Shapely/02_nearest_point_on_line_polygon.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"09_nearest_point_on_line_polygon.ipynb","provenance":[],"collapsed_sections":[],"authorship_tag":"ABX9TyNyg7XpLoMfSygyRHHMuAEk"},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"}},"cells":[{"cell_type":"markdown","metadata":{"id":"CJT-b5EgFjSR"},"source":["**Nearest point on line**"]},{"cell_type":"code","metadata":{"id":"P667TtOW-Jp0","executionInfo":{"status":"ok","timestamp":1632945514315,"user_tz":-120,"elapsed":491,"user":{"displayName":"ivan d'ortenzio","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjJkM9KEQgWMc1ULjLaQI2W6lPdYwYiT_UIeDuUmHw=s64","userId":"12592191603011211484"}}},"source":["import numpy as np\n","from shapely.geometry import Point, Polygon, LineString, LinearRing\n","import matplotlib.pyplot as plt"],"execution_count":1,"outputs":[]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"nmdpqBBJFToL","executionInfo":{"status":"ok","timestamp":1632945515063,"user_tz":-120,"elapsed":10,"user":{"displayName":"ivan d'ortenzio","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjJkM9KEQgWMc1ULjLaQI2W6lPdYwYiT_UIeDuUmHw=s64","userId":"12592191603011211484"}},"outputId":"a896d3ee-ebc8-44d3-fef8-5c0cba8fefa4"},"source":["# Start point\n","point_a = Point(1, 1.4)\n","\n","# Create a line\n","line_a = LineString([(1,1), (2,2)])\n","\n","# Measure the projection point along the line from the starting point\n","dist_a = line_a.project(point_a)\n","\n","# Get the closest point\n","closest_a = line_a.interpolate(dist_a)\n","print(f\"Closest point coordinates: {closest_a.wkt}\")"],"execution_count":2,"outputs":[{"output_type":"stream","name":"stdout","text":["Closest point coordinates: POINT (1.2 1.2)\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"XndHNNbBFUGS","executionInfo":{"status":"ok","timestamp":1632945515064,"user_tz":-120,"elapsed":10,"user":{"displayName":"ivan d'ortenzio","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjJkM9KEQgWMc1ULjLaQI2W6lPdYwYiT_UIeDuUmHw=s64","userId":"12592191603011211484"}},"outputId":"f4b50d6c-3412-4a11-b53f-af62a6c259d5"},"source":["# Creates a figure and one subplot\n","fig, ax = plt.subplots()\n","\n","# Get xy coordinates of the line\n","x,y = line_a.xy\n","\n","# Plot the line\n","ax.plot(x,y)\n","\n","# Plot and annotate the start point\n","ax.scatter(point_a.x, point_a.y, c=\"r\")\n","ax.annotate(f\"Start point:\\n{point_a.wkt}\", (point_a.x+0.02, point_a.y+0.05))\n","\n","# Plot and annotate the closest point\n","ax.scatter(closest_a.x, closest_a.y, c=\"g\")\n","ax.annotate(f\"Nearest point:\\n{closest_a.wkt}\", (closest_a.x+0.08, closest_a.y-0.05))\n","\n","# Show the plot\n","ax.set_aspect('equal', adjustable='datalim')\n","plt.show()"],"execution_count":3,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"pnLnbrwLFzli"},"source":["**Nearest point on Polygon**"]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"pz32YC-J9yOn","executionInfo":{"status":"ok","timestamp":1632945515065,"user_tz":-120,"elapsed":10,"user":{"displayName":"ivan d'ortenzio","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjJkM9KEQgWMc1ULjLaQI2W6lPdYwYiT_UIeDuUmHw=s64","userId":"12592191603011211484"}},"outputId":"f0958f05-65c6-45b9-f964-633b30916566"},"source":["# Start point\n","point_b = Point(3, 0)\n","\n","# Create a Polygon\n","poly_b = Polygon([(-1,1),(2,1),(2,2),(-1,2)])\n","\n","# Polygon exterior ring\n","exterior_ring = LinearRing(poly_b.exterior.coords)\n","\n","# Measure the projection point along the line from the starting point\n","dist_b = exterior_ring.project(point_b)\n","\n","# Get the closest point\n","closest_b = exterior_ring.interpolate(dist_b)\n","print(f\"Closest point coordinates: {closest_b.wkt}\")"],"execution_count":4,"outputs":[{"output_type":"stream","name":"stdout","text":["Closest point coordinates: POINT (2 1)\n"]}]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":265},"id":"Q9suFjh7-EY-","executionInfo":{"status":"ok","timestamp":1632945515066,"user_tz":-120,"elapsed":10,"user":{"displayName":"ivan d'ortenzio","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjJkM9KEQgWMc1ULjLaQI2W6lPdYwYiT_UIeDuUmHw=s64","userId":"12592191603011211484"}},"outputId":"9ca11ed6-6b67-4741-927e-f294016a8b5b"},"source":["# Creates a figure and one subplot\n","fig, ax = plt.subplots()\n","\n","# Get xy coordinates of the exterior\n","x_ext, y_ext = exterior_ring.xy\n","\n","# Plot the polygon\n","ax.fill(x_ext, y_ext, c=\"b\", alpha=0.2)\n","\n","# Plot and annotate the start point\n","ax.scatter(point_b.x, point_b.y, c=\"r\")\n","ax.annotate(f\"Start point:\\n{point_b.wkt}\", (point_b.x-0.8, point_b.y+0.05))\n","\n","# Plot and annotate the closest point\n","ax.scatter(closest_b.x, closest_b.y, c=\"g\")\n","ax.annotate(f\"Nearest point:\\n{closest_b.wkt}\", (closest_b.x+0.08, closest_b.y+0.05))\n","\n","# Show the plot\n","ax.set_aspect('equal', adjustable='datalim')\n","plt.show()"],"execution_count":5,"outputs":[{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["<Figure size 432x288 with 1 Axes>"]},"metadata":{"needs_background":"light"}}]}]}