{"id":1170047,"date":"2025-01-15T16:17:49","date_gmt":"2025-01-15T08:17:49","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1170047.html"},"modified":"2025-01-15T16:17:52","modified_gmt":"2025-01-15T08:17:52","slug":"%e7%94%a8python%e5%a6%82%e4%bd%95%e7%bb%99%e7%82%b9%e5%8a%a0%e6%8a%95%e5%bd%b1-2","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/1170047.html","title":{"rendered":"\u7528python\u5982\u4f55\u7ed9\u70b9\u52a0\u6295\u5f71"},"content":{"rendered":"

\"\u7528python\u5982\u4f55\u7ed9\u70b9\u52a0\u6295\u5f71\"<\/p>\n

\u5728Python\u4e2d\u7ed9\u70b9\u52a0\u6295\u5f71\u7684\u65b9\u6cd5\u6709\u5f88\u591a\uff0c\u5176\u4e2d\u4e00\u79cd\u5e38\u89c1\u65b9\u6cd5\u662f\u901a\u8fc7\u4f7f\u7528\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u5e93\uff0c\u5982matplotlib<\/code>\u548cnumpy<\/code>\u6765\u5b9e\u73b0\u3002\u4f7f\u7528numpy\u8fdb\u884c\u6570\u5b66\u8ba1\u7b97\u3001\u4f7f\u7528matplotlib\u8fdb\u884c\u53ef\u89c6\u5316\u3001\u901a\u8fc7\u5b9a\u4e49\u6295\u5f71\u77e9\u9635\u6765\u5b9e\u73b0\u70b9\u7684\u6295\u5f71<\/strong>\u3002\u4e0b\u9762\u6211\u5c06\u8be6\u7ec6\u63cf\u8ff0\u5982\u4f55\u4f7f\u7528\u8fd9\u4e9b\u5de5\u5177\u5b9e\u73b0\u8fd9\u4e00\u76ee\u6807\u3002<\/p>\n<\/p>\n

\u5b9a\u4e49\u6295\u5f71\u77e9\u9635<\/strong>\uff1a\u6295\u5f71\u77e9\u9635\u662f\u5c063D\u70b9\u6295\u5f71\u52302D\u5e73\u9762\u6240\u9700\u7684\u5de5\u5177\u3002\u4e00\u4e2a\u5e38\u89c1\u7684\u6295\u5f71\u77e9\u9635\u662f\u900f\u89c6\u6295\u5f71\u77e9\u9635\uff0c\u5b83\u53ef\u4ee5\u5c063D\u5750\u6807\u8f6c\u6362\u4e3a2D\u5750\u6807\u3002\u901a\u8fc7\u5b9a\u4e49\u8fd9\u4e2a\u77e9\u9635\uff0c\u53ef\u4ee5\u63a7\u5236\u6295\u5f71\u7684\u89c6\u89d2\u548c\u8ddd\u79bb\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u5b89\u88c5\u548c\u5bfc\u5165\u5fc5\u8981\u7684\u5e93<\/h2>\n<\/p>\n

\u9996\u5148\uff0c\u786e\u4fdd\u4f60\u5df2\u7ecf\u5b89\u88c5\u4e86numpy<\/code>\u548cmatplotlib<\/code>\u3002\u5982\u679c\u6ca1\u6709\u5b89\u88c5\uff0c\u53ef\u4ee5\u4f7f\u7528\u4ee5\u4e0b\u547d\u4ee4\u5b89\u88c5\uff1a<\/p>\n<\/p>\n

pip install numpy matplotlib<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u63a5\u7740\uff0c\u5728Python\u811a\u672c\u4e2d\u5bfc\u5165\u8fd9\u4e9b\u5e93\uff1a<\/p>\n<\/p>\n
import numpy as np<\/p>\n
import matplotlib.pyplot as plt<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e8c\u3001\u5b9a\u4e493D\u70b9\u548c\u6295\u5f71\u77e9\u9635<\/h2>\n<\/p>\n
\u9996\u5148\uff0c\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a3D\u70b9\u7684\u6570\u7ec4\u3002\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u4e9b3D\u70b9\uff0c\u5b83\u4eec\u7684\u5750\u6807\u7528\u4e00\u4e2anumpy\u6570\u7ec4\u8868\u793a\uff1a<\/p>\n<\/p>\n
# \u5b9a\u4e49\u4e00\u4e9b3D\u70b9<\/p>\n
points_3D = np.array([<\/p>\n
    [1, 1, 1],<\/p>\n
    [2, 2, 2],<\/p>\n
    [3, 3, 3],<\/p>\n
    [4, 4, 4]<\/p>\n
])<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u63a5\u7740\uff0c\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u7b80\u5355\u7684\u6295\u5f71\u77e9\u9635\u3002\u8fd9\u91cc\u6211\u4eec\u4f7f\u7528\u900f\u89c6\u6295\u5f71\u77e9\u9635\u4f5c\u4e3a\u793a\u4f8b\uff1a<\/p>\n<\/p>\n
# \u5b9a\u4e49\u4e00\u4e2a\u900f\u89c6\u6295\u5f71\u77e9\u9635<\/p>\n
projection_matrix = np.array([<\/p>\n
    [1, 0, 0],<\/p>\n
    [0, 1, 0]<\/p>\n
])<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e09\u3001\u5e94\u7528\u6295\u5f71\u77e9\u9635\u52303D\u70b9<\/h2>\n<\/p>\n
\u901a\u8fc7\u77e9\u9635\u4e58\u6cd5\uff0c\u5c063D\u70b9\u6295\u5f71\u52302D\u5e73\u9762\u4e0a\uff1a<\/p>\n<\/p>\n
# \u5e94\u7528\u6295\u5f71\u77e9\u9635\u52303D\u70b9<\/p>\n
points_2D = points_3D @ projection_matrix.T<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u56db\u3001\u53ef\u89c6\u5316\u6295\u5f71\u7ed3\u679c<\/h2>\n<\/p>\n
\u4f7f\u7528matplotlib<\/code>\u6765\u53ef\u89c6\u5316\u6295\u5f71\u7ed3\u679c\u3002\u6211\u4eec\u53ef\u4ee5\u7ed8\u5236\u539f\u59cb3D\u70b9\u548c\u6295\u5f71\u540e\u76842D\u70b9\uff1a<\/p>\n<\/p>\n
# \u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u56fe\u5f62<\/p>\n
fig = plt.figure()<\/p>\n
\u521b\u5efa3D\u56fe<\/strong><\/h2>\n
ax = fig.add_subplot(121, projection='3d')<\/p>\n
ax.scatter(points_3D[:, 0], points_3D[:, 1], points_3D[:, 2], c='r', marker='o')<\/p>\n
ax.set_title('3D Points')<\/p>\n
\u521b\u5efa2D\u56fe<\/strong><\/h2>\n
ax2 = fig.add_subplot(122)<\/p>\n
ax2.scatter(points_2D[:, 0], points_2D[:, 1], c='b', marker='x')<\/p>\n
ax2.set_title('2D Projection')<\/p>\n
\u663e\u793a\u56fe\u5f62<\/strong><\/h2>\n
plt.show()<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u901a\u8fc7\u4ee5\u4e0a\u4ee3\u7801\uff0c\u6211\u4eec\u53ef\u4ee5\u770b\u52303D\u70b9\u5728\u5e94\u7528\u6295\u5f71\u77e9\u9635\u540e\u76842D\u6295\u5f71\u7ed3\u679c\u3002<\/p>\n<\/p>\n
\u4e94\u3001\u6df1\u5165\u7406\u89e3\u6295\u5f71\u77e9\u9635<\/h2>\n<\/p>\n
\u6295\u5f71\u77e9\u9635\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u4e2d\u975e\u5e38\u91cd\u8981\uff0c\u5b83\u63a7\u5236\u4e86\u89c6\u89d2\u548c\u8ddd\u79bb\u7b49\u53c2\u6570\u3002\u8fdb\u4e00\u6b65\u7684\u7406\u89e3\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u66f4\u597d\u5730\u63a7\u5236\u6295\u5f71\u7ed3\u679c\u3002<\/p>\n<\/p>\n
1\u3001\u900f\u89c6\u6295\u5f71\u77e9\u9635<\/h3>\n<\/p>\n
\u900f\u89c6\u6295\u5f71\u77e9\u9635\u7684\u4e00\u79cd\u5f62\u5f0f\u5982\u4e0b\uff1a<\/p>\n<\/p>\n
fov = np.pi \/ 2  # \u89c6\u573a\u89d2<\/p>\n
aspect = 1  # \u7eb5\u6a2a\u6bd4<\/p>\n
near = 0.1  # \u8fd1\u526a\u88c1\u9762<\/p>\n
far = 100  # \u8fdc\u526a\u88c1\u9762<\/p>\n
f = 1 \/ np.tan(fov \/ 2)<\/p>\n
perspective_projection_matrix = np.array([<\/p>\n
    [f \/ aspect, 0, 0, 0],<\/p>\n
    [0, f, 0, 0],<\/p>\n
    [0, 0, (far + near) \/ (near - far), (2 * far * near) \/ (near - far)],<\/p>\n
    [0, 0, -1, 0]<\/p>\n
])<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u8fd9\u4e2a\u77e9\u9635\u5b9a\u4e49\u4e86\u89c6\u573a\u89d2\uff08FOV\uff09\u3001\u7eb5\u6a2a\u6bd4\uff08aspect ratio\uff09\u3001\u8fd1\u526a\u88c1\u9762\u548c\u8fdc\u526a\u88c1\u9762\u3002\u901a\u8fc7\u8c03\u6574\u8fd9\u4e9b\u53c2\u6570\uff0c\u53ef\u4ee5\u63a7\u5236\u6295\u5f71\u7684\u6548\u679c\u3002<\/p>\n<\/p>\n
2\u3001\u5e94\u7528\u900f\u89c6\u6295\u5f71\u77e9\u9635<\/h3>\n<\/p>\n
\u5c06\u900f\u89c6\u6295\u5f71\u77e9\u9635\u5e94\u7528\u52303D\u70b9\u4e0a\uff0c\u5e76\u8fdb\u884c\u9f50\u6b21\u5750\u6807\u7684\u5f52\u4e00\u5316\uff1a<\/p>\n<\/p>\n
# \u5c063D\u70b9\u6269\u5c55\u4e3a\u9f50\u6b21\u5750\u6807<\/p>\n
points_3D_homogeneous = np.hstack((points_3D, np.ones((points_3D.shape[0], 1))))<\/p>\n
\u5e94\u7528\u900f\u89c6\u6295\u5f71\u77e9\u9635<\/strong><\/h2>\n
points_2D_homogeneous = points_3D_homogeneous @ perspective_projection_matrix.T<\/p>\n
\u9f50\u6b21\u5750\u6807\u5f52\u4e00\u5316<\/strong><\/h2>\n
points_2D_projected = points_2D_homogeneous[:, :2] \/ points_2D_homogeneous[:, 3][:, np.newaxis]<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u901a\u8fc7\u8fd9\u4e9b\u6b65\u9aa4\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9e\u73b0\u66f4\u590d\u6742\u7684\u6295\u5f71\u6548\u679c\u3002<\/p>\n<\/p>\n
\u516d\u3001\u5176\u4ed6\u6295\u5f71\u65b9\u6cd5<\/h2>\n<\/p>\n
\u9664\u4e86\u900f\u89c6\u6295\u5f71\uff0c\u8fd8\u6709\u5176\u4ed6\u5e38\u89c1\u7684\u6295\u5f71\u65b9\u6cd5\uff0c\u5982\u6b63\u4ea4\u6295\u5f71\u3002\u6b63\u4ea4\u6295\u5f71\u662f\u4e00\u79cd\u7b80\u5355\u7684\u6295\u5f71\u65b9\u6cd5\uff0c\u4e0d\u8003\u8651\u89c6\u89d2\u548c\u8ddd\u79bb\uff0c\u53ea\u662f\u5c063D\u70b9\u76f4\u63a5\u6620\u5c04\u52302D\u5e73\u9762\u4e0a\u3002<\/p>\n<\/p>\n
1\u3001\u6b63\u4ea4\u6295\u5f71\u77e9\u9635<\/h3>\n<\/p>\n
\u6b63\u4ea4\u6295\u5f71\u77e9\u9635\u7684\u4e00\u79cd\u5f62\u5f0f\u5982\u4e0b\uff1a<\/p>\n<\/p>\n
orthographic_projection_matrix = np.array([<\/p>\n
    [1, 0, 0],<\/p>\n
    [0, 1, 0],<\/p>\n
    [0, 0, 0]<\/p>\n
])<\/p>\n
<\/code><\/pre>\n<\/p>\n
2\u3001\u5e94\u7528\u6b63\u4ea4\u6295\u5f71\u77e9\u9635<\/h3>\n<\/p>\n
\u5c06\u6b63\u4ea4\u6295\u5f71\u77e9\u9635\u5e94\u7528\u52303D\u70b9\u4e0a\uff1a<\/p>\n<\/p>\n
# \u5e94\u7528\u6b63\u4ea4\u6295\u5f71\u77e9\u9635<\/p>\n
points_2D_orthographic = points_3D @ orthographic_projection_matrix.T<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u6b63\u4ea4\u6295\u5f71\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u6bd4\u900f\u89c6\u6295\u5f71\u66f4\u7b80\u5355\u548c\u76f4\u63a5\uff0c\u9002\u7528\u4e8e\u4e0d\u9700\u8981\u8003\u8651\u89c6\u89d2\u548c\u8ddd\u79bb\u7684\u573a\u666f\u3002<\/p>\n<\/p>\n
\u4e03\u3001\u603b\u7ed3<\/h2>\n<\/p>\n
\u5728\u8fd9\u7bc7\u6587\u7ae0\u4e2d\uff0c\u6211\u4eec\u4ecb\u7ecd\u4e86\u5982\u4f55\u4f7f\u7528Python\u7ed9\u70b9\u52a0\u6295\u5f71\u3002\u901a\u8fc7\u4f7f\u7528numpy<\/code>\u8fdb\u884c\u6570\u5b66\u8ba1\u7b97\u3001\u4f7f\u7528matplotlib<\/code>\u8fdb\u884c\u53ef\u89c6\u5316\uff0c\u6211\u4eec\u53ef\u4ee5\u5b9e\u73b0\u5404\u79cd\u6295\u5f71\u65b9\u6cd5\uff0c\u5305\u62ec\u900f\u89c6\u6295\u5f71\u548c\u6b63\u4ea4\u6295\u5f71\u3002\u5b9a\u4e49\u6295\u5f71\u77e9\u9635\u3001\u5e94\u7528\u6295\u5f71\u77e9\u9635\u52303D\u70b9\u3001\u53ef\u89c6\u5316\u6295\u5f71\u7ed3\u679c<\/strong>\uff0c\u8fd9\u4e9b\u6b65\u9aa4\u662f\u5b9e\u73b0\u70b9\u6295\u5f71\u7684\u5173\u952e\u3002\u4e86\u89e3\u548c\u638c\u63e1\u8fd9\u4e9b\u6280\u672f\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u5728\u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u548c\u6570\u636e\u53ef\u89c6\u5316\u4e2d\u5b9e\u73b0\u66f4\u590d\u6742\u548c\u7cbe\u7f8e\u7684\u6548\u679c\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
 \u5982\u4f55\u5728Python\u4e2d\u4e3a\u70b9\u6dfb\u52a0\u6295\u5f71\u6548\u679c\uff1f<\/strong>
\u5728Python\u4e2d\uff0c\u60a8\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u5e93\u6765\u4e3a\u70b9\u6dfb\u52a0\u6295\u5f71\u6548\u679c\u3002\u6700\u5e38\u7528\u7684\u5e93\u5305\u62ecMatplotlib\u548cPygame\u3002Matplotlib\u9002\u5408\u4e8e\u7ed8\u5236\u9759\u6001\u56fe\u5f62\uff0c\u800cPygame\u9002\u5408\u4e8e\u5f00\u53d1\u6e38\u620f\u548c\u52a8\u6001\u6548\u679c\u3002\u60a8\u53ef\u4ee5\u901a\u8fc7\u8bbe\u7f6e\u70b9\u7684\u4f4d\u7f6e\u548c\u6295\u5f71\u7684\u989c\u8272\u3001\u5927\u5c0f\u6765\u5b9e\u73b0\u60f3\u8981\u7684\u6548\u679c\u3002<\/p>\n
\u4f7f\u7528\u54ea\u4e2a\u5e93\u6765\u5b9e\u73b0\u70b9\u7684\u6295\u5f71\u6548\u679c\u66f4\u597d\uff1f<\/strong>
\u9009\u62e9\u5e93\u4e3b\u8981\u53d6\u51b3\u4e8e\u60a8\u7684\u9700\u6c42\u3002\u5982\u679c\u60a8\u5e0c\u671b\u521b\u5efa\u9759\u6001\u56fe\u5f62\uff0c\u53ef\u4ee5\u4f7f\u7528Matplotlib\uff0c\u5b83\u63d0\u4f9b\u4e86\u4e30\u5bcc\u7684\u7ed8\u56fe\u529f\u80fd\u3002\u5982\u679c\u60a8\u60f3\u8981\u521b\u5efa\u52a8\u6001\u6548\u679c\u6216\u6e38\u620f\uff0c\u5219Pygame\u4f1a\u66f4\u52a0\u9002\u5408\u3002\u6bcf\u4e2a\u5e93\u90fd\u6709\u5176\u72ec\u7279\u7684\u4f18\u52bf\uff0c\u5177\u4f53\u9009\u62e9\u53ef\u4ee5\u6839\u636e\u9879\u76ee\u7684\u590d\u6742\u7a0b\u5ea6\u548c\u60a8\u7684\u4f7f\u7528\u4e60\u60ef\u6765\u51b3\u5b9a\u3002<\/p>\n
\u6295\u5f71\u6548\u679c\u7684\u5b9e\u73b0\u539f\u7406\u662f\u4ec0\u4e48\uff1f<\/strong>
\u6295\u5f71\u6548\u679c\u901a\u5e38\u57fa\u4e8e\u5149\u6e90\u548c\u89c2\u5bdf\u89d2\u5ea6\u7684\u8bbe\u7f6e\u3002\u901a\u8fc7\u8ba1\u7b97\u5149\u6e90\u4e0e\u70b9\u4e4b\u95f4\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u60a8\u53ef\u4ee5\u786e\u5b9a\u6295\u5f71\u7684\u65b9\u5411\u548c\u957f\u5ea6\u3002\u5728\u56fe\u5f62\u4e2d\uff0c\u8fd9\u901a\u5e38\u6d89\u53ca\u5230\u7b80\u5355\u7684\u51e0\u4f55\u8ba1\u7b97\uff0c\u5982\u4e09\u89d2\u51fd\u6570\u548c\u5411\u91cf\u8fd0\u7b97\u3002\u60a8\u53ef\u4ee5\u6839\u636e\u5149\u6e90\u7684\u4f4d\u7f6e\u6765\u52a8\u6001\u66f4\u65b0\u70b9\u7684\u6295\u5f71\uff0c\u4ece\u800c\u5b9e\u73b0\u66f4\u771f\u5b9e\u7684\u89c6\u89c9\u6548\u679c\u3002<\/p>\n
\u5982\u4f55\u8c03\u6574\u6295\u5f71\u7684\u900f\u660e\u5ea6\u548c\u6a21\u7cca\u6548\u679c\uff1f<\/strong>
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