{"id":958578,"date":"2024-12-27T03:30:42","date_gmt":"2024-12-26T19:30:42","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/958578.html"},"modified":"2024-12-27T03:30:45","modified_gmt":"2024-12-26T19:30:45","slug":"python%e5%a6%82%e4%bd%95%e6%b1%82%e8%a7%a3%e5%87%a0%e4%bd%95%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/958578.html","title":{"rendered":"python\u5982\u4f55\u6c42\u89e3\u51e0\u4f55\u95ee\u9898"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25101430\/024d5901-16ee-48cc-a459-5567ce5d6356.webp\" alt=\"python\u5982\u4f55\u6c42\u89e3\u51e0\u4f55\u95ee\u9898\" \/><\/p>\n<p><p> \u4e00\u3001\u5229\u7528Python\u5e93\u8fdb\u884c\u51e0\u4f55\u8ba1\u7b97<\/p>\n<\/p>\n<p><p><strong>Python\u5728\u89e3\u51b3\u51e0\u4f55\u95ee\u9898\u4e0a\u5341\u5206\u5f3a\u5927\uff0c\u4e3b\u8981\u4f9d\u8d56\u4e8e\u4e00\u4e9b\u4e13\u4e1a\u7684\u5e93\u5982SymPy\u3001Shapely\u3001NumPy\u7b49\uff0c\u8fd9\u4e9b\u5e93\u53ef\u4ee5\u8fdb\u884c\u7b26\u53f7\u6570\u5b66\u8ba1\u7b97\u3001\u51e0\u4f55\u5bf9\u8c61\u7684\u521b\u5efa\u548c\u64cd\u4f5c\u3001\u4ee5\u53ca\u77e9\u9635\u8fd0\u7b97\u548c\u5411\u91cf\u8ba1\u7b97\u3002<\/strong>\u5176\u4e2d\uff0cSymPy\u53ef\u4ee5\u8fdb\u884c\u7b26\u53f7\u8ba1\u7b97\uff0cShapely\u64c5\u957f\u5904\u7406\u4e8c\u7ef4\u51e0\u4f55\u5bf9\u8c61\uff0c\u800cNumPy\u5219\u5bf9\u8ba1\u7b97\u6548\u7387\u6709\u5f88\u5927\u63d0\u9ad8\u3002\u9009\u62e9\u5408\u9002\u7684\u5e93\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u9ad8\u6548\u3001\u51c6\u786e\u5730\u89e3\u51b3\u51e0\u4f55\u95ee\u9898\u3002<\/p>\n<\/p>\n<p><p>\u8be6\u7ec6\u63cf\u8ff0\uff1aSymPy\u662f\u4e00\u4e2a\u5f3a\u5927\u7684Python\u5e93\uff0c\u4e13\u6ce8\u4e8e\u7b26\u53f7\u6570\u5b66\u8ba1\u7b97\u3002\u5b83\u53ef\u4ee5\u8fdb\u884c\u5fae\u79ef\u5206\u3001\u4ee3\u6570\u3001\u79bb\u6563\u6570\u5b66\u7b49\u591a\u79cd\u6570\u5b66\u8ba1\u7b97\u3002\u5bf9\u4e8e\u51e0\u4f55\u95ee\u9898\uff0cSymPy\u80fd\u591f\u5b9a\u4e49\u70b9\u3001\u7ebf\u3001\u5706\u7b49\u51e0\u4f55\u5bf9\u8c61\uff0c\u5e76\u8fdb\u884c\u4ea4\u96c6\u3001\u5e76\u96c6\u3001\u8ddd\u79bb\u8ba1\u7b97\u3001\u53d8\u6362\u7b49\u64cd\u4f5c\u3002\u4f7f\u7528SymPy\uff0c\u6211\u4eec\u53ef\u4ee5\u4e0d\u7528\u5173\u5fc3\u6d6e\u70b9\u6570\u8bef\u5dee\uff0c\u76f4\u63a5\u8fdb\u884c\u7b26\u53f7\u5316\u7684\u51e0\u4f55\u63a8\u7406\u548c\u8ba1\u7b97\u3002<\/p>\n<\/p>\n<p><p>\u4e8c\u3001SymPy\u5728\u51e0\u4f55\u4e2d\u7684\u5e94\u7528<\/p>\n<\/p>\n<p><p>SymPy\u63d0\u4f9b\u4e86\u5e7f\u6cdb\u7684\u51e0\u4f55\u529f\u80fd\uff0c\u80fd\u591f\u5e2e\u52a9\u6211\u4eec\u89e3\u51b3\u590d\u6742\u7684\u51e0\u4f55\u95ee\u9898\u3002\u5728SymPy\u4e2d\uff0c\u6211\u4eec\u53ef\u4ee5\u521b\u5efa\u70b9\u3001\u7ebf\u3001\u5706\u3001\u591a\u8fb9\u5f62\u7b49\u57fa\u672c\u51e0\u4f55\u5bf9\u8c61\uff0c\u5e76\u5bf9\u5176\u8fdb\u884c\u5404\u79cd\u51e0\u4f55\u64cd\u4f5c\u3002<\/p>\n<\/p>\n<ol>\n<li><strong>\u57fa\u672c\u51e0\u4f55\u5bf9\u8c61\u7684\u521b\u5efa<\/strong><\/li>\n<\/ol>\n<p><p>\u5728SymPy\u4e2d\uff0c\u5b9a\u4e49\u51e0\u4f55\u5bf9\u8c61\u5341\u5206\u7b80\u5355\u3002\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528Point\u3001Line\u3001Circle\u7b49\u7c7b\u6765\u521b\u5efa\u51e0\u4f55\u5bf9\u8c61\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from sympy import Point, Line, Circle<\/p>\n<h2><strong>\u521b\u5efa\u70b9<\/strong><\/h2>\n<p>p1 = Point(0, 0)<\/p>\n<p>p2 = Point(1, 1)<\/p>\n<h2><strong>\u521b\u5efa\u7ebf<\/strong><\/h2>\n<p>line = Line(p1, p2)<\/p>\n<h2><strong>\u521b\u5efa\u5706<\/strong><\/h2>\n<p>circle = Circle(p1, 1)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<ol start=\"2\">\n<li><strong>\u51e0\u4f55\u64cd\u4f5c<\/strong><\/li>\n<\/ol>\n<p><p>SymPy\u63d0\u4f9b\u4e86\u4e00\u7cfb\u5217\u51e0\u4f55\u64cd\u4f5c\u51fd\u6570\uff0c\u5982\u8ba1\u7b97\u8ddd\u79bb\u3001\u6c42\u4ea4\u70b9\u3001\u53d8\u6362\u7b49\u3002\u8fd9\u4e9b\u64cd\u4f5c\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u89e3\u51b3\u5b9e\u9645\u7684\u51e0\u4f55\u95ee\u9898\u3002<\/p>\n<\/p>\n<ul>\n<li><strong>\u8ddd\u79bb\u8ba1\u7b97<\/strong><\/li>\n<\/ul>\n<p><p>SymPy\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97\u4e24\u4e2a\u51e0\u4f55\u5bf9\u8c61\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u8ba1\u7b97\u4e24\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb<\/p>\n<p>distance = p1.distance(p2)<\/p>\n<h2><strong>\u8ba1\u7b97\u70b9\u5230\u7ebf\u7684\u8ddd\u79bb<\/strong><\/h2>\n<p>point_line_distance = p1.distance(line)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<ul>\n<li><strong>\u6c42\u4ea4\u70b9<\/strong><\/li>\n<\/ul>\n<p><p>SymPy\u53ef\u4ee5\u6c42\u89e3\u4e24\u6761\u7ebf\u3001\u5706\u4e0e\u7ebf\u7b49\u51e0\u4f55\u5bf9\u8c61\u7684\u4ea4\u70b9\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u6c42\u4e24\u6761\u7ebf\u7684\u4ea4\u70b9<\/p>\n<p>intersection = line.intersection(Line(Point(0, 1), Point(1, 0)))<\/p>\n<h2><strong>\u6c42\u7ebf\u4e0e\u5706\u7684\u4ea4\u70b9<\/strong><\/h2>\n<p>circle_intersection = circle.intersection(line)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u4e09\u3001Shapely\u5728\u51e0\u4f55\u4e2d\u7684\u5e94\u7528<\/p>\n<\/p>\n<p><p>Shapely\u662f\u4e00\u4e2aPython\u5e93\uff0c\u4e13\u6ce8\u4e8e\u5206\u6790\u548c\u64cd\u4f5c\u4e8c\u7ef4\u51e0\u4f55\u5bf9\u8c61\u3002\u5b83\u80fd\u591f\u9ad8\u6548\u5904\u7406\u51e0\u4f55\u56fe\u5f62\u7684\u521b\u5efa\u3001\u64cd\u4f5c\u3001\u5206\u6790\u7b49\u4efb\u52a1\u3002<\/p>\n<\/p>\n<ol>\n<li><strong>\u521b\u5efa\u548c\u64cd\u4f5c\u51e0\u4f55\u5bf9\u8c61<\/strong><\/li>\n<\/ol>\n<p><p>Shapely\u53ef\u4ee5\u521b\u5efa\u70b9\u3001\u7ebf\u3001\u591a\u8fb9\u5f62\u7b49\u51e0\u4f55\u5bf9\u8c61\uff0c\u5e76\u652f\u6301\u591a\u79cd\u51e0\u4f55\u64cd\u4f5c\uff0c\u5982\u4ea4\u96c6\u3001\u5e76\u96c6\u3001\u5dee\u96c6\u7b49\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from shapely.geometry import Point, LineString, Polygon<\/p>\n<h2><strong>\u521b\u5efa\u70b9<\/strong><\/h2>\n<p>point = Point(0, 0)<\/p>\n<h2><strong>\u521b\u5efa\u7ebf<\/strong><\/h2>\n<p>line = LineString([(0, 0), (1, 1)])<\/p>\n<h2><strong>\u521b\u5efa\u591a\u8fb9\u5f62<\/strong><\/h2>\n<p>polygon = Polygon([(0, 0), (1, 0), (1, 1), (0, 1)])<\/p>\n<p><\/code><\/pre>\n<\/p>\n<ol start=\"2\">\n<li><strong>\u51e0\u4f55\u5206\u6790<\/strong><\/li>\n<\/ol>\n<p><p>Shapely\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u51e0\u4f55\u5206\u6790\u529f\u80fd\uff0c\u80fd\u591f\u5206\u6790\u51e0\u4f55\u5bf9\u8c61\u7684\u5c5e\u6027\u548c\u5173\u7cfb\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<ul>\n<li><strong>\u8ba1\u7b97\u9762\u79ef\u548c\u5468\u957f<\/strong><\/li>\n<\/ul>\n<p><pre><code class=\"language-python\"># \u8ba1\u7b97\u591a\u8fb9\u5f62\u7684\u9762\u79ef<\/p>\n<p>area = polygon.area<\/p>\n<h2><strong>\u8ba1\u7b97\u591a\u8fb9\u5f62\u7684\u5468\u957f<\/strong><\/h2>\n<p>length = polygon.length<\/p>\n<p><\/code><\/pre>\n<\/p>\n<ul>\n<li><strong>\u68c0\u67e5\u51e0\u4f55\u5bf9\u8c61\u7684\u5173\u7cfb<\/strong><\/li>\n<\/ul>\n<p><p>Shapely\u53ef\u4ee5\u68c0\u67e5\u4e24\u4e2a\u51e0\u4f55\u5bf9\u8c61\u662f\u5426\u76f8\u4ea4\u3001\u5305\u542b\u3001\u76f8\u79bb\u7b49\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u68c0\u67e5\u4e24\u4e2a\u51e0\u4f55\u5bf9\u8c61\u662f\u5426\u76f8\u4ea4<\/p>\n<p>intersects = line.intersects(polygon)<\/p>\n<h2><strong>\u68c0\u67e5\u4e00\u4e2a\u51e0\u4f55\u5bf9\u8c61\u662f\u5426\u5305\u542b\u53e6\u4e00\u4e2a<\/strong><\/h2>\n<p>cont<a href=\"https:\/\/docs.pingcode.com\/blog\/59162.html\" target=\"_blank\">AI<\/a>ns = polygon.contains(point)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u56db\u3001NumPy\u5728\u51e0\u4f55\u4e2d\u7684\u5e94\u7528<\/p>\n<\/p>\n<p><p>NumPy\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u6570\u503c\u8ba1\u7b97\u5e93\uff0c\u867d\u7136\u5b83\u4e0d\u662f\u4e13\u95e8\u4e3a\u51e0\u4f55\u8bbe\u8ba1\u7684\uff0c\u4f46\u5b83\u63d0\u4f9b\u7684\u77e9\u9635\u8fd0\u7b97\u548c\u7ebf\u6027\u4ee3\u6570\u529f\u80fd\u53ef\u4ee5\u7528\u4e8e\u89e3\u51b3\u51e0\u4f55\u95ee\u9898\u3002<\/p>\n<\/p>\n<ol>\n<li><strong>\u5411\u91cf\u548c\u77e9\u9635\u8fd0\u7b97<\/strong><\/li>\n<\/ol>\n<p><p>\u51e0\u4f55\u4e2d\u7684\u8bb8\u591a\u95ee\u9898\u53ef\u4ee5\u8f6c\u6362\u4e3a\u5411\u91cf\u548c\u77e9\u9635\u8fd0\u7b97\u3002NumPy\u63d0\u4f9b\u4e86\u9ad8\u6548\u7684\u5411\u91cf\u548c\u77e9\u9635\u8fd0\u7b97\u529f\u80fd\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<h2><strong>\u5b9a\u4e49\u4e24\u4e2a\u5411\u91cf<\/strong><\/h2>\n<p>v1 = np.array([1, 2])<\/p>\n<p>v2 = np.array([3, 4])<\/p>\n<h2><strong>\u8ba1\u7b97\u5411\u91cf\u7684\u70b9\u79ef<\/strong><\/h2>\n<p>dot_product = np.dot(v1, v2)<\/p>\n<h2><strong>\u8ba1\u7b97\u5411\u91cf\u7684\u53c9\u79ef\uff08\u4ec5\u9650\u4e09\u7ef4\uff09<\/strong><\/h2>\n<p>v3 = np.array([1, 2, 3])<\/p>\n<p>v4 = np.array([4, 5, 6])<\/p>\n<p>cross_product = np.cross(v3, v4)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<ol start=\"2\">\n<li><strong>\u7ebf\u6027\u53d8\u6362<\/strong><\/li>\n<\/ol>\n<p><p>NumPy\u53ef\u4ee5\u7528\u4e8e\u8fdb\u884c\u51e0\u4f55\u5bf9\u8c61\u7684\u7ebf\u6027\u53d8\u6362\u3002\u901a\u8fc7\u77e9\u9635\u4e58\u6cd5\uff0c\u6211\u4eec\u53ef\u4ee5\u5bf9\u70b9\u3001\u7ebf\u3001\u9762\u8fdb\u884c\u7f29\u653e\u3001\u65cb\u8f6c\u3001\u5e73\u79fb\u7b49\u53d8\u6362\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\"># \u5b9a\u4e49\u4e00\u4e2a\u65cb\u8f6c\u77e9\u9635<\/p>\n<p>theta = np.pi \/ 4  # 45\u5ea6<\/p>\n<p>rotation_matrix = np.array([[np.cos(theta), -np.sin(theta)], [np.sin(theta), np.cos(theta)]])<\/p>\n<h2><strong>\u5bf9\u70b9\u8fdb\u884c\u65cb\u8f6c<\/strong><\/h2>\n<p>original_point = np.array([1, 0])<\/p>\n<p>rotated_point = np.dot(rotation_matrix, original_point)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u4e94\u3001Python\u89e3\u51b3\u51e0\u4f55\u95ee\u9898\u7684\u5b9e\u9645\u5e94\u7528<\/p>\n<\/p>\n<p><p>Python\u5728\u51e0\u4f55\u95ee\u9898\u4e0a\u7684\u5e94\u7528\u975e\u5e38\u5e7f\u6cdb\uff0c\u4ece\u7b80\u5355\u7684\u56fe\u5f62\u8ba1\u7b97\u5230\u590d\u6742\u7684\u7a7a\u95f4\u5206\u6790\uff0cPython\u90fd\u80fd\u63d0\u4f9b\u6709\u6548\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n<\/p>\n<ol>\n<li><strong>\u56fe\u5f62\u5b66<\/strong><\/li>\n<\/ol>\n<p><p>\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\uff0cPython\u53ef\u4ee5\u7528\u4e8e\u521b\u5efa\u3001\u64cd\u4f5c\u548c\u5206\u6790\u590d\u6742\u7684\u51e0\u4f55\u56fe\u5f62\u3002\u901a\u8fc7\u4f7f\u7528Python\u7684\u56fe\u5f62\u5e93\uff0c\u5982Matplotlib\u3001Pygame\u7b49\uff0c\u53ef\u4ee5\u5b9e\u73b0\u56fe\u5f62\u7684\u53ef\u89c6\u5316\u548c\u52a8\u753b\u3002<\/p>\n<\/p>\n<ol start=\"2\">\n<li><strong>\u5730\u7406\u4fe1\u606f\u7cfb\u7edf\uff08GIS\uff09<\/strong><\/li>\n<\/ol>\n<p><p>Python\u5728GIS\u9886\u57df\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u5229\u7528Shapely\u3001GeoPandas\u7b49\u5e93\uff0c\u6211\u4eec\u53ef\u4ee5\u5bf9\u5730\u7406\u6570\u636e\u8fdb\u884c\u5904\u7406\u548c\u5206\u6790\uff0c\u5b9e\u73b0\u5730\u7406\u4fe1\u606f\u7684\u53ef\u89c6\u5316\u548c\u7a7a\u95f4\u5206\u6790\u3002<\/p>\n<\/p>\n<ol start=\"3\">\n<li><strong>\u673a\u5668\u4eba\u548c\u81ea\u52a8\u9a7e\u9a76<\/strong><\/li>\n<\/ol>\n<p><p>\u5728\u673a\u5668\u4eba\u548c\u81ea\u52a8\u9a7e\u9a76\u9886\u57df\uff0c\u51e0\u4f55\u8ba1\u7b97\u662f\u8def\u5f84\u89c4\u5212\u548c\u73af\u5883\u5efa\u6a21\u7684\u57fa\u7840\u3002Python\u53ef\u4ee5\u7528\u4e8e\u5b9e\u73b0\u8def\u5f84\u89c4\u5212\u7b97\u6cd5\u3001\u4f20\u611f\u5668\u6570\u636e\u5904\u7406\u548c\u73af\u5883\u5efa\u6a21\u7b49\u4efb\u52a1\u3002<\/p>\n<\/p>\n<p><p>\u7efc\u4e0a\u6240\u8ff0\uff0cPython\u901a\u8fc7\u5176\u5f3a\u5927\u7684\u5e93\u548c\u5de5\u5177\uff0c\u80fd\u591f\u5728\u51e0\u4f55\u95ee\u9898\u7684\u6c42\u89e3\u4e2d\u53d1\u6325\u91cd\u8981\u4f5c\u7528\u3002\u901a\u8fc7\u9009\u62e9\u5408\u9002\u7684\u5e93\uff0c\u6211\u4eec\u53ef\u4ee5\u9ad8\u6548\u3001\u51c6\u786e\u5730\u89e3\u51b3\u5404\u79cd\u51e0\u4f55\u95ee\u9898\uff0c\u4ece\u800c\u5728\u591a\u4e2a\u9886\u57df\u4e2d\u5b9e\u73b0\u5b9e\u9645\u5e94\u7528\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> 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