin)\n",
"\n",
"def ax_angle(c, p1, p2, size, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" ax.figure.canvas.draw()\n",
"\n",
" bbox = ax.get_window_extent()\n",
" aspect = (1., bbox.width / bbox.height)\n",
"\n",
" c_d = ax.transData.transform(c)\n",
" v1 = (ax.transData.transform(p1) - c_d) * aspect\n",
" v2 = (ax.transData.transform(p2) - c_d) * aspect\n",
"\n",
" p = ax.transAxes.inverted().transform(ax.transData.transform(c))\n",
" ax.add_patch(mpl.patches.Arc(p, size, size * aspect[1],\n",
" theta1=np.degrees(atan2(v1)),\n",
" theta2=np.degrees(atan2(v2)),\n",
" transform=ax.transAxes, **kw))\n",
"\n",
"def ax_annotate_angle(c, p1, p2, text, size, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
"\n",
" bbox = ax.get_window_extent()\n",
" aspect = (bbox.width / bbox.height, 1)\n",
"\n",
" tf = mpl.transforms.CompositeGenericTransform(ax.transData, ax.transAxes.inverted())\n",
"\n",
" c_d = tf.transform(c)\n",
" v1 = (tf.transform(p1) - c_d) * aspect\n",
" v2 = (tf.transform(p2) - c_d) * aspect\n",
" d = normalize(normalize(v1) + normalize(v2))/aspect\n",
"\n",
" ax_text(c_d + d * size, text, ha='center',va='center', transform=ax.transAxes, ax=ax, **kw)\n",
"\n",
"def ax_curly_brace(p0, p1, r, offset=0, ax=None, **kw):\n",
" ax = ax or plt.gca()\n",
" p0, p1 = ax.transData.transform(p0), ax.transData.transform(p1)\n",
"\n",
" dx = normalize(p1 - p0)\n",
" dy = rot90(dx)\n",
"\n",
" p0 = p0 + dy * offset\n",
"\n",
" l = np.linalg.norm(p1 - p0)\n",
" r = min(l * .25, r)\n",
" s = (l - 4 * r) * .5\n",
" K = 0.5522847498\n",
"\n",
" c0 = p0 + r * dx\n",
" c1 = p0 + (r + s) * dx + (r * 2) * dy\n",
" c2 = p0 + (r * 3 + s) * dx + (r * 2) * dy\n",
" c3 = p0 + (r * 3 + s * 2) * dx\n",
"\n",
" q1 = p0 + (r + s) * dx + r * dy\n",
" q3 = p0 + (r * 3 + s * 2) * dx + r * dy\n",
"\n",
" verts = ax.transAxes.inverted().transform([\n",
" c0 + -r * dx,\n",
" c0 + -r * dx + r * K * dy,\n",
" c0 + -r * K * dx + r * dy,\n",
" c0 + r * dy,\n",
" q1,\n",
" c1 + r * K * dx + -r * dy,\n",
" c1 + r * dx + -r * K * dy,\n",
" c1 + r * dx,\n",
" c2 + -r * dx,\n",
" c2 + -r * dx + -r * K * dy,\n",
" c2 + -r * K * dx + -r * dy,\n",
" c2 + -r * dy,\n",
" q3,\n",
" c3 + r * K * dx + r * dy,\n",
" c3 + r * dx + r * K * dy,\n",
" c3 + r * dx\n",
" ])\n",
"\n",
" codes = [Path.MOVETO,Path.CURVE4,Path.CURVE4,Path.CURVE4,\n",
" Path.LINETO,Path.CURVE4,Path.CURVE4,Path.CURVE4,\n",
" Path.MOVETO,Path.CURVE4,Path.CURVE4,Path.CURVE4,\n",
" Path.LINETO,Path.CURVE4,Path.CURVE4,Path.CURVE4]\n",
"\n",
" return ax.add_patch(mpl.patches.PathPatch(\n",
" Path(verts, codes), fc='none', transform=ax.transAxes, **kw))\n",
"\n",
"def circumcircle(a, b, c, axis=-1):\n",
" \"\"\"https://www.desmos.com/calculator/hwsqfnoczj\"\"\"\n",
" ax, ay = a.take(0,axis), a.take(1,axis)\n",
" bx, by = b.take(0,axis), b.take(1,axis)\n",
" cx, cy = c.take(0,axis), c.take(1,axis)\n",
" ab, bc, ca = a - b, b - c, c - a\n",
" D = 2 * (ax * bc.take(1,axis) + bx * ca.take(1,axis) + cx * ab.take(1,axis))\n",
" ha, hb, hc = ax**2 + ay**2, bx**2 + by**2, cx**2 + cy**2\n",
" x = ha * bc.take(1,axis) + hb * ca.take(1,axis) + hc * ab.take(1,axis)\n",
" y = ha * -bc.take(0,axis) + hb * -ca.take(0,axis) + hc * -ab.take(0,axis)\n",
" O = np.stack((x,y),axis) / D\n",
"\n",
" la = np.linalg.norm(ab,axis=axis)\n",
" lb = np.linalg.norm(bc,axis=axis)\n",
" lc = np.linalg.norm(ca,axis=axis)\n",
" s = (la + lb + lc) * .5\n",
" r = (la * lb * lc) / np.sqrt(s * (s - la) * (s - lb) * (s - lc)) * .25\n",
" return O, r"
],
"metadata": {
"id": "E7TQLVybSPrQ"
},
"execution_count": 8,
"outputs": []
},
{
"cell_type": "code",
"source": [
"P = np.array([[0,0],\n",
" [1,0],\n",
" [.7,1]])\n",
"\n",
"pa, ba = P[2] - P[0], P[1] - P[0]\n",
"h = (pa[0]*ba[0]+pa[1]*ba[1])/(ba[0]*ba[0]+ba[1]*ba[1])\n",
"pc = ba * h\n",
"\n",
"cc, r = circumcircle(P[0],P[1], P[2])\n",
"\n",
"p_text = cc + (P - cc) * 1.1"
],
"metadata": {
"id": "95PAJD9-UjW1"
},
"execution_count": 9,
"outputs": []
},
{
"cell_type": "code",
"source": [
"fig = plt.figure(figsize=(4,4))\n",
"\n",
"ax = fig.add_subplot()\n",
"ax.set(xlim=(-.25,1.25),ylim=(-.25,1.25),aspect='equal')\n",
"ax.set_axis_off()\n",
"\n",
"ax_lines([np.concatenate([P,P[:1]]),[P[2],pc]],lw=.3,ec=COLORS[\"gray80\"])\n",
"ax_text(p_text[0],r\"$p_j$\",ha='center',va='center',color=COLORS[\"gray90\"],fontsize=10,usetex=True)\n",
"ax_text(p_text[1],r\"$p_k$\",ha='center',va='center',color=COLORS[\"gray90\"],fontsize=10,usetex=True)\n",
"ax_text(p_text[2],r\"$p_i$\",ha='center',va='center',color=COLORS[\"gray90\"],fontsize=10,usetex=True)\n",
"ax_text(pc + (-.03, .05), r\"$q$\",ha='center',va='center',color=COLORS[\"gray90\"],fontsize=10,usetex=True)\n",
"ax_scatter(np.insert(P,-1,pc,axis=0),s=10,color=COLORS[\"gray80\"])\n",
"\n",
"ax_angle(P[0], P[1], P[2], size=.1, lw=.5, ec=COLORS[\"gray80\"])\n",
"ax_angle(P[1], P[2], P[0], size=.1, lw=.5, ec=COLORS[\"gray80\"])\n",
"\n",
"ax_annotate_angle(P[0], P[1], P[2], r\"$\\alpha$\", .08, fontsize=10,color=COLORS[\"gray90\"],usetex=True)\n",
"ax_annotate_angle(P[1], P[0], P[2], r\"$\\beta$\", .08, fontsize=10,color=COLORS[\"gray90\"],usetex=True)\n",
"\n",
"ax_curly_brace(pc-(.002,0), P[0], 5, offset=10, ec=COLORS[\"gray60\"], lw=.5)\n",
"ax_curly_brace(P[1], pc+(.002,0), 5, offset=10, ec=COLORS[\"gray60\"], lw=.5)\n",
"\n",
"ax_text(lerp(P[0], pc, .5) + rot90(normalize(P[0] - pc)) * .12, f\"$w_1$\",\n",
" ha=\"center\",va=\"center\",fontsize=10,color=COLORS[\"gray90\"],usetex=True)\n",
"ax_text(lerp(P[1], pc, .5) + rot90(normalize(pc - P[1])) * .12, f\"$w_2$\",\n",
" ha=\"center\",va=\"center\",fontsize=10,color=COLORS[\"gray90\"],usetex=True)\n",
"\n",
"plt_show(0)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 407
},
"id": "VEJUJGlOUoI2",
"outputId": "f6818ee0-def5-463c-ae1f-bd766fb1e0a4"
},
"execution_count": 10,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 400x400 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"image/png": {
"width": 390,
"height": 390
}
}
}
]
},
{
"cell_type": "code",
"source": [
"k = np.sqrt(3) * .5\n",
"lines = [\n",
" [[k,.5],\n",
" [0,1],\n",
" [-k,.5],\n",
" [-k,-.5],\n",
" [0,-1],\n",
" [k,-.5],\n",
" [k,.5]],\n",
" [[k,.5],[-k,-.5]],\n",
" [[k,-.5],[-k,.5]],\n",
" [[0,1],[0,-1]]\n",
"]"
],
"metadata": {
"id": "6wQYREdeq_4F"
},
"execution_count": 11,
"outputs": []
},
{
"cell_type": "code",
"source": [
"fig = plt.figure(figsize=(4,4))\n",
"\n",
"ax = fig.add_subplot()\n",
"ax.set(xlim=(-1.3,1.3),ylim=(-1.3,1.3),aspect=\"equal\")\n",
"ax.set_axis_off()\n",
"\n",
"ax_lines(lines,lw=.5,ec=COLORS[\"gray70\"])\n",
"ax.text(-.17, .1, r\"$p_i$\",\n",
" color=COLORS[\"gray80\"],va='center',ha='center',\n",
" path_effects=[withStroke(linewidth=12, foreground=COLORS[\"gray10\"])],\n",
" fontsize=10,usetex=True)\n",
"ax.text(0, -1.12, r\"$p_j$\",\n",
" color=COLORS[\"gray80\"],va='center',ha='center',\n",
" path_effects=[withStroke(linewidth=12, foreground=COLORS[\"gray10\"])],\n",
" fontsize=10,usetex=True)\n",
"ax_scatter(np.array([[0,0],[0,-1]]),s=10,color=COLORS[\"gray80\"])\n",
"\n",
"ax_angle(np.array([-k,-.5]), np.array([0,-1]), np.array([0,0]),\n",
" size=.1, lw=.5, ec=COLORS[\"gray70\"])\n",
"ax_angle(np.array([k,-.5]), np.array([0,0]), np.array([0,-1]),\n",
" size=.1, lw=.5, ec=COLORS[\"gray70\"])\n",
"\n",
"ax_annotate_angle(np.array([-k,-.5]), np.array([0,-1]), np.array([0,0]), r\"$\\alpha_j$\",\n",
" .1, fontsize=10,color=COLORS[\"gray80\"],usetex=True)\n",
"ax_annotate_angle(np.array([k,-.5]), np.array([0,0]), np.array([0,-1]), r\"$\\beta_j$\",\n",
" .1, fontsize=10,color=COLORS[\"gray80\"],usetex=True)\n",
"\n",
"plt_show(0)"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 407
},
"id": "G-qUH7hKfOBg",
"outputId": "830de7d3-c02e-4477-b256-6219709f01de"
},
"execution_count": 73,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 400x400 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"image/png": {
"width": 390,
"height": 390
}
}
}
]
},
{
"cell_type": "code",
"source": [],
"metadata": {
"id": "wVj4bJLUfO9C"
},
"execution_count": null,
"outputs": []
}
]
}
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