{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
Manim Community v0.18.0\n",
"\n",
"
\n"
],
"text/plain": [
"Manim Community \u001b[32mv0.\u001b[0m\u001b[32m18.0\u001b[0m\n",
"\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from manim import *\n",
"from manim_geometry import *\n",
"\n",
"config.media_embed = True\n",
"config.media_width = \"100%\"\n",
"_RV = \"-v WARNING -qm --progress_bar None --disable_caching\"\n",
"_RI = \"-v WARNING -s --progress_bar None --disable_caching\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Intersections\n",
"\n",
"## Line-Line intersection"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
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