{"id":359,"date":"2024-07-30T08:08:51","date_gmt":"2024-07-30T00:08:51","guid":{"rendered":"https:\/\/thereisno.top:4430\/?p=359"},"modified":"2024-10-22T16:00:00","modified_gmt":"2024-10-22T08:00:00","slug":"%e5%8f%98%e6%8d%a2%e7%9a%84%e7%9f%a9%e9%98%b5%e8%a1%a8%e7%a4%ba%e5%bd%a2%e5%bc%8f","status":"publish","type":"post","link":"https:\/\/thereisno.top\/?p=359","title":{"rendered":"\u53d8\u6362\u7684\u77e9\u9635\u8868\u793a\u5f62\u5f0f"},"content":{"rendered":"\n

m\u00d7n <\/em>\u77e9\u9635\u662f\u6392\u5217\u5728 m<\/em> \u884c\u548c n<\/em> \u5217\u4e2d\u7684\u4e00\u7cfb\u5217\u6570\u3002 \u4e0b\u56fe\u663e\u793a\u51e0\u4e2a\u77e9\u9635\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n\n\n\n\n

\u60a8\u53ef\u4ee5\u901a\u8fc7\u5c06\u5355\u4e2a\u5143\u7d20\u76f8\u52a0\u6765\u52a0\u5408\u4e24\u4e2a\u5c3a\u5bf8\u76f8\u540c\u7684\u77e9\u9635\u3002 \u4e0b\u56fe\u663e\u793a\u4e86\u4e24\u4e2a\u77e9\u9635\u76f8\u52a0\u7684\u793a\u4f8b\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

m\u00d7n <\/em>\u77e9\u9635\u53ef\u4e0e\u4e00\u4e2a n\u00d7p <\/em>\u77e9\u9635\u76f8\u4e58\uff0c\u7ed3\u679c\u4e3a\u4e00\u4e2a m\u00d7p <\/em>\u77e9\u9635\u3002 \u7b2c\u4e00\u4e2a\u77e9\u9635\u7684\u5217\u6570\u5fc5\u987b\u4e0e\u7b2c\u4e8c\u4e2a\u77e9\u9635\u7684\u884c\u6570\u76f8\u540c\u3002 \u4f8b\u5982\uff0c\u4e00\u4e2a 4\u00d72 \u77e9\u9635\u4e0e\u4e00\u4e2a 2\u00d73 \u77e9\u9635\u76f8\u4e58\uff0c\u4ea7\u751f\u4e00\u4e2a 4\u00d73 \u77e9\u9635\u3002<\/p>\n\n\n\n

\u77e9\u9635\u7684\u884c\u5217\u7684\u5e73\u9762\u70b9\u53ef\u89c6\u4e3a\u77e2\u91cf\u3002 \u4f8b\u5982\uff0c(2, 5) \u662f\u5177\u6709\u4e24\u4e2a\u7ec4\u4ef6\u7684\u77e2\u91cf\uff0c(3, 7, 1) \u662f\u5177\u6709\u4e09\u4e2a\u7ec4\u4ef6\u7684\u77e2\u91cf\u3002 \u4e24\u4e2a\u77e2\u91cf\u7684\u70b9\u79ef\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n\n\n\n

(a, b) \u2022 (c, d) = ac + bd<\/p>\n\n\n\n

(a, b, c) \u2022 (d, e, f) = ad + be + cf<\/p>\n\n\n\n

\u4f8b\u5982\uff0c(2, 3) \u548c (5, 4) \u7684\u70b9\u79ef\u4e3a (2)(5) + (3)(4) = 22\u3002 (2, 5, 1) \u548c (4, 3, 1) \u7684\u70b9\u79ef\u4e3a (2)(4) + (5)(3) + (1)(1) = 24\u3002 \u8bf7\u6ce8\u610f\uff0c\u4e24\u4e2a\u77e2\u91cf\u7684\u70b9\u79ef\u662f\u4e00\u4e2a\u6570\u5b57\uff0c\u800c\u4e0d\u662f\u53e6\u4e00\u4e2a\u77e2\u91cf\u3002 \u53e6\u5916\u8bf7\u6ce8\u610f\uff0c\u53ea\u6709\u5f53\u4e24\u4e2a\u77e2\u91cf\u7684\u7ec4\u4ef6\u6570\u76f8\u540c\u65f6\uff0c\u624d\u80fd\u8ba1\u7b97\u70b9\u79ef\u3002<\/p>\n\n\n\n

\u5c06 A(i, j) \u4f5c\u4e3a\u77e9\u9635 A \u4e2d\u7b2c i \u884c\u3001\u7b2c j \u5217\u7684\u9879\u3002 \u4f8b\u5982\uff0cA\uff083, 2\uff09\u662f\u77e9\u9635 A \u4e2d\u7b2c 3 \u884c\u3001\u7b2c 2 \u5217\u7684\u9879\u3002 \u5047\u5b9a A\u3001B \u548c C \u662f\u77e9\u9635\uff0c\u4e14 AB = C\uff0c \u5219 C \u7684\u9879\u8ba1\u7b97\u5982\u4e0b\uff1a<\/p>\n\n\n\n

C(i, j) =\uff08A \u7684\u7b2c i \u884c\uff09\u2022\uff08B \u7684\u7b2c j \u5217\uff09<\/p>\n\n\n\n

\u4e0b\u56fe\u663e\u793a\u4e86\u77e9\u9635\u76f8\u4e58\u7684\u51e0\u4e2a\u793a\u4f8b\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u5982\u679c\u5c06\u5e73\u9762\u4e2d\u7684\u70b9\u89c6\u4e3a 1\u00d72 \u77e9\u9635\uff0c\u5219\u53ef\u901a\u8fc7\u5c06\u8be5\u70b9\u4e58\u4ee5\u4e00\u4e2a 2\u00d72 \u77e9\u9635\u6765\u5c06\u8be5\u70b9\u53d8\u6362\u3002 \u4e0b\u56fe\u663e\u793a\u4e86\u5e94\u7528\u4e8e\u70b9 (2, 1) \u7684\u51e0\u4e2a\u53d8\u6362\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u524d\u56fe\u4e2d\u663e\u793a\u7684\u6240\u6709\u53d8\u6362\u90fd\u662f\u7ebf\u6027\u53d8\u6362\u3002 \u67d0\u4e9b\u5176\u4ed6\u53d8\u6362\uff08\u5982\u5e73\u79fb\uff09\u4e0d\u662f\u7ebf\u6027\u7684\uff0c\u4e0d\u80fd\u8868\u793a\u4e3a\u4e0e 2\u00d72 \u77e9\u9635\u76f8\u4e58\u7684\u5f62\u5f0f\u3002 \u5047\u5b9a\u60a8\u8981\u4ece\u70b9 (2, 1) \u5f00\u59cb\uff0c\u5c06\u5176\u65cb\u8f6c 90 \u5ea6\uff0c\u5728 x \u65b9\u5411\u5c06\u5176\u5e73\u79fb 3 \u4e2a\u5355\u4f4d\uff0c\u5728 y \u65b9\u5411\u5c06\u5176\u5e73\u79fb 4 \u4e2a\u5355\u4f4d\u3002 \u53ef\u901a\u8fc7\u5148\u4f7f\u7528\u77e9\u9635\u4e58\u6cd5\u518d\u4f7f\u7528\u77e9\u9635\u52a0\u6cd5\u6765\u5b8c\u6210\u6b64\u64cd\u4f5c\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u540e\u9762\u8ddf\u4e00\u5e73\u79fb\uff08\u4e0e 1\u00d72 \u77e9\u9635\u76f8\u52a0\uff09\u7684\u7ebf\u6027\u53d8\u6362\uff08\u4e0e 2\u00d72 \u77e9\u9635\u76f8\u4e58\uff09\u79f0\u4e3a\u4eff\u5c04\u53d8\u6362\u3002 \u5c06\u4eff\u5c04\u53d8\u6362\u5b58\u50a8\u4e8e\u4e00\u5bf9\u77e9\u9635\uff08\u4e00\u4e2a\u7528\u4e8e\u7ebf\u6027\u90e8\u5206\uff0c\u4e00\u4e2a\u7528\u4e8e\u5e73\u79fb\uff09\u7684\u66ff\u6362\u65b9\u6848\u662f\u5c06\u6574\u4e2a\u53d8\u6362\u5b58\u50a8\u4e8e 3\u00d73 \u77e9\u9635\u3002 \u82e5\u8981\u4f7f\u5176\u8d77\u4f5c\u7528\uff0c\u5e73\u9762\u4e0a\u7684\u70b9\u5fc5\u987b\u5b58\u50a8\u4e8e\u5177\u6709\u865a\u62df\u7b2c\u4e09\u5750\u6807\u7684 1\u00d73 \u77e9\u9635\u4e2d\u3002 \u901a\u5e38\u7684\u65b9\u6cd5\u662f\u4f7f\u6240\u6709\u7684\u7b2c\u4e09\u5750\u6807\u7b49\u4e8e 1\u3002 \u4f8b\u5982\uff0c\u77e9\u9635 [2 1 1] \u4ee3\u8868\u70b9 (2, 1)\u3002 \u4e0b\u56fe\u6f14\u793a\u4e86\u8868\u793a\u4e3a\u4e0e\u5355\u4e2a 3\u00d73 \u77e9\u9635\u76f8\u4e58\u7684\u4eff\u5c04\u53d8\u6362\uff08\u65cb\u8f6c 90 \u5ea6\uff1b\u5728 x \u65b9\u5411\u4e0a\u5e73\u79fb 3 \u4e2a\u5355\u4f4d\uff0c\u5728 y \u65b9\u5411\u4e0a\u5e73\u79fb 4 \u4e2a\u5355\u4f4d\uff09\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u5728\u524d\u9762\u7684\u793a\u4f8b\u4e2d\uff0c\u70b9 (2, 1) \u6620\u5c04\u5230\u4e86\u70b9 (2, 6)\u3002 \u8bf7\u6ce8\u610f\uff0c3\u00d73 \u77e9\u9635\u7684\u7b2c\u4e09\u5217\u5305\u542b\u6570\u5b57 0\uff0c0\uff0c1\u3002 \u5bf9\u4e8e\u4eff\u5c04\u53d8\u6362\u7684 3\u00d73 \u77e9\u9635\u800c\u8a00\uff0c\u60c5\u51b5\u5c06\u603b\u662f\u5982\u6b64\u3002 \u91cd\u8981\u7684\u6570\u5b57\u662f\u5217 1 \u548c\u5217 2 \u4e2d\u7684 6 \u4e2a\u6570\u5b57\u3002 \u77e9\u9635\u5de6\u4e0a\u89d2\u7684 2\u00d72 \u90e8\u5206\u8868\u793a\u53d8\u6362\u7684\u7ebf\u6027\u90e8\u5206\uff0c\u7b2c 3 \u884c\u4e2d\u7684\u524d\u4e24\u9879\u8868\u793a\u5e73\u79fb\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u5728 GDI+ \u4e2d\uff0c\u53ef\u4ee5\u5728 Matrix<\/a> \u5bf9\u8c61\u4e2d\u5b58\u50a8\u4eff\u5c04\u53d8\u6362\u3002 \u7531\u4e8e\u8868\u793a\u4eff\u5c04\u53d8\u6362\u7684\u77e9\u9635\u7684\u7b2c\u4e09\u5217\u603b\u662f\uff080\uff0c0\uff0c1\uff09\uff0c\u56e0\u6b64\u5728\u6784\u9020 Matrix<\/a> \u5bf9\u8c61\u65f6\uff0c\u53ea\u9700\u6307\u5b9a\u524d\u4e24\u5217\u4e2d\u7684 6 \u4e2a\u6570\u3002 Matrix myMatrix = new Matrix(0, 1, -1, 0, 3, 4) \u8bed\u53e5\u6784\u9020\u4e0a\u9762\u56fe\u5f62\u4e2d\u663e\u793a\u7684\u77e9\u9635\u3002<\/p>\n\n\n\n

\u590d\u5408\u53d8\u6362<\/strong><\/p>\n\n\n\n

\u590d\u5408\u53d8\u6362\u662f\u4e00\u4e2a\u63a5\u4e00\u4e2a\u7684\u53d8\u6362\u5e8f\u5217\u3002 \u8bf7\u8003\u8651\u4e0b\u9762\u5217\u8868\u4e2d\u7684\u77e9\u9635\u548c\u53d8\u6362\uff1a<\/p>\n\n\n\n

\u77e9\u9635 A<\/td>\u65cb\u8f6c 90 \u5ea6<\/td><\/tr>
\u77e9\u9635 B<\/td>\u5728 x \u65b9\u5411\u4e0a\u7f29\u653e 2 \u500d<\/td><\/tr>
\u77e9\u9635 C<\/td>\u5728 y \u65b9\u5411\u4e0a\u5e73\u79fb 3 \u4e2a\u5355\u4f4d<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

\u5982\u679c\u4ece\u7531\u77e9\u9635 [2 1 1] \u8868\u793a\u7684\u70b9 (2, 1) \u5f00\u59cb\uff0c\u5e76\u5148\u540e\u4e58\u4ee5 A\u3001B\u3001C\uff0c\u5219\u70b9 (2, 1) \u5c06\u6309\u5217\u51fa\u7684\u987a\u5e8f\u7ecf\u5386\u4e09\u79cd\u53d8\u6362\u3002<\/p>\n\n\n\n

[2 1 1]ABC = [-2 5 1]<\/p>\n\n\n\n

\u53ef\u4ee5\u4e0d\u5c06\u590d\u5408\u53d8\u6362\u7684\u4e09\u90e8\u5206\u5b58\u50a8\u4e8e\u4e09\u4e2a\u72ec\u7acb\u7684\u77e9\u9635\uff0c\u800c\u662f\u4e00\u8d77\u4e58\u4ee5 A\u3001B \u548c C \u6765\u5f97\u5230\u5b58\u50a8\u6574\u4e2a\u590d\u5408\u53d8\u6362\u7684\u5355\u4e2a\u7684 3\u00d73 \u77e9\u9635\u3002 \u5047\u5b9a ABC = D\uff0c \u5219\u4e00\u4e2a\u70b9\u4e58\u4ee5 D \u5f97\u51fa\u7684\u7ed3\u679c\u4e0e\u4e00\u4e2a\u70b9\u5148\u540e\u4e58\u4ee5 A\u3001B\u3001C \u7684\u7ed3\u679c\u76f8\u540c\u3002<\/p>\n\n\n\n

[2 1 1]D = [-2 5 1]<\/p>\n\n\n\n

\u4e0b\u56fe\u663e\u793a\u4e86\u77e9\u9635 A\u3001B\u3001C \u548c D\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

\u590d\u5408\u53d8\u6362\u7684\u77e9\u9635\u53ef\u901a\u8fc7\u5c06\u51e0\u4e2a\u5355\u72ec\u7684\u53d8\u6362\u77e9\u9635\u76f8\u4e58\u800c\u5f97\u5230\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u4efb\u4f55\u4eff\u5c04\u53d8\u6362\u7684\u5e8f\u5217\u5747\u53ef\u5b58\u50a8\u4e8e\u5355\u4e2a\u7684 Matrix<\/a> \u5bf9\u8c61\u4e2d\u3002<\/p>\n\n\n\n

\"System_CAPS_caution\" \u5c0f\u5fc3<\/strong><\/td><\/tr>
\u590d\u5408\u53d8\u6362\u7684\u987a\u5e8f\u975e\u5e38\u91cd\u8981\u3002 \u4e00\u822c\u8bf4\u6765\uff0c\u5148\u65cb\u8f6c\u3001\u518d\u7f29\u653e\u3001\u7136\u540e\u5e73\u79fb\uff0c\u4e0e\u5148\u7f29\u653e\u3001\u518d\u65cb\u8f6c\u3001\u7136\u540e\u5e73\u79fb\u662f\u4e0d\u540c\u7684\u3002 \u540c\u6837\uff0c\u77e9\u9635\u76f8\u4e58\u7684\u987a\u5e8f\u4e5f\u662f\u91cd\u8981\u7684\u3002 \u4e00\u822c\u8bf4\u6765\uff0cABC \u4e0e BAC \u4e0d\u540c\u3002<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Matrix<\/a> \u7c7b\u63d0\u4f9b\u4e86\u51e0\u79cd\u6784\u5efa\u590d\u5408\u53d8\u6362\u7684\u65b9\u6cd5\uff1aMultiply<\/a>\u3001Rotate<\/a>\u3001RotateAt<\/a>\u3001Scale<\/a>\u3001Shear<\/a> \u548c Translate<\/a>\u3002 \u4e0b\u9762\u7684\u793a\u4f8b\u521b\u5efa\u4e86\u590d\u5408\u53d8\u6362\uff08\u5148\u65cb\u8f6c 30 \u5ea6\uff0c\u518d\u5728 y \u65b9\u5411\u4e0a\u7f29\u653e 2 \u500d\uff0c\u7136\u540e\u5728 x \u65b9\u5411\u5e73\u79fb 5 \u4e2a\u5355\u4f4d\uff09\u7684\u77e9\u9635\u3002<\/p>\n\n\n\n

C#<\/p>\n\n\n\n

VB<\/a><\/p>\n\n\n\n

Matrix myMatrix = new Matrix();
myMatrix.Rotate(30);
myMatrix.Scale(1, 2, MatrixOrder.Append);
myMatrix.Translate(5, 0, MatrixOrder.Append);<\/p>\n\n\n\n

\u4e0b\u56fe\u663e\u793a\u8be5\u77e9\u9635\u3002<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

m\u00d7n \u77e9\u9635\u662f\u6392\u5217\u5728 m \u884c\u548c n \u5217\u4e2d\u7684\u4e00\u7cfb\u5217\u6570\u3002 \u4e0b\u56fe\u663e\u793a\u51e0\u4e2a\u77e9\u9635\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[90],"class_list":["post-359","post","type-post","status-publish","format-standard","hentry","category-91","tag-90"],"_links":{"self":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/359","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=359"}],"version-history":[{"count":2,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/359\/revisions"}],"predecessor-version":[{"id":1356,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/359\/revisions\/1356"}],"wp:attachment":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=359"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=359"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=359"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}