{"id":1034280,"date":"2024-12-31T11:49:02","date_gmt":"2024-12-31T03:49:02","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1034280.html"},"modified":"2024-12-31T11:49:06","modified_gmt":"2024-12-31T03:49:06","slug":"python%e5%a6%82%e4%bd%95%e8%ae%a9%e7%82%b9%e4%b9%8b%e9%97%b4%e6%8a%98%e7%ba%bf%e5%8f%98%e6%88%90%e6%9b%b2%e7%ba%bf","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1034280.html","title":{"rendered":"python\u5982\u4f55\u8ba9\u70b9\u4e4b\u95f4\u6298\u7ebf\u53d8\u6210\u66f2\u7ebf"},"content":{"rendered":"

\"python\u5982\u4f55\u8ba9\u70b9\u4e4b\u95f4\u6298\u7ebf\u53d8\u6210\u66f2\u7ebf\"<\/p>\n

\u4f7f\u7528Python\u7ed8\u5236\u66f2\u7ebf\u800c\u4e0d\u662f\u6298\u7ebf\uff0c\u53ef\u4ee5\u901a\u8fc7\u51e0\u79cd\u4e0d\u540c\u7684\u65b9\u6cd5\u5b9e\u73b0\uff0c\u5305\u62ec\u4f7f\u7528\u63d2\u503c\u3001\u6837\u6761\u66f2\u7ebf\u7b49\u6280\u672f\u6765\u5e73\u6ed1\u70b9\u4e4b\u95f4\u7684\u8fde\u63a5\u3002\u5177\u4f53\u7684\u65b9\u6cd5\u6709\uff1a\u4f7f\u7528scipy<\/code>\u5e93\u7684\u63d2\u503c\u51fd\u6570\u3001\u4f7f\u7528numpy<\/code>\u548cmatplotlib<\/code>\u5e93\u8fdb\u884c\u6570\u636e\u5904\u7406\u548c\u7ed8\u56fe\u7b49\u3002\u672c\u6587\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5176\u4e2d\u7684\u4e00\u79cd\u65b9\u6cd5\u2014\u2014\u4f7f\u7528scipy<\/code>\u5e93\u7684CubicSpline<\/code>\u51fd\u6570\u6765\u5b9e\u73b0\u3002<\/strong><\/p>\n<\/p>\n

\u4e00\u3001\u4f7f\u7528\u63d2\u503c\u65b9\u6cd5<\/h3>\n<\/p>\n

\u63d2\u503c\u65b9\u6cd5\u662f\u5c06\u79bb\u6563\u7684\u70b9\u8fdb\u884c\u5e73\u6ed1\u5904\u7406\uff0c\u4f7f\u5f97\u5728\u8fd9\u4e9b\u70b9\u4e4b\u95f4\u5f62\u6210\u8fde\u7eed\u7684\u66f2\u7ebf\u3002scipy.interpolate<\/code>\u6a21\u5757\u63d0\u4f9b\u4e86\u591a\u79cd\u63d2\u503c\u65b9\u6cd5\uff0c\u5305\u62ec\u7ebf\u6027\u63d2\u503c\u3001\u591a\u9879\u5f0f\u63d2\u503c\u548c\u6837\u6761\u63d2\u503c\u7b49\u3002\u8fd9\u91cc\u6211\u4eec\u91cd\u70b9\u4ecb\u7ecd\u6837\u6761\u63d2\u503c\u4e2d\u7684\u4e09\u6b21\u6837\u6761\u63d2\u503c\u3002<\/p>\n<\/p>\n

1\u3001\u4e09\u6b21\u6837\u6761\u63d2\u503c<\/h4>\n<\/p>\n

\u4e09\u6b21\u6837\u6761\u63d2\u503c\u662f\u4e00\u79cd\u5e38\u7528\u7684\u63d2\u503c\u65b9\u6cd5\uff0c\u5b83\u4e0d\u4ec5\u80fd\u901a\u8fc7\u6240\u6709\u7684\u5df2\u77e5\u6570\u636e\u70b9\uff0c\u8fd8\u80fd\u5728\u6bcf\u4e2a\u63d2\u503c\u70b9\u5904\u4fdd\u8bc1\u51fd\u6570\u503c\u548c\u51fd\u6570\u7684\u4e00\u9636\u3001\u4e8c\u9636\u5bfc\u6570\u8fde\u7eed\u3002\u5177\u4f53\u5b9e\u73b0\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n<\/p>\n

import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
from scipy.interpolate import CubicSpline<\/p>\n
\u5b9a\u4e49\u6570\u636e\u70b9<\/strong><\/h2>\n
x = np.array([0, 1, 2, 3, 4, 5])<\/p>\n
y = np.array([0, 1, 0, 1, 0, 1])<\/p>\n
\u521b\u5efa\u4e09\u6b21\u6837\u6761\u63d2\u503c\u5bf9\u8c61<\/strong><\/h2>\n
cs = CubicSpline(x, y)<\/p>\n
\u751f\u6210\u5e73\u6ed1\u66f2\u7ebf\u7684x\u503c<\/strong><\/h2>\n
x_new = np.linspace(0, 5, 100)<\/p>\n
\u8ba1\u7b97\u5bf9\u5e94\u7684y\u503c<\/strong><\/h2>\n
y_new = cs(x_new)<\/p>\n
\u7ed8\u5236\u56fe\u5f62<\/strong><\/h2>\n
plt.plot(x, y, 'o', label='data points')<\/p>\n
plt.plot(x_new, y_new, '-', label='cubic spline')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e8c\u3001\u4f7f\u7528B\u6837\u6761\u66f2\u7ebf<\/h3>\n<\/p>\n
\u9664\u4e86\u4f7f\u7528\u4e09\u6b21\u6837\u6761\u63d2\u503c\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u4f7f\u7528B\u6837\u6761\u66f2\u7ebf\u6765\u5b9e\u73b0\u70b9\u4e4b\u95f4\u7684\u5e73\u6ed1\u8fde\u63a5\u3002B\u6837\u6761\u66f2\u7ebf\u662f\u4e00\u79cd\u57fa\u4e8eB\u6837\u6761\u51fd\u6570\u7684\u66f2\u7ebf\u8868\u793a\u65b9\u6cd5\uff0c\u5177\u6709\u826f\u597d\u7684\u5e73\u6ed1\u6027\u548c\u5c40\u90e8\u63a7\u5236\u7279\u6027\u3002scipy.interpolate<\/code>\u6a21\u5757\u4e2d\u7684BSpline<\/code>\u51fd\u6570\u53ef\u4ee5\u7528\u6765\u6784\u9020B\u6837\u6761\u66f2\u7ebf\u3002<\/p>\n<\/p>\n
1\u3001B\u6837\u6761\u66f2\u7ebf\u7684\u5b9e\u73b0<\/h4>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
from scipy.interpolate import make_interp_spline<\/p>\n
\u5b9a\u4e49\u6570\u636e\u70b9<\/strong><\/h2>\n
x = np.array([0, 1, 2, 3, 4, 5])<\/p>\n
y = np.array([0, 1, 0, 1, 0, 1])<\/p>\n
\u521b\u5efaB\u6837\u6761\u66f2\u7ebf\u5bf9\u8c61<\/strong><\/h2>\n
spl = make_interp_spline(x, y)<\/p>\n
\u751f\u6210\u5e73\u6ed1\u66f2\u7ebf\u7684x\u503c<\/strong><\/h2>\n
x_new = np.linspace(0, 5, 100)<\/p>\n
\u8ba1\u7b97\u5bf9\u5e94\u7684y\u503c<\/strong><\/h2>\n
y_new = spl(x_new)<\/p>\n
\u7ed8\u5236\u56fe\u5f62<\/strong><\/h2>\n
plt.plot(x, y, 'o', label='data points')<\/p>\n
plt.plot(x_new, y_new, '-', label='B-spline')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e09\u3001\u4f7f\u7528\u8d1d\u585e\u5c14\u66f2\u7ebf<\/h3>\n<\/p>\n
\u8d1d\u585e\u5c14\u66f2\u7ebf\u662f\u4e00\u79cd\u5e38\u7528\u4e8e\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u548c\u52a8\u753b\u4e2d\u7684\u66f2\u7ebf\u8868\u793a\u65b9\u6cd5\uff0c\u901a\u8fc7\u63a7\u5236\u70b9\u6765\u5b9a\u4e49\u66f2\u7ebf\u7684\u5f62\u72b6\u3002\u867d\u7136\u8d1d\u585e\u5c14\u66f2\u7ebf\u5728\u63d2\u503c\u95ee\u9898\u4e2d\u4f7f\u7528\u8f83\u5c11\uff0c\u4f46\u5b83\u5728\u9700\u8981\u7cbe\u786e\u63a7\u5236\u66f2\u7ebf\u5f62\u72b6\u65f6\u975e\u5e38\u6709\u7528\u3002<\/p>\n<\/p>\n
1\u3001\u8d1d\u585e\u5c14\u66f2\u7ebf\u7684\u5b9e\u73b0<\/h4>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
def bezier_curve(points, num=200):<\/p>\n
    n = len(points) - 1<\/p>\n
    xvals = np.array([p[0] for p in points])<\/p>\n
    yvals = np.array([p[1] for p in points])<\/p>\n
    t = np.linspace(0, 1, num)<\/p>\n
    curve = np.zeros((num, 2))<\/p>\n
    for i in range(num):<\/p>\n
        for j in range(n + 1):<\/p>\n
            bernstein_poly = binomial_coefficient(n, j) * (t[i]<strong>j) * ((1 - t[i])<\/strong>(n - j))<\/p>\n
            curve[i, 0] += bernstein_poly * xvals[j]<\/p>\n
            curve[i, 1] += bernstein_poly * yvals[j]<\/p>\n
    return curve<\/p>\n
def binomial_coefficient(n, k):<\/p>\n
    return np.math.factorial(n) \/\/ (np.math.factorial(k) * np.math.factorial(n - k))<\/p>\n
\u5b9a\u4e49\u63a7\u5236\u70b9<\/strong><\/h2>\n
points = np.array([[0, 0], [1, 1], [2, 0], [3, 1], [4, 0], [5, 1]])<\/p>\n
\u751f\u6210\u8d1d\u585e\u5c14\u66f2\u7ebf<\/strong><\/h2>\n
curve = bezier_curve(points)<\/p>\n
\u7ed8\u5236\u56fe\u5f62<\/strong><\/h2>\n
plt.plot(points[:, 0], points[:, 1], 'o', label='control points')<\/p>\n
plt.plot(curve[:, 0], curve[:, 1], '-', label='bezier curve')<\/p>\n
plt.legend()<\/p>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u56db\u3001\u6bd4\u8f83\u4e0d\u540c\u65b9\u6cd5\u7684\u4f18\u7f3a\u70b9<\/h3>\n<\/p>\n
\u4e0d\u540c\u7684\u5e73\u6ed1\u66f2\u7ebf\u65b9\u6cd5\u5404\u6709\u4f18\u7f3a\u70b9\uff0c\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\u5e94\u6839\u636e\u5177\u4f53\u5e94\u7528\u9700\u6c42\u3002<\/p>\n<\/p>\n
1\u3001\u4e09\u6b21\u6837\u6761\u63d2\u503c<\/h4>\n<\/p>\n
\u4f18\u70b9\uff1a<\/strong><\/p>\n<\/p>\n
    \n
  • \u63d2\u503c\u6548\u679c\u597d\uff0c\u66f2\u7ebf\u5e73\u6ed1\uff0c\u80fd\u901a\u8fc7\u6240\u6709\u5df2\u77e5\u6570\u636e\u70b9\u3002<\/li>\n
  • \u4fdd\u8bc1\u51fd\u6570\u503c\u548c\u4e00\u9636\u3001\u4e8c\u9636\u5bfc\u6570\u7684\u8fde\u7eed\u6027\uff0c\u9002\u7528\u4e8e\u9700\u8981\u9ad8\u9636\u5bfc\u6570\u8fde\u7eed\u7684\u573a\u666f\u3002<\/li>\n<\/ul>\n
    \u7f3a\u70b9\uff1a<\/strong><\/p>\n<\/p>\n
      \n
    • \u8ba1\u7b97\u590d\u6742\u5ea6\u8f83\u9ad8\uff0c\u63d2\u503c\u70b9\u8f83\u591a\u65f6\u6027\u80fd\u53ef\u80fd\u4e0b\u964d\u3002<\/li>\n
    • \u5bf9\u63d2\u503c\u70b9\u7684\u5206\u5e03\u8981\u6c42\u8f83\u9ad8\uff0c\u63d2\u503c\u70b9\u95f4\u8ddd\u8fc7\u5927\u6216\u8fc7\u5c0f\u53ef\u80fd\u5f71\u54cd\u63d2\u503c\u6548\u679c\u3002<\/li>\n<\/ul>\n
      2\u3001B\u6837\u6761\u66f2\u7ebf<\/h4>\n<\/p>\n
      \u4f18\u70b9\uff1a<\/strong><\/p>\n<\/p>\n
        \n
      • \u5177\u6709\u826f\u597d\u7684\u5e73\u6ed1\u6027\u548c\u5c40\u90e8\u63a7\u5236\u7279\u6027\u3002<\/li>\n
      • \u9002\u7528\u4e8e\u63d2\u503c\u70b9\u8f83\u591a\u4e14\u5206\u5e03\u4e0d\u5747\u5300\u7684\u573a\u666f\u3002<\/li>\n<\/ul>\n
        \u7f3a\u70b9\uff1a<\/strong><\/p>\n<\/p>\n
          \n
        • \u9700\u8981\u9009\u62e9\u5408\u9002\u7684\u8282\u70b9\u5411\u91cf\uff0c\u8282\u70b9\u9009\u62e9\u4e0d\u5f53\u53ef\u80fd\u5f71\u54cd\u63d2\u503c\u6548\u679c\u3002<\/li>\n
        • \u5bf9\u9ad8\u9636\u5bfc\u6570\u8fde\u7eed\u6027\u8981\u6c42\u8f83\u9ad8\u7684\u573a\u666f\u4e0d\u5982\u4e09\u6b21\u6837\u6761\u63d2\u503c\u6548\u679c\u597d\u3002<\/li>\n<\/ul>\n
          3\u3001\u8d1d\u585e\u5c14\u66f2\u7ebf<\/h4>\n<\/p>\n
          \u4f18\u70b9\uff1a<\/strong><\/p>\n<\/p>\n
            \n
          • \u63a7\u5236\u70b9\u5c11\u65f6\u80fd\u7cbe\u786e\u63a7\u5236\u66f2\u7ebf\u5f62\u72b6\uff0c\u9002\u7528\u4e8e\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u548c\u52a8\u753b\u4e2d\u7684\u66f2\u7ebf\u8868\u793a\u3002<\/li>\n
          • \u8ba1\u7b97\u7b80\u5355\uff0c\u9002\u7528\u4e8e\u5b9e\u65f6\u6027\u8981\u6c42\u8f83\u9ad8\u7684\u573a\u666f\u3002<\/li>\n<\/ul>\n
            \u7f3a\u70b9\uff1a<\/strong><\/p>\n<\/p>\n
              \n
            • \u63a7\u5236\u70b9\u8f83\u591a\u65f6\u96be\u4ee5\u7cbe\u786e\u63a7\u5236\u66f2\u7ebf\u5f62\u72b6\u3002<\/li>\n
            • \u4e0d\u4fdd\u8bc1\u901a\u8fc7\u6240\u6709\u5df2\u77e5\u6570\u636e\u70b9\uff0c\u9002\u7528\u4e8e\u9700\u8981\u7cbe\u786e\u63a7\u5236\u66f2\u7ebf\u5f62\u72b6\u4f46\u4e0d\u8981\u6c42\u901a\u8fc7\u6240\u6709\u6570\u636e\u70b9\u7684\u573a\u666f\u3002<\/li>\n<\/ul>\n
              \u4e94\u3001\u5e94\u7528\u573a\u666f\u53ca\u9009\u62e9\u5efa\u8bae<\/h3>\n<\/p>\n
              \u6839\u636e\u4e0d\u540c\u7684\u5e94\u7528\u573a\u666f\u548c\u9700\u6c42\uff0c\u53ef\u4ee5\u9009\u62e9\u5408\u9002\u7684\u5e73\u6ed1\u66f2\u7ebf\u65b9\u6cd5\uff1a<\/p>\n<\/p>\n
                \n
              • \u6570\u636e\u53ef\u89c6\u5316\uff1a<\/strong> \u5982\u679c\u9700\u8981\u5c06\u79bb\u6563\u6570\u636e\u70b9\u8fdb\u884c\u5e73\u6ed1\u5904\u7406\u5e76\u7ed8\u5236\u6210\u66f2\u7ebf\uff0c\u63a8\u8350\u4f7f\u7528\u4e09\u6b21\u6837\u6761\u63d2\u503c\u6216B\u6837\u6761\u66f2\u7ebf\u3002<\/li>\n
              • \u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u548c\u52a8\u753b\uff1a<\/strong> \u5982\u679c\u9700\u8981\u7cbe\u786e\u63a7\u5236\u66f2\u7ebf\u5f62\u72b6\uff0c\u63a8\u8350\u4f7f\u7528\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002<\/li>\n
              • \u5b9e\u65f6\u6027\u8981\u6c42\u8f83\u9ad8\u7684\u573a\u666f\uff1a<\/strong> \u5982\u679c\u9700\u8981\u5728\u5b9e\u65f6\u6027\u8981\u6c42\u8f83\u9ad8\u7684\u573a\u666f\u4e2d\u8fdb\u884c\u5e73\u6ed1\u5904\u7406\uff0c\u63a8\u8350\u4f7f\u7528\u8ba1\u7b97\u7b80\u5355\u7684\u8d1d\u585e\u5c14\u66f2\u7ebf\u3002<\/li>\n<\/ul>\n
                \u7ed3\u8bba<\/h3>\n<\/p>\n
                \u901a\u8fc7\u672c\u6587\u7684\u4ecb\u7ecd\uff0c\u6211\u4eec\u4e86\u89e3\u4e86\u5982\u4f55\u4f7f\u7528Python\u7ed8\u5236\u70b9\u4e4b\u95f4\u7684\u66f2\u7ebf\uff0c\u800c\u4e0d\u662f\u7b80\u5355\u7684\u6298\u7ebf\u3002\u5177\u4f53\u65b9\u6cd5\u5305\u62ec\u4f7f\u7528scipy<\/code>\u5e93\u7684CubicSpline<\/code>\u51fd\u6570\u8fdb\u884c\u4e09\u6b21\u6837\u6761\u63d2\u503c\u3001\u4f7f\u7528BSpline<\/code>\u51fd\u6570\u8fdb\u884cB\u6837\u6761\u66f2\u7ebf\u63d2\u503c\uff0c\u4ee5\u53ca\u4f7f\u7528\u8d1d\u585e\u5c14\u66f2\u7ebf\u8fdb\u884c\u5e73\u6ed1\u5904\u7406\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5e94\u6839\u636e\u5177\u4f53\u9700\u6c42\u9009\u62e9\u5408\u9002\u7684\u65b9\u6cd5\uff0c\u4ee5\u8fbe\u5230\u6700\u4f73\u6548\u679c\u3002<\/p>\n<\/p>\n
                \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
                 \u5982\u4f55\u4f7f\u7528Python\u5c06\u6298\u7ebf\u56fe\u8f6c\u6362\u4e3a\u66f2\u7ebf\u56fe\uff1f<\/strong>
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