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Python Line Segment Intersection example.
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"from random import random"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# intersection between line(p1, p2) and line(p3, p4)\n",
"def intersect(p1, p2, p3, p4):\n",
" x1,y1 = p1\n",
" x2,y2 = p2\n",
" x3,y3 = p3\n",
" x4,y4 = p4\n",
" denom = (y4-y3)*(x2-x1) - (x4-x3)*(y2-y1)\n",
" if denom == 0: # parallel\n",
" return None\n",
" ua = ((x4-x3)*(y1-y3) - (y4-y3)*(x1-x3)) / denom\n",
" if ua < 0 or ua > 1: # out of range\n",
" return None\n",
" ub = ((x2-x1)*(y1-y3) - (y2-y1)*(x1-x3)) / denom\n",
" if ub < 0 or ub > 1: # out of range\n",
" return None\n",
" x = x1 + ua * (x2-x1)\n",
" y = y1 + ua * (y2-y1)\n",
" return (x,y)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 288x288 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 250,
"width": 269
},
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 288x288 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 250,
"width": 262
},
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 288x288 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 250,
"width": 262
},
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 288x288 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 250,
"width": 268
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"for i in range(4):\n",
" points = [(random(), random()) for i in range(4)]\n",
"\n",
" (x1,y1),(x2,y2),(x3,y3),(x4,y4) = points\n",
" plt.figure(figsize=(4,4))\n",
" plt.plot((x1,x2), (y1,y2), '.r--')\n",
" plt.plot((x3,x4), (y3,y4), '.b--')\n",
"\n",
" inter = intersect(*points) \n",
" if inter is not None:\n",
" plt.plot(*inter, 'ok', markersize=10)\n",
"\n",
" plt.show()"
]
}
],
"metadata": {
"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": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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