{"id":88763,"date":"2024-12-18T09:42:10","date_gmt":"2024-12-18T06:12:10","guid":{"rendered":"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/"},"modified":"2024-12-18T09:42:10","modified_gmt":"2024-12-18T06:12:10","slug":"optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc","status":"publish","type":"post","link":"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/","title":{"rendered":"\u0628\u0647\u06cc\u0646\u0647 \u0633\u0627\u0632\u06cc \u062a\u0634\u062e\u06cc\u0635 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc \u0647\u0646\u062f\u0633\u06cc: \u0641\u0631\u0648 \u0631\u0641\u062a\u0646 \u0639\u0645\u06cc\u0642 \u062f\u0631 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0628\u0627 \u067e\u0627\u06cc\u062a\u0648\u0646"},"content":{"rendered":"<p>Summarize this content to 400 words in Persian Lang<br \/>\n              \u067e\u0631\u062f\u0627\u0632\u0634 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0645\u06a9\u0627\u0646\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0627\u0632 \u0646\u0638\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u06af\u0631\u0627\u0646 \u0628\u0627\u0634\u062f\u060c \u0628\u0647\u200c\u0648\u06cc\u0698\u0647 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0633\u0631\u0648\u06a9\u0627\u0631 \u062f\u0627\u0631\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647\u060c \u0631\u0648\u06cc\u06a9\u0631\u062f\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0631\u0627\u06cc \u062a\u0634\u062e\u06cc\u0635 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc\u200c\u0647\u0627\u06cc \u0647\u0646\u062f\u0633\u06cc \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646\u060c \u0628\u0627 \u062a\u0645\u0631\u06a9\u0632 \u0628\u0631 \u0639\u0645\u0644\u06a9\u0631\u062f \u062a\u06a9\u0646\u06cc\u06a9\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0646\u0645\u0627\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.<\/p>\n<p>  \ud83c\udfaf \u0686\u0627\u0644\u0634 \u062a\u0642\u0627\u0637\u0639 \u0647\u0627\u06cc \u0647\u0646\u062f\u0633\u06cc<\/p>\n<p>\u0647\u0646\u06af\u0627\u0645 \u06a9\u0627\u0631 \u0628\u0627 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u06a9\u0627\u0646\u06cc\u060c \u06cc\u06a9\u06cc \u0627\u0632 \u0648\u0638\u0627\u06cc\u0641 \u0631\u0627\u06cc\u062c \u062a\u0634\u062e\u06cc\u0635 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc \u0647\u0627 \u06cc\u0627 \u062a\u0642\u0627\u0637\u0639 \u0647\u0627 \u0628\u06cc\u0646 \u0686\u0646\u062f \u0636\u0644\u0639\u06cc \u0647\u0627 \u0627\u0633\u062a. \u06cc\u06a9 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647 \u0644\u0648\u062d\u0627\u0646\u0647 \u062f\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0631 \u0647\u0646\u062f\u0633\u0647 \u0628\u0627 \u0647\u0631 \u0647\u0646\u062f\u0633\u0647 \u062f\u06cc\u06af\u0631 \u0628\u0647 \u0633\u0631\u0639\u062a \u0628\u0627 \u0631\u0634\u062f \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0646\u0627\u06a9\u0627\u0631\u0622\u0645\u062f \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p>  \ud83d\udd0d \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u062a\u0641\u0627\u0648\u062a \u0628\u06cc\u0646 \u0631\u0648\u06cc\u06a9\u0631\u062f\u0647\u0627\u06cc \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0633\u0627\u062f\u0647 \u0648 \u0641\u0636\u0627\u06cc\u06cc \u0631\u0627 \u0645\u062c\u0633\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<p>  \ud83d\udc0c \u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647 \u0644\u0648\u062d\u0627\u0646\u0647: \u0631\u0648\u0634 \u0646\u06cc\u0631\u0648\u06cc \u0628\u06cc \u0631\u062d\u0645<\/p>\n<p>def check_overlaps_naive(gdf):<br \/>\n    errors = []\n    for i in range(len(gdf)):<br \/>\n        for j in range(i + 1, len(gdf)):<br \/>\n            geom1 = gdf.iloc[i].geometry<br \/>\n            geom2 = gdf.iloc[j].geometry<\/p>\n<p>            if geom1.intersects(geom2):<br \/>\n                # Process intersection<br \/>\n                intersection = geom1.intersection(geom2)<br \/>\n                # Add to errors list<br \/>\n    return errors<\/p>\n<p>    \u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/p>\n<p>    \u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/p>\n<p>\u26a0\ufe0f \u0686\u0631\u0627 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647 \u0644\u0648\u062d\u0627\u0646\u0647 \u062a\u0648\u0635\u06cc\u0647 \u0646\u0645\u06cc \u0634\u0648\u062f:<\/p>\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc O(n\u00b2) \u0627\u0633\u062a\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 n \u062a\u0639\u062f\u0627\u062f \u0647\u0646\u062f\u0633\u0647 \u0647\u0627 \u0627\u0633\u062a<br \/>\n\u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647\u060c \u0639\u0645\u0644\u06a9\u0631\u062f \u0628\u0647 \u0637\u0648\u0631 \u062a\u0635\u0627\u0639\u062f\u06cc \u06a9\u0627\u0647\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f<br \/>\n\u0628\u0631\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af (\u0647\u0632\u0627\u0631\u0627\u0646 \u0647\u0646\u062f\u0633\u0647) \u063a\u06cc\u0631 \u0639\u0645\u0644\u06cc \u0645\u06cc \u0634\u0648\u062f<\/p>\n<p>  \u26a1 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc: \u06cc\u06a9 \u0628\u0627\u0632\u06cc \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u0646\u062f\u0647 \u0639\u0645\u0644\u06a9\u0631\u062f<\/p>\n<p>\u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0628\u0627 \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 \u0633\u0644\u0633\u0644\u0647 \u0645\u0631\u0627\u062a\u0628\u06cc \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u0647\u0646\u062f\u0633\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0648\u0633\u0639\u062a \u0641\u0636\u0627\u06cc\u06cc \u0622\u0646\u0647\u0627 \u0633\u0627\u0632\u0645\u0627\u0646\u062f\u0647\u06cc \u0645\u06cc \u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0627\u0645\u06a9\u0627\u0646 \u062d\u0630\u0641 \u0633\u0631\u06cc\u0639 \u0647\u0646\u062f\u0633\u0647\u200c\u0647\u0627\u06cc\u06cc \u0631\u0627 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u064b \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0642\u0637\u0639 \u0634\u0648\u0646\u062f \u0648 \u062a\u0639\u062f\u0627\u062f \u0628\u0631\u0631\u0633\u06cc\u200c\u0647\u0627\u06cc \u062f\u0642\u06cc\u0642 \u062a\u0642\u0627\u0637\u0639 \u0631\u0627 \u0628\u0647\u200c\u0637\u0648\u0631 \u0686\u0634\u0645\u06af\u06cc\u0631\u06cc \u06a9\u0627\u0647\u0634 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/p>\n<p>  1\ufe0f\u20e3 STRtree (\u062f\u0631\u062e\u062a \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc-\u06a9\u0627\u0634\u06cc-\u0628\u0627\u0632\u06af\u0634\u062a\u06cc)<\/p>\n<p>from shapely import STRtree<\/p>\n<p>def check_overlaps_strtree(gdf):<br \/>\n    # Create the spatial index<br \/>\n    tree = STRtree(gdf.geometry.values)<\/p>\n<p>    # Process each geometry<br \/>\n    for i, geom in enumerate(gdf.geometry):<br \/>\n        # Query potential intersections efficiently<br \/>\n        potential_matches_idx = tree.query(geom)<\/p>\n<p>        # Check only potential matches<br \/>\n        for j in potential_matches_idx:<br \/>\n            if j &lt;= i:<br \/>\n                continue<\/p>\n<p>            other_geom = gdf.geometry[j]\n            # Detailed intersection test<br \/>\n            if geom.intersects(other_geom):<br \/>\n                # Process intersection<br \/>\n                intersection = geom.intersection(other_geom)<br \/>\n                # Record results<\/p>\n<p>    \u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/p>\n<p>    \u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/p>\n<p>  \ud83d\udd11 \u0645\u0641\u0627\u0647\u06cc\u0645 \u06a9\u0644\u06cc\u062f\u06cc STRtree:<\/p>\n<p>\ud83d\udce6 \u0641\u0636\u0627 \u0631\u0627 \u0628\u0647 \u0645\u0646\u0627\u0637\u0642 \u0633\u0644\u0633\u0644\u0647 \u0645\u0631\u0627\u062a\u0628\u06cc \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f<br \/>\n\ud83d\udccf \u0627\u0632 \u0645\u0633\u062a\u0637\u06cc\u0644 \u0647\u0627\u06cc \u062d\u062f\u0627\u0642\u0644 \u0645\u062d\u062f\u0648\u062f (MBR) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f<br \/>\n\ud83d\ude80 \u0627\u0645\u06a9\u0627\u0646 \u0641\u06cc\u0644\u062a\u0631 \u06a9\u0631\u062f\u0646 \u0633\u0631\u06cc\u0639 \u0647\u0646\u062f\u0633\u0647 \u0647\u0627\u06cc \u063a\u06cc\u0631 \u0645\u062a\u0642\u0627\u0637\u0639 \u0631\u0627 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc \u06a9\u0646\u062f<br \/>\n\ud83d\udcc8 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0631\u0627 \u0627\u0632 O(n\u00b2) \u0628\u0647 O(n log n) \u06a9\u0627\u0647\u0634 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<p>  2\ufe0f\u20e3 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc Rtree<\/p>\n<p>import rtree<\/p>\n<p>def check_overlaps_rtree(gdf):<br \/>\n    # Create spatial index<br \/>\n    idx = rtree.index.Index()<\/p>\n<p>    # Insert geometries with their bounding boxes<br \/>\n    for i, geom in enumerate(gdf.geometry):<br \/>\n        idx.insert(i, geom.bounds)<\/p>\n<p>    # Process geometries<br \/>\n    for i, row in enumerate(gdf.itertuples()):<br \/>\n        geom1 = row.geometry<\/p>\n<p>        # Find potential intersections using bounding boxes<br \/>\n        for j in idx.intersection(geom1.bounds):<br \/>\n            if j &lt;= i:<br \/>\n                continue<\/p>\n<p>            geom2 = gdf.iloc[j].geometry<br \/>\n            # Detailed intersection test<br \/>\n            if geom1.intersects(geom2):<br \/>\n                # Process intersection<br \/>\n                intersection = geom1.intersection(geom2)<\/p>\n<p>    \u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/p>\n<p>    \u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/p>\n<p>  \ud83d\udd11 \u0645\u0641\u0627\u0647\u06cc\u0645 \u06a9\u0644\u06cc\u062f\u06cc RTree:<\/p>\n<p>\ud83c\udf33 \u0647\u0646\u062f\u0633\u0647 \u0647\u0627 \u0631\u0627 \u062f\u0631 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0631\u062e\u062a\u06cc \u0645\u062a\u0639\u0627\u062f\u0644 \u0633\u0627\u0632\u0645\u0627\u0646\u062f\u0647\u06cc \u0645\u06cc \u06a9\u0646\u062f<br \/>\n\ud83d\udce6 \u0627\u0632 \u0633\u0644\u0633\u0644\u0647 \u0645\u0631\u0627\u062a\u0628 \u062c\u0639\u0628\u0647 \u0645\u062d\u062f\u0648\u062f \u0628\u0631\u0627\u06cc \u0641\u06cc\u0644\u062a\u0631 \u06a9\u0631\u062f\u0646 \u0633\u0631\u06cc\u0639 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f<br \/>\n\u26a1 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0627\u06cc \u063a\u06cc\u0631 \u0636\u0631\u0648\u0631\u06cc \u0631\u0627 \u06a9\u0627\u0647\u0634 \u0645\u06cc \u062f\u0647\u062f<br \/>\n\ud83d\udd0d \u067e\u0631\u0633 \u0648 \u062c\u0648\u06cc \u0641\u0636\u0627\u06cc\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f<\/p>\n<p>  \ud83d\udcca \u062a\u062d\u0644\u06cc\u0644 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0627\u06cc<\/p>\n<p>\u0648\u06cc\u0698\u06af\u06cc<br \/>\nSTRtree (\u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc-\u06a9\u0627\u0634\u06cc-\u062f\u0631\u062e\u062a \u0628\u0627\u0632\u06af\u0634\u062a\u06cc)<br \/>\nRTree (\u062f\u0631\u062e\u062a \u0645\u062a\u0639\u0627\u062f\u0644)<\/p>\n<p>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc<br \/>\nO(n log n)<br \/>\nO(n log n)<\/p>\n<p>\u067e\u0627\u0631\u062a\u06cc\u0634\u0646 \u0628\u0646\u062f\u06cc \u0641\u0636\u0627<br \/>\n\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc &#8211; \u06a9\u0627\u0634\u06cc &#8211; \u0628\u0627\u0632\u06af\u0634\u062a\u06cc<br \/>\n\u062f\u0631\u062e\u062a \u0645\u062a\u0639\u0627\u062f\u0644<\/p>\n<p>\u0639\u0645\u0644\u06a9\u0631\u062f<br \/>\n\u0633\u0631\u06cc\u0639\u062a\u0631<br \/>\n\u0646\u0633\u0628\u062a\u0627 \u06a9\u0646\u062f\u062a\u0631<\/p>\n<p>\u0633\u0631\u0628\u0627\u0631 \u062d\u0627\u0641\u0638\u0647<br \/>\n\u0645\u062a\u0648\u0633\u0637<br \/>\n\u06a9\u0645\u06cc \u0628\u0627\u0644\u0627\u062a\u0631<\/p>\n<p>  \ud83d\udcc8 \u0646\u062a\u0627\u06cc\u062c \u0645\u062d\u06a9<\/p>\n<p>\u0645\u0627 \u0627\u06cc\u0646 \u0631\u0648\u06cc\u06a9\u0631\u062f\u0647\u0627 \u0631\u0627 \u0631\u0648\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0627\u06cc \u0627\u0632 45746 \u0647\u0646\u062f\u0633\u0647 \u0686\u0646\u062f \u0636\u0644\u0639\u06cc \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0631\u062f\u06cc\u0645<\/p>\n<p>  \u26a1 \u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u0639\u0645\u0644\u06a9\u0631\u062f<\/p>\n<p>\u0645\u062a\u0631\u06cc\u06a9<br \/>\nSTRtree<br \/>\nRTree<br \/>\n\u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647 \u0644\u0648\u062d\u0627\u0646\u0647<\/p>\n<p>\u0632\u0645\u0627\u0646 \u0627\u062c\u0631\u0627<br \/>\n1.3747 \u062b\u0627\u0646\u06cc\u0647<br \/>\n6.6556 \u062b\u0627\u0646\u06cc\u0647<br \/>\n\u0627\u062c\u0631\u0627 \u0646\u0645\u06cc \u0634\u0648\u062f<\/p>\n<p>\u0647\u0646\u062f\u0633\u0647 \u067e\u0631\u062f\u0627\u0632\u0634 \u0634\u062f\u0647<br \/>\n45746<br \/>\n45746<br \/>\nN\/A<\/p>\n<p>\u0646\u0631\u062e \u067e\u0631\u062f\u0627\u0632\u0634<br \/>\n~33219 \u0648\u06cc\u0698\u06af\u06cc \u062f\u0631 \u062b\u0627\u0646\u06cc\u0647<br \/>\n~9718 \u0648\u06cc\u0698\u06af\u06cc \u062f\u0631 \u062b\u0627\u0646\u06cc\u0647<br \/>\nN\/A<\/p>\n<p>  \ud83d\udd04 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc<\/p>\n<p>\u0646\u0648\u0639 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc<br \/>\nSTRtree<br \/>\nRTree<\/p>\n<p>\u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc \u0647\u0627\u06cc \u0639\u0645\u062f\u0647 (\u226520%)<br \/>\n5<br \/>\n5<\/p>\n<p>\u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc \u0647\u0627\u06cc \u062c\u0632\u0626\u06cc (<\/p>\n<div data-article-id=\"2162268\" id=\"article-body\">\n<p>\u067e\u0631\u062f\u0627\u0632\u0634 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0645\u06a9\u0627\u0646\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0627\u0632 \u0646\u0638\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u06af\u0631\u0627\u0646 \u0628\u0627\u0634\u062f\u060c \u0628\u0647\u200c\u0648\u06cc\u0698\u0647 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0633\u0631\u0648\u06a9\u0627\u0631 \u062f\u0627\u0631\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647\u060c \u0631\u0648\u06cc\u06a9\u0631\u062f\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0631\u0627\u06cc \u062a\u0634\u062e\u06cc\u0635 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc\u200c\u0647\u0627\u06cc \u0647\u0646\u062f\u0633\u06cc \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646\u060c \u0628\u0627 \u062a\u0645\u0631\u06a9\u0632 \u0628\u0631 \u0639\u0645\u0644\u06a9\u0631\u062f \u062a\u06a9\u0646\u06cc\u06a9\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0646\u0645\u0627\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_84 counter-hierarchy ez-toc-counter-rtl ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0641\u0647\u0631\u0633\u062a \u0645\u0637\u0627\u0644\u0628<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 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href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%90%8C_%D8%B1%D9%88%DB%8C%DA%A9%D8%B1%D8%AF_%D8%B3%D8%A7%D8%AF%D9%87_%D9%84%D9%88%D8%AD%D8%A7%D9%86%D9%87_%D8%B1%D9%88%D8%B4_%D9%86%DB%8C%D8%B1%D9%88%DB%8C_%D8%A8%DB%8C_%D8%B1%D8%AD%D9%85\" >\ud83d\udc0c \u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647 \u0644\u0648\u062d\u0627\u0646\u0647: \u0631\u0648\u0634 \u0646\u06cc\u0631\u0648\u06cc \u0628\u06cc \u0631\u062d\u0645<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%E2%9A%A1_%D9%86%D9%85%D8%A7%DB%8C%D9%87_%D8%B3%D8%A7%D8%B2%DB%8C_%D9%81%D8%B6%D8%A7%DB%8C%DB%8C_%DB%8C%DA%A9_%D8%A8%D8%A7%D8%B2%DB%8C_%D8%AA%D8%BA%DB%8C%DB%8C%D8%B1_%D8%AF%D9%87%D9%86%D8%AF%D9%87_%D8%B9%D9%85%D9%84%DA%A9%D8%B1%D8%AF\" >\u26a1 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc: \u06cc\u06a9 \u0628\u0627\u0632\u06cc \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u0646\u062f\u0647 \u0639\u0645\u0644\u06a9\u0631\u062f<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#1%EF%B8%8F%E2%83%A3_STRtree_%D8%AF%D8%B1%D8%AE%D8%AA_%D9%85%D8%B1%D8%AA%D8%A8_%D8%B3%D8%A7%D8%B2%DB%8C-%DA%A9%D8%A7%D8%B4%DB%8C-%D8%A8%D8%A7%D8%B2%DA%AF%D8%B4%D8%AA%DB%8C\" >1\ufe0f\u20e3 STRtree (\u062f\u0631\u062e\u062a \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc-\u06a9\u0627\u0634\u06cc-\u0628\u0627\u0632\u06af\u0634\u062a\u06cc)<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%94%91_%D9%85%D9%81%D8%A7%D9%87%DB%8C%D9%85_%DA%A9%D9%84%DB%8C%D8%AF%DB%8C_STRtree\" >\ud83d\udd11 \u0645\u0641\u0627\u0647\u06cc\u0645 \u06a9\u0644\u06cc\u062f\u06cc STRtree:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#2%EF%B8%8F%E2%83%A3_%D9%86%D9%85%D8%A7%DB%8C%D9%87_%D8%B3%D8%A7%D8%B2%DB%8C_Rtree\" >2\ufe0f\u20e3 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc Rtree<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%94%91_%D9%85%D9%81%D8%A7%D9%87%DB%8C%D9%85_%DA%A9%D9%84%DB%8C%D8%AF%DB%8C_RTree\" >\ud83d\udd11 \u0645\u0641\u0627\u0647\u06cc\u0645 \u06a9\u0644\u06cc\u062f\u06cc RTree:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%93%8A_%D8%AA%D8%AD%D9%84%DB%8C%D9%84_%D9%85%D9%82%D8%A7%DB%8C%D8%B3%D9%87_%D8%A7%DB%8C\" >\ud83d\udcca \u062a\u062d\u0644\u06cc\u0644 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0627\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%93%88_%D9%86%D8%AA%D8%A7%DB%8C%D8%AC_%D9%85%D8%AD%DA%A9\" >\ud83d\udcc8 \u0646\u062a\u0627\u06cc\u062c \u0645\u062d\u06a9<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%E2%9A%A1_%D9%85%D8%B9%DB%8C%D8%A7%D8%B1%D9%87%D8%A7%DB%8C_%D8%B9%D9%85%D9%84%DA%A9%D8%B1%D8%AF\" >\u26a1 \u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u0639\u0645\u0644\u06a9\u0631\u062f<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%94%84_%D8%AA%D8%AC%D8%B2%DB%8C%D9%87_%D9%88_%D8%AA%D8%AD%D9%84%DB%8C%D9%84_%D9%87%D9%85%D9%BE%D9%88%D8%B4%D8%A7%D9%86%DB%8C\" >\ud83d\udd04 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%92%BE%D9%85%D8%B5%D8%B1%D9%81_%D8%AD%D8%A7%D9%81%D8%B8%D9%87\" >\ud83d\udcbe\u0645\u0635\u0631\u0641 \u062d\u0627\u0641\u0638\u0647<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%92%A1_%D8%AA%D9%88%D8%B5%DB%8C%D9%87_%D9%87%D8%A7\" >\ud83d\udca1 \u062a\u0648\u0635\u06cc\u0647 \u0647\u0627<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%8E%AF_%D8%B2%D9%85%D8%A7%D9%86_%D8%A7%D8%B3%D8%AA%D9%81%D8%A7%D8%AF%D9%87_%D8%A7%D8%B2_%D9%87%D8%B1_%DA%A9%D8%AF%D8%A7%D9%85\" >\ud83c\udfaf \u0632\u0645\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0647\u0631 \u06a9\u062f\u0627\u0645<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#STRtree\" >STRtree<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#RTree\" >RTree<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%9B%A0%EF%B8%8F_%D8%AE%D9%88%D8%B1%D8%A7%DA%A9%DB%8C_%D9%87%D8%A7%DB%8C_%DA%A9%D8%A7%D8%B1%D8%A8%D8%B1%D8%AF%DB%8C\" >\ud83d\udee0\ufe0f \u062e\u0648\u0631\u0627\u06a9\u06cc \u0647\u0627\u06cc \u06a9\u0627\u0631\u0628\u0631\u062f\u06cc<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/nabfollower.com\/blog\/optimizing-geometric-overlap-detection-a-deep-dive-into-spatial-indexing-with-python-2ndc\/#%F0%9F%8E%89_%D9%86%D8%AA%DB%8C%D8%AC%D9%87_%DA%AF%DB%8C%D8%B1%DB%8C\" >\ud83c\udf89 \u0646\u062a\u06cc\u062c\u0647 \u06af\u06cc\u0631\u06cc<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"%F0%9F%8E%AF_%DA%86%D8%A7%D9%84%D8%B4_%D8%AA%D9%82%D8%A7%D8%B7%D8%B9_%D9%87%D8%A7%DB%8C_%D9%87%D9%86%D8%AF%D8%B3%DB%8C\"><\/span>\n<p>  \ud83c\udfaf \u0686\u0627\u0644\u0634 \u062a\u0642\u0627\u0637\u0639 \u0647\u0627\u06cc \u0647\u0646\u062f\u0633\u06cc<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0647\u0646\u06af\u0627\u0645 \u06a9\u0627\u0631 \u0628\u0627 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0645\u06a9\u0627\u0646\u06cc\u060c \u06cc\u06a9\u06cc \u0627\u0632 \u0648\u0638\u0627\u06cc\u0641 \u0631\u0627\u06cc\u062c \u062a\u0634\u062e\u06cc\u0635 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc \u0647\u0627 \u06cc\u0627 \u062a\u0642\u0627\u0637\u0639 \u0647\u0627 \u0628\u06cc\u0646 \u0686\u0646\u062f \u0636\u0644\u0639\u06cc \u0647\u0627 \u0627\u0633\u062a. \u06cc\u06a9 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647 \u0644\u0648\u062d\u0627\u0646\u0647 \u062f\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0631 \u0647\u0646\u062f\u0633\u0647 \u0628\u0627 \u0647\u0631 \u0647\u0646\u062f\u0633\u0647 \u062f\u06cc\u06af\u0631 \u0628\u0647 \u0633\u0631\u0639\u062a \u0628\u0627 \u0631\u0634\u062f \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0646\u0627\u06a9\u0627\u0631\u0622\u0645\u062f \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"%F0%9F%94%8D_%D9%86%D9%85%D8%A7%DB%8C%D9%87_%D8%B3%D8%A7%D8%B2%DB%8C_%D9%81%D8%B6%D8%A7%DB%8C%DB%8C_%DA%86%DA%AF%D9%88%D9%86%D9%87_%DA%A9%D8%A7%D8%B1_%D9%85%DB%8C_%DA%A9%D9%86%D8%AF\"><\/span>\n<p>  \ud83d\udd0d \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0686\u06af\u0648\u0646\u0647 \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u062a\u0641\u0627\u0648\u062a \u0628\u06cc\u0646 \u0631\u0648\u06cc\u06a9\u0631\u062f\u0647\u0627\u06cc \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0633\u0627\u062f\u0647 \u0648 \u0641\u0636\u0627\u06cc\u06cc \u0631\u0627 \u0645\u062c\u0633\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<p><\/p>\n<hr\/>\n<h3><span class=\"ez-toc-section\" id=\"%F0%9F%90%8C_%D8%B1%D9%88%DB%8C%DA%A9%D8%B1%D8%AF_%D8%B3%D8%A7%D8%AF%D9%87_%D9%84%D9%88%D8%AD%D8%A7%D9%86%D9%87_%D8%B1%D9%88%D8%B4_%D9%86%DB%8C%D8%B1%D9%88%DB%8C_%D8%A8%DB%8C_%D8%B1%D8%AD%D9%85\"><\/span>\n<p>  \ud83d\udc0c \u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647 \u0644\u0648\u062d\u0627\u0646\u0647: \u0631\u0648\u0634 \u0646\u06cc\u0631\u0648\u06cc \u0628\u06cc \u0631\u062d\u0645<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"highlight js-code-highlight\">\n<pre class=\"highlight python\"><code><span class=\"k\">def<\/span> <span class=\"nf\">check_overlaps_naive<\/span><span class=\"p\">(<\/span><span class=\"n\">gdf<\/span><span class=\"p\">):<\/span>\n    <span class=\"n\">errors<\/span> <span class=\"o\">=<\/span> <span class=\"p\">[]<\/span>\n    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span> <span class=\"ow\">in<\/span> <span class=\"nf\">range<\/span><span class=\"p\">(<\/span><span class=\"nf\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">gdf<\/span><span class=\"p\">)):<\/span>\n        <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"nf\">range<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span> <span class=\"o\">+<\/span> <span class=\"mi\">1<\/span><span class=\"p\">,<\/span> <span class=\"nf\">len<\/span><span class=\"p\">(<\/span><span class=\"n\">gdf<\/span><span class=\"p\">)):<\/span>\n            <span class=\"n\">geom1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">gdf<\/span><span class=\"p\">.<\/span><span class=\"n\">iloc<\/span><span class=\"p\">[<\/span><span class=\"n\">i<\/span><span class=\"p\">].<\/span><span class=\"n\">geometry<\/span>\n            <span class=\"n\">geom2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">gdf<\/span><span class=\"p\">.<\/span><span class=\"n\">iloc<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">].<\/span><span class=\"n\">geometry<\/span>\n\n            <span class=\"k\">if<\/span> <span class=\"n\">geom1<\/span><span class=\"p\">.<\/span><span class=\"nf\">intersects<\/span><span class=\"p\">(<\/span><span class=\"n\">geom2<\/span><span class=\"p\">):<\/span>\n                <span class=\"c1\"># Process intersection\n<\/span>                <span class=\"n\">intersection<\/span> <span class=\"o\">=<\/span> <span class=\"n\">geom1<\/span><span class=\"p\">.<\/span><span class=\"nf\">intersection<\/span><span class=\"p\">(<\/span><span class=\"n\">geom2<\/span><span class=\"p\">)<\/span>\n                <span class=\"c1\"># Add to errors list\n<\/span>    <span class=\"k\">return<\/span> <span class=\"n\">errors<\/span>\n<\/code><\/pre>\n<div class=\"highlight__panel js-actions-panel\">\n<div class=\"highlight__panel-action js-fullscreen-code-action\">\n    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-on\"><title>\u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M16 3h6v6h-2V5h-4V3zM2 3h6v2H4v4H2V3zm18 16v-4h2v6h-6v-2h4zM4 19h4v2H2v-6h2v4z\"\/>\n<\/svg><\/p>\n<p>    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-off\"><title>\u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M18 7h4v2h-6V3h2v4zM8 9H2V7h4V3h2v6zm10 8v4h-2v-6h6v2h-4zM8 15v6H6v-4H2v-2h6z\"\/>\n<\/svg><\/p>\n<\/div>\n<\/div>\n<\/div>\n<blockquote>\n<p>\u26a0\ufe0f <strong>\u0686\u0631\u0627 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647 \u0644\u0648\u062d\u0627\u0646\u0647 \u062a\u0648\u0635\u06cc\u0647 \u0646\u0645\u06cc \u0634\u0648\u062f:<\/strong><\/p>\n<ul>\n<li>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc O(n\u00b2) \u0627\u0633\u062a\u060c \u06a9\u0647 \u062f\u0631 \u0622\u0646 n \u062a\u0639\u062f\u0627\u062f \u0647\u0646\u062f\u0633\u0647 \u0647\u0627 \u0627\u0633\u062a<\/li>\n<li>\u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 \u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647\u060c \u0639\u0645\u0644\u06a9\u0631\u062f \u0628\u0647 \u0637\u0648\u0631 \u062a\u0635\u0627\u0639\u062f\u06cc \u06a9\u0627\u0647\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f<\/li>\n<li>\u0628\u0631\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af (\u0647\u0632\u0627\u0631\u0627\u0646 \u0647\u0646\u062f\u0633\u0647) \u063a\u06cc\u0631 \u0639\u0645\u0644\u06cc \u0645\u06cc \u0634\u0648\u062f<\/li>\n<\/ul>\n<\/blockquote>\n<hr\/>\n<h2><span class=\"ez-toc-section\" id=\"%E2%9A%A1_%D9%86%D9%85%D8%A7%DB%8C%D9%87_%D8%B3%D8%A7%D8%B2%DB%8C_%D9%81%D8%B6%D8%A7%DB%8C%DB%8C_%DB%8C%DA%A9_%D8%A8%D8%A7%D8%B2%DB%8C_%D8%AA%D8%BA%DB%8C%DB%8C%D8%B1_%D8%AF%D9%87%D9%86%D8%AF%D9%87_%D8%B9%D9%85%D9%84%DA%A9%D8%B1%D8%AF\"><\/span>\n<p>  \u26a1 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc: \u06cc\u06a9 \u0628\u0627\u0632\u06cc \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u0646\u062f\u0647 \u0639\u0645\u0644\u06a9\u0631\u062f<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0628\u0627 \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0627\u062f\u0647 \u0633\u0644\u0633\u0644\u0647 \u0645\u0631\u0627\u062a\u0628\u06cc \u06a9\u0627\u0631 \u0645\u06cc \u06a9\u0646\u062f \u06a9\u0647 \u0647\u0646\u062f\u0633\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0648\u0633\u0639\u062a \u0641\u0636\u0627\u06cc\u06cc \u0622\u0646\u0647\u0627 \u0633\u0627\u0632\u0645\u0627\u0646\u062f\u0647\u06cc \u0645\u06cc \u06a9\u0646\u062f. \u0627\u06cc\u0646 \u0627\u0645\u06a9\u0627\u0646 \u062d\u0630\u0641 \u0633\u0631\u06cc\u0639 \u0647\u0646\u062f\u0633\u0647\u200c\u0647\u0627\u06cc\u06cc \u0631\u0627 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc\u200c\u06a9\u0646\u062f \u06a9\u0647 \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u064b \u0646\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0642\u0637\u0639 \u0634\u0648\u0646\u062f \u0648 \u062a\u0639\u062f\u0627\u062f \u0628\u0631\u0631\u0633\u06cc\u200c\u0647\u0627\u06cc \u062f\u0642\u06cc\u0642 \u062a\u0642\u0627\u0637\u0639 \u0631\u0627 \u0628\u0647\u200c\u0637\u0648\u0631 \u0686\u0634\u0645\u06af\u06cc\u0631\u06cc \u06a9\u0627\u0647\u0634 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"1%EF%B8%8F%E2%83%A3_STRtree_%D8%AF%D8%B1%D8%AE%D8%AA_%D9%85%D8%B1%D8%AA%D8%A8_%D8%B3%D8%A7%D8%B2%DB%8C-%DA%A9%D8%A7%D8%B4%DB%8C-%D8%A8%D8%A7%D8%B2%DA%AF%D8%B4%D8%AA%DB%8C\"><\/span>\n<p>  1\ufe0f\u20e3 STRtree (\u062f\u0631\u062e\u062a \u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc-\u06a9\u0627\u0634\u06cc-\u0628\u0627\u0632\u06af\u0634\u062a\u06cc)<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/media2.dev.to\/dynamic\/image\/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto\/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fjbeiqx6vi61v59gg7j3e.png\" alt=\"\u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc Strtree\" loading=\"lazy\" width=\"771\" height=\"463\" title=\"\"><\/p>\n<div class=\"highlight js-code-highlight\">\n<pre class=\"highlight python\"><code><span class=\"kn\">from<\/span> <span class=\"n\">shapely<\/span> <span class=\"kn\">import<\/span> <span class=\"n\">STRtree<\/span>\n\n<span class=\"k\">def<\/span> <span class=\"nf\">check_overlaps_strtree<\/span><span class=\"p\">(<\/span><span class=\"n\">gdf<\/span><span class=\"p\">):<\/span>\n    <span class=\"c1\"># Create the spatial index\n<\/span>    <span class=\"n\">tree<\/span> <span class=\"o\">=<\/span> <span class=\"nc\">STRtree<\/span><span class=\"p\">(<\/span><span class=\"n\">gdf<\/span><span class=\"p\">.<\/span><span class=\"n\">geometry<\/span><span class=\"p\">.<\/span><span class=\"n\">values<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"c1\"># Process each geometry\n<\/span>    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">geom<\/span> <span class=\"ow\">in<\/span> <span class=\"nf\">enumerate<\/span><span class=\"p\">(<\/span><span class=\"n\">gdf<\/span><span class=\"p\">.<\/span><span class=\"n\">geometry<\/span><span class=\"p\">):<\/span>\n        <span class=\"c1\"># Query potential intersections efficiently\n<\/span>        <span class=\"n\">potential_matches_idx<\/span> <span class=\"o\">=<\/span> <span class=\"n\">tree<\/span><span class=\"p\">.<\/span><span class=\"nf\">query<\/span><span class=\"p\">(<\/span><span class=\"n\">geom<\/span><span class=\"p\">)<\/span>\n\n        <span class=\"c1\"># Check only potential matches\n<\/span>        <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">potential_matches_idx<\/span><span class=\"p\">:<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">j<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">i<\/span><span class=\"p\">:<\/span>\n                <span class=\"k\">continue<\/span>\n\n            <span class=\"n\">other_geom<\/span> <span class=\"o\">=<\/span> <span class=\"n\">gdf<\/span><span class=\"p\">.<\/span><span class=\"n\">geometry<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">]<\/span>\n            <span class=\"c1\"># Detailed intersection test\n<\/span>            <span class=\"k\">if<\/span> <span class=\"n\">geom<\/span><span class=\"p\">.<\/span><span class=\"nf\">intersects<\/span><span class=\"p\">(<\/span><span class=\"n\">other_geom<\/span><span class=\"p\">):<\/span>\n                <span class=\"c1\"># Process intersection\n<\/span>                <span class=\"n\">intersection<\/span> <span class=\"o\">=<\/span> <span class=\"n\">geom<\/span><span class=\"p\">.<\/span><span class=\"nf\">intersection<\/span><span class=\"p\">(<\/span><span class=\"n\">other_geom<\/span><span class=\"p\">)<\/span>\n                <span class=\"c1\"># Record results\n<\/span><\/code><\/pre>\n<div class=\"highlight__panel js-actions-panel\">\n<div class=\"highlight__panel-action js-fullscreen-code-action\">\n    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-on\"><title>\u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M16 3h6v6h-2V5h-4V3zM2 3h6v2H4v4H2V3zm18 16v-4h2v6h-6v-2h4zM4 19h4v2H2v-6h2v4z\"\/>\n<\/svg><\/p>\n<p>    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-off\"><title>\u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M18 7h4v2h-6V3h2v4zM8 9H2V7h4V3h2v6zm10 8v4h-2v-6h6v2h-4zM8 15v6H6v-4H2v-2h6z\"\/>\n<\/svg><\/p>\n<\/div>\n<\/div>\n<\/div>\n<h4><span class=\"ez-toc-section\" id=\"%F0%9F%94%91_%D9%85%D9%81%D8%A7%D9%87%DB%8C%D9%85_%DA%A9%D9%84%DB%8C%D8%AF%DB%8C_STRtree\"><\/span>\n<p>  \ud83d\udd11 \u0645\u0641\u0627\u0647\u06cc\u0645 \u06a9\u0644\u06cc\u062f\u06cc STRtree:<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\ud83d\udce6 \u0641\u0636\u0627 \u0631\u0627 \u0628\u0647 \u0645\u0646\u0627\u0637\u0642 \u0633\u0644\u0633\u0644\u0647 \u0645\u0631\u0627\u062a\u0628\u06cc \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u062f<\/li>\n<li>\ud83d\udccf \u0627\u0632 \u0645\u0633\u062a\u0637\u06cc\u0644 \u0647\u0627\u06cc \u062d\u062f\u0627\u0642\u0644 \u0645\u062d\u062f\u0648\u062f (MBR) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f<\/li>\n<li>\ud83d\ude80 \u0627\u0645\u06a9\u0627\u0646 \u0641\u06cc\u0644\u062a\u0631 \u06a9\u0631\u062f\u0646 \u0633\u0631\u06cc\u0639 \u0647\u0646\u062f\u0633\u0647 \u0647\u0627\u06cc \u063a\u06cc\u0631 \u0645\u062a\u0642\u0627\u0637\u0639 \u0631\u0627 \u0641\u0631\u0627\u0647\u0645 \u0645\u06cc \u06a9\u0646\u062f<\/li>\n<li>\ud83d\udcc8 \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0631\u0627 \u0627\u0632 O(n\u00b2) \u0628\u0647 O(n log n) \u06a9\u0627\u0647\u0634 \u0645\u06cc \u062f\u0647\u062f.<\/li>\n<\/ul>\n<hr\/>\n<h3><span class=\"ez-toc-section\" id=\"2%EF%B8%8F%E2%83%A3_%D9%86%D9%85%D8%A7%DB%8C%D9%87_%D8%B3%D8%A7%D8%B2%DB%8C_Rtree\"><\/span>\n<p>  2\ufe0f\u20e3 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc Rtree<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img decoding=\"async\" src=\"https:\/\/media2.dev.to\/dynamic\/image\/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto\/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fopqukru8a0fzw7ojq20b.png\" alt=\"Rtree Indexing\" loading=\"lazy\" width=\"654\" height=\"495\" title=\"\"><\/p>\n<div class=\"highlight js-code-highlight\">\n<pre class=\"highlight python\"><code><span class=\"kn\">import<\/span> <span class=\"n\">rtree<\/span>\n\n<span class=\"k\">def<\/span> <span class=\"nf\">check_overlaps_rtree<\/span><span class=\"p\">(<\/span><span class=\"n\">gdf<\/span><span class=\"p\">):<\/span>\n    <span class=\"c1\"># Create spatial index\n<\/span>    <span class=\"n\">idx<\/span> <span class=\"o\">=<\/span> <span class=\"n\">rtree<\/span><span class=\"p\">.<\/span><span class=\"n\">index<\/span><span class=\"p\">.<\/span><span class=\"nc\">Index<\/span><span class=\"p\">()<\/span>\n\n    <span class=\"c1\"># Insert geometries with their bounding boxes\n<\/span>    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">geom<\/span> <span class=\"ow\">in<\/span> <span class=\"nf\">enumerate<\/span><span class=\"p\">(<\/span><span class=\"n\">gdf<\/span><span class=\"p\">.<\/span><span class=\"n\">geometry<\/span><span class=\"p\">):<\/span>\n        <span class=\"n\">idx<\/span><span class=\"p\">.<\/span><span class=\"nf\">insert<\/span><span class=\"p\">(<\/span><span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">geom<\/span><span class=\"p\">.<\/span><span class=\"n\">bounds<\/span><span class=\"p\">)<\/span>\n\n    <span class=\"c1\"># Process geometries\n<\/span>    <span class=\"k\">for<\/span> <span class=\"n\">i<\/span><span class=\"p\">,<\/span> <span class=\"n\">row<\/span> <span class=\"ow\">in<\/span> <span class=\"nf\">enumerate<\/span><span class=\"p\">(<\/span><span class=\"n\">gdf<\/span><span class=\"p\">.<\/span><span class=\"nf\">itertuples<\/span><span class=\"p\">()):<\/span>\n        <span class=\"n\">geom1<\/span> <span class=\"o\">=<\/span> <span class=\"n\">row<\/span><span class=\"p\">.<\/span><span class=\"n\">geometry<\/span>\n\n        <span class=\"c1\"># Find potential intersections using bounding boxes\n<\/span>        <span class=\"k\">for<\/span> <span class=\"n\">j<\/span> <span class=\"ow\">in<\/span> <span class=\"n\">idx<\/span><span class=\"p\">.<\/span><span class=\"nf\">intersection<\/span><span class=\"p\">(<\/span><span class=\"n\">geom1<\/span><span class=\"p\">.<\/span><span class=\"n\">bounds<\/span><span class=\"p\">):<\/span>\n            <span class=\"k\">if<\/span> <span class=\"n\">j<\/span> <span class=\"o\">&lt;=<\/span> <span class=\"n\">i<\/span><span class=\"p\">:<\/span>\n                <span class=\"k\">continue<\/span>\n\n            <span class=\"n\">geom2<\/span> <span class=\"o\">=<\/span> <span class=\"n\">gdf<\/span><span class=\"p\">.<\/span><span class=\"n\">iloc<\/span><span class=\"p\">[<\/span><span class=\"n\">j<\/span><span class=\"p\">].<\/span><span class=\"n\">geometry<\/span>\n            <span class=\"c1\"># Detailed intersection test\n<\/span>            <span class=\"k\">if<\/span> <span class=\"n\">geom1<\/span><span class=\"p\">.<\/span><span class=\"nf\">intersects<\/span><span class=\"p\">(<\/span><span class=\"n\">geom2<\/span><span class=\"p\">):<\/span>\n                <span class=\"c1\"># Process intersection\n<\/span>                <span class=\"n\">intersection<\/span> <span class=\"o\">=<\/span> <span class=\"n\">geom1<\/span><span class=\"p\">.<\/span><span class=\"nf\">intersection<\/span><span class=\"p\">(<\/span><span class=\"n\">geom2<\/span><span class=\"p\">)<\/span>\n<\/code><\/pre>\n<div class=\"highlight__panel js-actions-panel\">\n<div class=\"highlight__panel-action js-fullscreen-code-action\">\n    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-on\"><title>\u0648\u0627\u0631\u062f \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M16 3h6v6h-2V5h-4V3zM2 3h6v2H4v4H2V3zm18 16v-4h2v6h-6v-2h4zM4 19h4v2H2v-6h2v4z\"\/>\n<\/svg><\/p>\n<p>    <svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" class=\"highlight-action crayons-icon highlight-action--fullscreen-off\"><title>\u0627\u0632 \u062d\u0627\u0644\u062a \u062a\u0645\u0627\u0645 \u0635\u0641\u062d\u0647 \u062e\u0627\u0631\u062c \u0634\u0648\u06cc\u062f<\/title>\n    <path d=\"M18 7h4v2h-6V3h2v4zM8 9H2V7h4V3h2v6zm10 8v4h-2v-6h6v2h-4zM8 15v6H6v-4H2v-2h6z\"\/>\n<\/svg><\/p>\n<\/div>\n<\/div>\n<\/div>\n<h4><span class=\"ez-toc-section\" id=\"%F0%9F%94%91_%D9%85%D9%81%D8%A7%D9%87%DB%8C%D9%85_%DA%A9%D9%84%DB%8C%D8%AF%DB%8C_RTree\"><\/span>\n<p>  \ud83d\udd11 \u0645\u0641\u0627\u0647\u06cc\u0645 \u06a9\u0644\u06cc\u062f\u06cc RTree:<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\ud83c\udf33 \u0647\u0646\u062f\u0633\u0647 \u0647\u0627 \u0631\u0627 \u062f\u0631 \u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0631\u062e\u062a\u06cc \u0645\u062a\u0639\u0627\u062f\u0644 \u0633\u0627\u0632\u0645\u0627\u0646\u062f\u0647\u06cc \u0645\u06cc \u06a9\u0646\u062f<\/li>\n<li>\ud83d\udce6 \u0627\u0632 \u0633\u0644\u0633\u0644\u0647 \u0645\u0631\u0627\u062a\u0628 \u062c\u0639\u0628\u0647 \u0645\u062d\u062f\u0648\u062f \u0628\u0631\u0627\u06cc \u0641\u06cc\u0644\u062a\u0631 \u06a9\u0631\u062f\u0646 \u0633\u0631\u06cc\u0639 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u062f<\/li>\n<li>\u26a1 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0627\u06cc \u063a\u06cc\u0631 \u0636\u0631\u0648\u0631\u06cc \u0631\u0627 \u06a9\u0627\u0647\u0634 \u0645\u06cc \u062f\u0647\u062f<\/li>\n<li>\ud83d\udd0d \u067e\u0631\u0633 \u0648 \u062c\u0648\u06cc \u0641\u0636\u0627\u06cc\u06cc \u06a9\u0627\u0631\u0622\u0645\u062f \u0631\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc \u062f\u0647\u062f<\/li>\n<\/ul>\n<hr\/>\n<h2><span class=\"ez-toc-section\" id=\"%F0%9F%93%8A_%D8%AA%D8%AD%D9%84%DB%8C%D9%84_%D9%85%D9%82%D8%A7%DB%8C%D8%B3%D9%87_%D8%A7%DB%8C\"><\/span>\n<p>  \ud83d\udcca \u062a\u062d\u0644\u06cc\u0644 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0627\u06cc<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"table-wrapper-paragraph\">\n<table>\n<thead>\n<tr>\n<th>\u0648\u06cc\u0698\u06af\u06cc<\/th>\n<th>STRtree (\u0645\u0631\u062a\u0628\u200c\u0633\u0627\u0632\u06cc-\u06a9\u0627\u0634\u06cc-\u062f\u0631\u062e\u062a \u0628\u0627\u0632\u06af\u0634\u062a\u06cc)<\/th>\n<th>RTree (\u062f\u0631\u062e\u062a \u0645\u062a\u0639\u0627\u062f\u0644)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0632\u0645\u0627\u0646\u06cc<\/strong><\/td>\n<td>O(n log n)<\/td>\n<td>O(n log n)<\/td>\n<\/tr>\n<tr>\n<td><strong>\u067e\u0627\u0631\u062a\u06cc\u0634\u0646 \u0628\u0646\u062f\u06cc \u0641\u0636\u0627<\/strong><\/td>\n<td>\u0645\u0631\u062a\u0628 \u0633\u0627\u0632\u06cc &#8211; \u06a9\u0627\u0634\u06cc &#8211; \u0628\u0627\u0632\u06af\u0634\u062a\u06cc<\/td>\n<td>\u062f\u0631\u062e\u062a \u0645\u062a\u0639\u0627\u062f\u0644<\/td>\n<\/tr>\n<tr>\n<td><strong>\u0639\u0645\u0644\u06a9\u0631\u062f<\/strong><\/td>\n<td>\u0633\u0631\u06cc\u0639\u062a\u0631<\/td>\n<td>\u0646\u0633\u0628\u062a\u0627 \u06a9\u0646\u062f\u062a\u0631<\/td>\n<\/tr>\n<tr>\n<td><strong>\u0633\u0631\u0628\u0627\u0631 \u062d\u0627\u0641\u0638\u0647<\/strong><\/td>\n<td>\u0645\u062a\u0648\u0633\u0637<\/td>\n<td>\u06a9\u0645\u06cc \u0628\u0627\u0644\u0627\u062a\u0631<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<hr\/>\n<h2><span class=\"ez-toc-section\" id=\"%F0%9F%93%88_%D9%86%D8%AA%D8%A7%DB%8C%D8%AC_%D9%85%D8%AD%DA%A9\"><\/span>\n<p>  \ud83d\udcc8 \u0646\u062a\u0627\u06cc\u062c \u0645\u062d\u06a9<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<blockquote>\n<p>\u0645\u0627 \u0627\u06cc\u0646 \u0631\u0648\u06cc\u06a9\u0631\u062f\u0647\u0627 \u0631\u0627 \u0631\u0648\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0627\u06cc \u0627\u0632 45746 \u0647\u0646\u062f\u0633\u0647 \u0686\u0646\u062f \u0636\u0644\u0639\u06cc \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0631\u062f\u06cc\u0645<\/p>\n<\/blockquote>\n<h3><span class=\"ez-toc-section\" id=\"%E2%9A%A1_%D9%85%D8%B9%DB%8C%D8%A7%D8%B1%D9%87%D8%A7%DB%8C_%D8%B9%D9%85%D9%84%DA%A9%D8%B1%D8%AF\"><\/span>\n<p>  \u26a1 \u0645\u0639\u06cc\u0627\u0631\u0647\u0627\u06cc \u0639\u0645\u0644\u06a9\u0631\u062f<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"table-wrapper-paragraph\">\n<table>\n<thead>\n<tr>\n<th>\u0645\u062a\u0631\u06cc\u06a9<\/th>\n<th>STRtree<\/th>\n<th>RTree<\/th>\n<th>\u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647 \u0644\u0648\u062d\u0627\u0646\u0647<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0632\u0645\u0627\u0646 \u0627\u062c\u0631\u0627<\/td>\n<td>1.3747 \u062b\u0627\u0646\u06cc\u0647<\/td>\n<td>6.6556 \u062b\u0627\u0646\u06cc\u0647<\/td>\n<td>\u0627\u062c\u0631\u0627 \u0646\u0645\u06cc \u0634\u0648\u062f<\/td>\n<\/tr>\n<tr>\n<td>\u0647\u0646\u062f\u0633\u0647 \u067e\u0631\u062f\u0627\u0632\u0634 \u0634\u062f\u0647<\/td>\n<td>45746<\/td>\n<td>45746<\/td>\n<td>N\/A<\/td>\n<\/tr>\n<tr>\n<td>\u0646\u0631\u062e \u067e\u0631\u062f\u0627\u0632\u0634<\/td>\n<td>~33219 \u0648\u06cc\u0698\u06af\u06cc \u062f\u0631 \u062b\u0627\u0646\u06cc\u0647<\/td>\n<td>~9718 \u0648\u06cc\u0698\u06af\u06cc \u062f\u0631 \u062b\u0627\u0646\u06cc\u0647<\/td>\n<td>N\/A<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h3><span class=\"ez-toc-section\" id=\"%F0%9F%94%84_%D8%AA%D8%AC%D8%B2%DB%8C%D9%87_%D9%88_%D8%AA%D8%AD%D9%84%DB%8C%D9%84_%D9%87%D9%85%D9%BE%D9%88%D8%B4%D8%A7%D9%86%DB%8C\"><\/span>\n<p>  \ud83d\udd04 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"table-wrapper-paragraph\">\n<table>\n<thead>\n<tr>\n<th>\u0646\u0648\u0639 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc<\/th>\n<th>STRtree<\/th>\n<th>RTree<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc \u0647\u0627\u06cc \u0639\u0645\u062f\u0647 (\u226520%)<\/td>\n<td>5<\/td>\n<td>5<\/td>\n<\/tr>\n<tr>\n<td>\u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc \u0647\u0627\u06cc \u062c\u0632\u0626\u06cc (<20%)<\/td>\n<td>23<\/td>\n<td>23<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u062c\u0645\u0648\u0639 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc \u0647\u0627<\/td>\n<td>28<\/td>\n<td>28<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h3><span class=\"ez-toc-section\" id=\"%F0%9F%92%BE%D9%85%D8%B5%D8%B1%D9%81_%D8%AD%D8%A7%D9%81%D8%B8%D9%87\"><\/span>\n<p>  \ud83d\udcbe\u0645\u0635\u0631\u0641 \u062d\u0627\u0641\u0638\u0647<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"table-wrapper-paragraph\">\n<table>\n<thead>\n<tr>\n<th>\u0645\u0631\u062d\u0644\u0647<\/th>\n<th>\u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062d\u0627\u0641\u0638\u0647<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u062d\u0627\u0641\u0638\u0647 \u0627\u0648\u0644\u06cc\u0647<\/td>\n<td>145.1 \u0645\u06af\u0627\u0628\u0627\u06cc\u062a<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0648\u062c \u062d\u0627\u0641\u0638\u0647<\/td>\n<td>330.9 \u0645\u06af\u0627\u0628\u0627\u06cc\u062a<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0641\u0632\u0627\u06cc\u0634 \u062d\u0627\u0641\u0638\u0647<\/td>\n<td>~ 185.8 \u0645\u06af\u0627\u0628\u0627\u06cc\u062a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<hr\/>\n<h2><span class=\"ez-toc-section\" id=\"%F0%9F%92%A1_%D8%AA%D9%88%D8%B5%DB%8C%D9%87_%D9%87%D8%A7\"><\/span>\n<p>  \ud83d\udca1 \u062a\u0648\u0635\u06cc\u0647 \u0647\u0627<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ol>\n<li>\n<strong>\u0627\u0632 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f<\/strong>: \u0647\u0645\u06cc\u0634\u0647 \u0627\u0632 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0628\u0631\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f<\/li>\n<li>\n<strong>STRtree \u0631\u0627 \u062a\u0631\u062c\u06cc\u062d \u062f\u0647\u06cc\u062f<\/strong>: \u062f\u0631 \u0645\u0639\u06cc\u0627\u0631 \u0645\u0627\u060c STRtree \u0628\u0647\u062a\u0631 \u0627\u0632 RTree \u0639\u0645\u0644 \u06a9\u0631\u062f<\/li>\n<li>\n<strong>\u0627\u0646\u062f\u0627\u0632\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f<\/strong>: \u0628\u0631\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u06a9\u0648\u0686\u06a9 (<1000 \u0647\u0646\u062f\u0633\u0647)\u060c \u06cc\u06a9 \u0631\u0648\u06cc\u06a9\u0631\u062f \u0633\u0627\u062f\u0647 \u0644\u0648\u062d\u0627\u0646\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0642\u0627\u0628\u0644 \u0642\u0628\u0648\u0644 \u0628\u0627\u0634\u062f<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"%F0%9F%8E%AF_%D8%B2%D9%85%D8%A7%D9%86_%D8%A7%D8%B3%D8%AA%D9%81%D8%A7%D8%AF%D9%87_%D8%A7%D8%B2_%D9%87%D8%B1_%DA%A9%D8%AF%D8%A7%D9%85\"><\/span>\n<p>  \ud83c\udfaf \u0632\u0645\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0647\u0631 \u06a9\u062f\u0627\u0645<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"STRtree\"><\/span>\n<p>  STRtree<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ol>\n<li>\ud83d\udcca \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0628\u0627 \u062a\u0648\u0632\u06cc\u0639 \u06cc\u06a9\u0646\u0648\u0627\u062e\u062a<\/li>\n<li>\u26a1 \u0648\u0642\u062a\u06cc \u0633\u0631\u0639\u062a \u062d\u06cc\u0627\u062a\u06cc \u0627\u0633\u062a<\/li>\n<li>\ud83c\udf0d \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u062c\u063a\u0631\u0627\u0641\u06cc\u0627\u06cc\u06cc \u0628\u0627 \u0647\u0646\u062f\u0633\u0647 \u0647\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631<\/li>\n<\/ol>\n<h4><span class=\"ez-toc-section\" id=\"RTree\"><\/span>\n<p>  RTree<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ol>\n<li>\ud83d\udd04 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0628\u0627 \u062a\u0648\u0632\u06cc\u0639 \u0647\u0627\u06cc \u0641\u0636\u0627\u06cc\u06cc \u067e\u06cc\u0686\u06cc\u062f\u0647<\/li>\n<li>\ud83c\udfaf \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0645\u06a9\u0627\u0646\u06cc \u062f\u0642\u06cc\u0642 \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0627\u0633\u062a<\/li>\n<li>\ud83d\udd0d \u0628\u0631\u0646\u0627\u0645\u0647 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0647 \u067e\u0631\u0633 \u0648 \u062c\u0648\u0647\u0627\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0627\u0646\u0639\u0637\u0627\u0641 \u067e\u0630\u06cc\u0631 \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u0646\u062f<\/li>\n<\/ol>\n<hr\/>\n<h3><span class=\"ez-toc-section\" id=\"%F0%9F%9B%A0%EF%B8%8F_%D8%AE%D9%88%D8%B1%D8%A7%DA%A9%DB%8C_%D9%87%D8%A7%DB%8C_%DA%A9%D8%A7%D8%B1%D8%A8%D8%B1%D8%AF%DB%8C\"><\/span>\n<p>  \ud83d\udee0\ufe0f \u062e\u0648\u0631\u0627\u06a9\u06cc \u0647\u0627\u06cc \u06a9\u0627\u0631\u0628\u0631\u062f\u06cc<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<blockquote>\n<p>\ud83d\udca1 <strong>\u0646\u06a9\u0627\u062a \u06a9\u0644\u06cc\u062f\u06cc \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0628\u0647 \u062e\u0627\u0637\u0631 \u0628\u0633\u067e\u0627\u0631\u06cc\u062f<\/strong><\/p>\n<ul>\n<li>\u0647\u0645\u06cc\u0634\u0647 \u0628\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u062e\u0627\u0635 \u062e\u0648\u062f \u0645\u062d\u06a9 \u0628\u0632\u0646\u06cc\u062f<\/li>\n<li>\u0645\u062d\u062f\u0648\u062f\u06cc\u062a \u0647\u0627\u06cc \u062d\u0627\u0641\u0638\u0647 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0628\u06af\u06cc\u0631\u06cc\u062f<\/li>\n<li>\u0627\u0632 \u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0628\u0631\u0627\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0647\u0646\u062f\u0633\u06cc \u0628\u0632\u0631\u06af \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f<\/li>\n<li>\u0645\u0634\u062e\u0635\u0627\u062a \u0648 \u0628\u0631 \u0627\u0633\u0627\u0633 \u0645\u0648\u0631\u062f \u062e\u0627\u0635 \u062e\u0648\u062f \u0631\u0627 \u0628\u0647\u06cc\u0646\u0647 \u06a9\u0646\u06cc\u062f<\/li>\n<\/ul>\n<\/blockquote>\n<hr\/>\n<h2><span class=\"ez-toc-section\" id=\"%F0%9F%8E%89_%D9%86%D8%AA%DB%8C%D8%AC%D9%87_%DA%AF%DB%8C%D8%B1%DB%8C\"><\/span>\n<p>  \ud83c\udf89 \u0646\u062a\u06cc\u062c\u0647 \u06af\u06cc\u0631\u06cc<br \/>\n<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0646\u0645\u0627\u06cc\u0647 \u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0628\u0631\u0627\u06cc \u062a\u0634\u062e\u06cc\u0635 \u06a9\u0627\u0631\u0622\u0645\u062f \u062a\u0642\u0627\u0637\u0639 \u0647\u0646\u062f\u0633\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0645\u0647\u0645 \u0627\u0633\u062a. \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u062a\u06a9\u0646\u06cc\u06a9 \u0647\u0627\u06cc\u06cc \u0645\u0627\u0646\u0646\u062f STRtree\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u067e\u06cc\u0686\u06cc\u062f\u06af\u06cc \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u0648 \u0632\u0645\u0627\u0646 \u067e\u0631\u062f\u0627\u0632\u0634 \u0631\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0686\u0634\u0645\u06af\u06cc\u0631\u06cc \u06a9\u0627\u0647\u0634 \u062f\u0647\u06cc\u062f.<\/p>\n<blockquote>\n<p>\ud83d\udca1 <strong>\u0628\u0631\u0627\u06cc \u0646\u06a9\u062a\u0647<\/strong>: \u0647\u0645\u06cc\u0634\u0647 \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0627\u0635 \u062e\u0648\u062f \u0631\u0627 \u0646\u0645\u0627\u06cc\u0647 \u0648 \u0645\u062d\u06a9 \u0628\u0632\u0646\u06cc\u062f\u060c \u0632\u06cc\u0631\u0627 \u0639\u0645\u0644\u06a9\u0631\u062f \u0645\u06cc \u062a\u0648\u0627\u0646\u062f \u0628\u0631 \u0627\u0633\u0627\u0633 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u0645\u062a\u0641\u0627\u0648\u062a \u0628\u0627\u0634\u062f.<\/p>\n<\/blockquote>\n<hr\/>\n<p><em>\u0628\u0627 \u062a\u0634\u06a9\u0631 \u0627\u0632 \u0634\u0645\u0627 \u0628\u0631\u0627\u06cc \u062e\u0648\u0627\u0646\u062f\u0646! \u0627\u06af\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0631\u0627\u06cc \u0634\u0645\u0627 \u0645\u0641\u06cc\u062f \u0628\u0648\u062f\u060c \u0644\u0637\u0641\u0627\u064b \u0622\u0646 \u0631\u0627 \u2764\ufe0f \u0628\u062f\u0647\u06cc\u062f \u0648 \u0622\u0646 \u0631\u0627 \u0628\u0627 \u062f\u06cc\u06af\u0631\u0627\u0646\u06cc \u06a9\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0627\u0632 \u0622\u0646 \u0633\u0648\u062f \u0628\u0628\u0631\u0646\u062f \u0628\u0647 \u0627\u0634\u062a\u0631\u0627\u06a9 \u0628\u06af\u0630\u0627\u0631\u06cc\u062f.<\/em><\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Summarize this content to 400 words in Persian Lang \u067e\u0631\u062f\u0627\u0632\u0634 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0645\u06a9\u0627\u0646\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u062f \u0627\u0632 \u0646\u0638\u0631 \u0645\u062d\u0627\u0633\u0628\u0627\u062a\u06cc \u06af\u0631\u0627\u0646 \u0628\u0627\u0634\u062f\u060c \u0628\u0647\u200c\u0648\u06cc\u0698\u0647 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0628\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0633\u0631\u0648\u06a9\u0627\u0631 \u062f\u0627\u0631\u06cc\u0645. \u062f\u0631 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647\u060c \u0631\u0648\u06cc\u06a9\u0631\u062f\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0628\u0631\u0627\u06cc \u062a\u0634\u062e\u06cc\u0635 \u0647\u0645\u067e\u0648\u0634\u0627\u0646\u06cc\u200c\u0647\u0627\u06cc \u0647\u0646\u062f\u0633\u06cc \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646\u060c \u0628\u0627 \u062a\u0645\u0631\u06a9\u0632 \u0628\u0631 \u0639\u0645\u0644\u06a9\u0631\u062f \u062a\u06a9\u0646\u06cc\u06a9\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0646\u0645\u0627\u06cc\u0647\u200c\u0633\u0627\u0632\u06cc \u0641\u0636\u0627\u06cc\u06cc \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f. \ud83c\udfaf \u0686\u0627\u0644\u0634 \u062a\u0642\u0627\u0637\u0639 \u0647\u0627\u06cc \u0647\u0646\u062f\u0633\u06cc &hellip;<\/p>\n","protected":false},"author":2,"featured_media":88764,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":"","footnotes":""},"categories":[339],"tags":[],"class_list":["post-88763","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-dev"],"_links":{"self":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts\/88763","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/comments?post=88763"}],"version-history":[{"count":0,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/posts\/88763\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/media\/88764"}],"wp:attachment":[{"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/media?parent=88763"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/categories?post=88763"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/nabfollower.com\/blog\/wp-json\/wp\/v2\/tags?post=88763"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}