{"id":1778,"date":"2022-11-29T17:32:04","date_gmt":"2022-11-29T09:32:04","guid":{"rendered":"https:\/\/courtship.top\/?p=1778"},"modified":"2022-11-29T17:32:04","modified_gmt":"2022-11-29T09:32:04","slug":"section03-shader%e6%95%b0%e5%ad%a6%e5%9f%ba%e7%a1%80","status":"publish","type":"post","link":"https:\/\/courtship.top\/index.php\/2022\/11\/29\/section03-shader%e6%95%b0%e5%ad%a6%e5%9f%ba%e7%a1%80\/","title":{"rendered":"Section03 Shader\u6570\u5b66\u57fa\u7840"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u7b1b\u5361\u5c14\u5750\u6807\u7cfb<\/h2>\n\n\n\n<p>\u6211\u4eec\u4f7f\u7528\u6570\u5b66\u7edd\u5927\u90e8\u5206\u662f\u4e3a\u4e86\u8ba1\u7b97\u4f4d\u7f6e\uff0c\u8ddd\u79bb\u548c\u89d2\u5ea6\u7b49\u53d8\u91cf\uff0c\u800c\u8fd9\u4e9b\u8ba1\u7b97\u5927\u591a\u6570\u5728<strong>\u7b1b\u5361\u5c14\u5750\u6807\u7cfb<\/strong>\u4e2d\u8fdb\u884c\u7684\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e8c\u7ef4\u7b1b\u5361\u5c14\u5750\u6807\u7cfb<\/h3>\n\n\n\n<p>\u5305\u542b\u4e86\u4e24\u4e2a\u90e8\u5206\u4fe1\u606f\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e00\u4e2a\u7279\u6b8a\u7684\u4f4d\u7f6e\uff0c\u5373\u539f\u70b9\uff0c\u5b83\u662f\u6574\u4e2a\u5750\u6807\u7cfb\u7684\u4e2d\u5fc3<\/li>\n\n\n\n<li>\u4e24\u6761\u8fc7\u539f\u70b9\u7684\u4e92\u76f8\u5782\u76f4\u7684\u77e2\u91cf\uff0c\u5373x\u8f74\u548cy\u8f74\u3002\u8fd9\u4e9b\u5750\u6807\u8f74\u4e5f\u88ab\u79f0\u4e3a\u662f\u8be5\u5750\u6807\u7cfb\u7684\u57fa\u77e2\u91cf\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u5728\u5c4f\u5e55\u6620\u5c04\u65f6\uff0cOpenGL\u548cDirectX\u4f7f\u7528\u4e86\u4e0d\u540c\u65b9\u5411\u7684\u4e8c\u7ef4\u7b1b\u5361\u5c14\u5750\u6807\u7cfb<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e09\u7ef4\u7b1b\u5361\u5c14\u5750\u6807\u7cfb<\/h3>\n\n\n\n<p>\u5728\u4e09\u7ef4\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\u4e2d\u6211\u4eec\u9700\u8981\u5b9a\u4e493\u4e2a\u5750\u6807\u8f74\u548c\u4e00\u4e2a\u539f\u70b9\uff0c\u8fd9\u4e09\u4e2a\u5750\u6807\u8f74\u4e5f\u88ab\u79f0\u4e3a\u662f\u8be5\u5750\u6807\u7cfb\u7684<strong>\u57fa\u77e2\u91cf<\/strong>\u3002<\/p>\n\n\n\n<p>\u901a\u5e38\u60c5\u51b5\u4e0b\uff0c\u8fd93\u4e2a\u5750\u6807\u8f74\u4e4b\u95f4\u662f\u4e92\u76f8\u5782\u76f4\u7684\uff0c\u4e14\u957f\u5ea6\u4e3a1\uff0c\u8fd9\u6837\u7684\u57fa\u77e2\u91cf\u88ab\u79f0\u4e3a<strong>\u6807\u51c6\u6b63\u4ea4\u57fa<\/strong>\u3002<\/p>\n\n\n\n<p>\u548c\u4e8c\u7ef4\u7b1b\u5361\u513f\u5750\u6807\u7cfb\u7c7b\u4f3c\uff0c<strong>\u4e09\u7ef4\u7b1b\u5361\u513f\u5750\u6807\u7cfb\u4e2d\u7684\u5750\u6807\u8f74\u65b9\u5411\u4e5f\u4e0d\u662f\u56fa\u5b9a\u7684\uff0c\u8fd9\u79cd\u4e0d\u540c\u5bfc\u81f4\u4e86\u4e24\u79cd\u4e0d\u540c\u79cd\u7c7b\u7684\u5750\u6807\u7cfb<\/strong> \uff1a\u5de6\u624b\u5750\u6807\u7cfb (left-handed coordinate space) \u53f3\u624b\u5750\u6807\u7cfb (right-handed coordinate space)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5de6\u624b\u5750\u6807\u7cfb\u548c\u53f3\u624b\u5750\u6807\u7cfb<\/h3>\n\n\n\n<p>\u4ece\u8fd9\u79cd\u610f\u4e49\u4e0a\u6765\u8bf4\uff0c\u6240\u6709\u7684\u4e8c\u7ef4\u7b1b\u5361\u513f\u5750\u6807\u7cfb\u90fd\u662f\u7b49\u4ef7\u7684\u3002\u4f46\u5bf9\u4e8e\u4e09\u7ef4\u7b1b\u5361\u513f\u5750\u6807\u7cfb\uff0c\u9760\u8fd9\u79cd\u65cb\u8f6c\u6709\u65f6\u5e76\u4e0d\u80fd\u4f7f\u4e24\u4e2a\u4e0d\u540c\u671d\u5411\u7684\u5750\u6807\u7cfb\u91cd\u5408\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-medium\"><img decoding=\"async\" src=\"https:\/\/courtship.top\/wp-content\/uploads\/2022\/11\/\u56fe\u7247-8-243x300.png\" alt=\"\" class=\"wp-image-1784\"\/><figcaption class=\"wp-element-caption\">\u5de6\u624b\u5750\u6807\u7cfb<\/figcaption><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\">\u786e\u5b9a\u5750\u6807\u7cfb<\/h4>\n\n\n\n<p><strong>\u786e\u5b9a\u662f\u5de6\u624b\u8fd8\u662f\u53f3\u624b\u5750\u6807\u7cfb\u7684\u65b9\u6cd5\u662f\uff0c\u5224\u65ad\u524d\u5411 (forward) \u7684\u65b9\u5411<\/strong>\u3002\u8bf7\u8bfb\u8005\u5750\u76f4\uff0c\u5411\u53f3\u4f38\u76f4\u4f60\u7684\u53f3\u624b\uff0c\u6b64\u65f6\u53f3\u624b\u65b9\u5411\u5c31\u662f \u8f74\u7684\u6b63\u5411\uff0c\u800c\u4f60\u7684\u5934\u9876\u5411\u4e0a\u7684\u65b9\u5411\u5c31\u662f \u8f74\u7684\u6b63\u5411 \u3002\u8fd9\u65f6\uff0c\u5982\u679c\u4f60\u7684\u6b63\u524d\u65b9\u7684\u65b9\u5411\u662f \u8f74\u7684\u6b63\u5411\uff0c\u90a3\u4e48\u4f60\u672c\u8eab\u6240\u5728\u7684\u5750\u6807\u7cfb\u5c31\u662f\u4e00\u4e2a\u5de6\u624b\u5750\u6807\u7cfb\u3002\u5982\u679c\u4f60\u7684\u6b63\u524d\u65b9\u7684\u65b9\u5411\u5bf9\u5e94\u7684\u662f \u8f74\u7684\u8d1f\u5411\uff0c\u90a3\u4e48\u8fd9\u5c31\u662f\u4e00\u4e2a\u53f3\u624b\u5750\u6807\u7cfb\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u65cb\u8f6c\u6cd5\u5219<\/h4>\n\n\n\n<p>\u5728\u5de6\u624b\u5750\u6807\u7cfb\u4e2d\uff0c\u8fd9\u4e2a\u65cb\u8f6c\u6b63\u65b9\u5411\u662f\u7531\u5de6\u624b\u6cd5\u5219\u5b9a\u4e49\u7684\uff0c\u800c\u5728\u53f3\u624b\u5750\u6807\u7cfb\u4e2d\u5219\u662f\u7531\u53f3\u624b\u6cd5\u5219\u5b9a\u4e49\u7684\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Unity\u6240\u4f7f\u7528\u7684\u7684\u5750\u6807\u7cfb<\/h3>\n\n\n\n<p><strong>\u5bf9\u5343\u6a21\u578b\u7a7a\u95f4\u548c\u4e16\u754c\u7a7a\u95f4\uff0cUnity \u4f7f\u7528\u7684\u662f\u5de6\u624b\u5750\u6807\u7cfb\u3002<\/strong><\/p>\n\n\n\n<p><strong>\u5bf9\u4e8e\u89c2\u5bdf\u7a7a\u95f4\u6765\u8bf4\uff0cUnity \u4f7f\u7528\u7684\u662f\u53f3\u624b\u5750\u6807\u7cfb\u3002<\/strong>\u89c2\u5bdf\u7a7a\u95f4 \uff0c\u901a\u4fd7\u6765\u8bb2\u5c31\u662f\u4ee5\u6444\u50cf\u673a\u4e3a\u539f\u70b9\u7684\u5750\u6807\u7cfb\u3002\u5728\u8fd9\u4e2a\u5750\u6807\u7cfb\u4e2d\uff0c\u6444\u50cf\u673a\u7684\u524d\u5411\u662fz\u8f74\u7684\u8d1f\u65b9\u5411\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u70b9\u548c\u77e2\u91cf<\/h2>\n\n\n\n<p>\u70b9(point) \u662fn\u7ef4\u7a7a\u95f4\uff08\u6e38\u620f\u4e2d\u4e3b\u8981\u4f7f\u7528\u4e8c\u7ef4\u548c\u4e09\u7ef4\u7a7a\u95f4\uff09\u4e2d\u7684\u4e00\u4e2a\u4f4d\u7f6e\u3002\u5b83\u6ca1\u6709\u5927\u5c0f\u3001\u5bbd\u5ea6\u8fd9\u7c7b\u6982\u5ff5\u3002<\/p>\n\n\n\n<p><strong>\u77e2\u91cf\uff0c\u4e5f\u88ab\u79f0\u4e3a\u5411\u91cf<\/strong>\u3002\u77e2\u91cf\u5b58\u5728\u7684\u610f\u4e49\u66f4\u591a\u662f\u4e3a\u4e86\u548c<strong>\u6807\u91cf<\/strong>\u533a\u5206\u5f00\u6765\u3002\u77e2\u91cf\u662f\u6307n\u7ef4\u7a7a\u95f4\u4e2d\u4e00\u79cd\u5305\u542b\u4e86<strong>\u6a21<\/strong>\u548c<strong>\u65b9\u5411<\/strong>\u7684\u6709\u5411\u7ebf\u6bb5\uff0c\u6211\u4eec\u901a\u5e38\u8bb2\u5230\u7684\u901f\u5ea6\u5c31\u662f\u4e00\u79cd\u5178\u578b\u7684\u77e2\u91cf\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u77e2\u91cf\u7684\u6a21\u6307\u7684\u662f\u8fd9\u4e2a\u77e2\u91cf\u7684\u957f\u5ea6<\/li>\n\n\n\n<li>\u77e2\u91cf\u7684\u65b9\u5411\u5219\u63cf\u8ff0\u4e86\u8fd9\u4e2a\u77e2\u91cf\u5728\u7a7a\u95f4\u4e2d\u7684\u6307\u5411<\/li>\n<\/ul>\n\n\n\n<p>\u901a\u5e38\uff0c\u77e2\u91cf\u88ab\u7528\u4e8e\u8868\u793a\u76f8\u5bf9\u4e8e\u67d0\u4e2a\u70b9\u7684\u504f\u79fb\uff0c\u4e5f\u5c31\u662f\u8bf4\u5b83\u662f\u4e00\u4e2a\u76f8\u5bf9\u91cf\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e2\u91cf\u8fd0\u7b97<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e00\u4e2a\u77e2\u91cf\u53ef\u4ee5\u88ab\u4e00\u4e2a\u975e\u96f6\u7684\u6807\u91cf\u9664<\/li>\n\n\n\n<li>\u53ef\u4ee5\u5bf9\u4e24\u4e2a\u77e2\u91cf\u8fdb\u884c\u76f8\u52a0\u6216\u76f8\u51cf\uff0c\u5176\u7ed3\u679c\u662f\u4e00\u4e2a\u76f8\u540c\u7ef4\u5ea6\u7684\u65b0\u77e2\u91cf\u3002\u5728\u56fe\u5f62\u5b66\u4e2d\u901a\u5e38\u7528\u4e8e\u63cf\u8ff0\u4f4d\u7f6e\u504f\u79fb<\/li>\n\n\n\n<li>\u77e2\u91cf\u7684\u6a21\u662f\u4e00\u4e2a\u6807\u91cf<\/li>\n\n\n\n<li>\u5355\u4f4d\u77e2\u91cf\u662f\u6307\u90a3\u4e9b\u6a21\u4e3a1 \u7684\u77e2\u91cf\u3002\u4e5f\u88ab\u79f0\u4e3a\u88ab<strong>\u5f52\u4e00\u5316\u7684\u77e2\u91cf<\/strong>\u3002\u6cd5\u7ebf\u6cd5\u76f8\u4e5f\u88ab\u79f0\u4e3a\u6cd5\u77e2\u91cf<\/li>\n<\/ul>\n\n\n\n<p>\u77e2\u91cf\u4e4b\u95f4\u4e5f\u53ef\u4ee5\u8fdb\u884c\u4e58\u6cd5\uff0c\u4f46\u662f\u548c\u6807\u91cf\u4e4b\u95f4\u7684\u4e58\u6cd5\u6709\u5f88\u5927\u4e0d\u540c\u3002\u77e2\u91cf\u7684\u4e58\u6cd5\u6709\u4e24\u79cd\u6700\u5e38\u7528\u7684<br \/>\u79cd\u7c7b\uff1a\u70b9\u79ef (dot product, \u4e5f\u88ab\u79f0\u4e3a\u5185\u79ef\uff0c inner product) \u548c\u53c9\u79ef (cross product, \u4e5f\u88ab\u79f0\u4e3a\u5916<br \/>\u79ef\uff0c outer product)\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e2\u91cf\u7684\u70b9\u79ef<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u516c\u5f0f\u4e00\uff1a<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>a\u00b7b=(ax, ay, az)\u00b7(bx, by, bz)= axbx+ayby+azbz<\/strong><\/p>\n\n\n\n<p>\u77e2\u91cf\u7684\u70b9\u79ef\u6ee1\u8db3\u4ea4\u6362\u5f8b\uff0c\u5373 a\u00b7b = b\u00b7a<br \/><strong>\u70b9\u79ef\u7684\u51e0\u4f55\u610f\u4e49\u5f88\u91cd\u8981\uff0c\u56e0\u4e3a\u70b9\u79ef\u51e0\u4e4e\u5e94\u7528\u5230\u4e86\u56fe\u5f62\u5b66\u7684\u5404\u4e2a\u65b9\u9762\u3002\u5176\u4e2d\u4e00\u4e2a\u51e0\u4f55\u610f\u4e49\u5c31\u662f<br \/>\u6295\u5f71 (projection)<\/strong>\u3002\u6295\u5f71\u7684\u503c\u53ef\u80fd\u662f\u8d1f\u6570\u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>\u4e5f\u662f\u5c31\u662f\u8bf4 \u70b9\u79ef\u7684\u7b26\u53f7\u53ef\u4ee5\u8ba9\u6211\u4eec\u77e5\u9053\u4e24\u4e2a\u77e2\u91cf\u7684\u65b9\u5411\u5173\u7cfb\u3002<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u70b9\u79ef\u7684\u6027\u8d28<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u70b9\u79ef\u53ef\u7ed3\u5408\u6807\u91cf\u4e58\u6cd5\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5bf9\u70b9\u79ef\u4e2d\u5176\u4e2d\u4e00\u4e2a\u77e2\u91cf\u8fdb\u884c\u7f29\u653e\u7684\u7ed3\u679c \uff0c\u76f8\u5f53\u4e8e\u5bf9\u6700\u540e\u7684\u70b9\u79ef\u7ed3\u679c\u8fdb\u884c\u7f29\u653e\u3002<\/li>\n\n\n\n<li>\u70b9\u79ef\u53ef\u7ed3\u5408\u77e2\u91cf\u52a0\u6cd5\u548c\u51cf\u6cd5<\/li>\n\n\n\n<li>\u4e00\u4e2a\u77e2\u91cf\u548c\u672c\u8eab\u8fdb\u884c\u70b9\u79ef\u7684\u7ed3\u679c\uff0c\u662f\u8be5\u77e2\u91cf\u7684\u6a21\u7684\u5e73\u65b9\u3002\u8fd9\u610f\u5473\u7740\uff0c\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u5229\u7528\u70b9\u79ef\u6765\u6c42\u77e2\u91cf\u7684\u6a21\uff0c \u800c\u4e0d\u9700\u8981\u4f7f\u7528\u6a21\u7684\u8ba1\u7b97\u516c\u5f0f<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u516c\u5f0f\u4e8c<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>a \u00b7 b = |a||b|cos\u03b8<\/strong><\/p>\n\n\n\n<p>\u4e24\u4e2a\u5355\u4f4d\u77e2\u91cf\u7684\u70b9\u79ef\u7b49\u4e8e\u5b83\u4eec\u4e4b\u95f4\u5939\u89d2\u7684\u4f59\u5f26\u503c<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e2\u91cf\u7684\u53c9\u79ef<\/h3>\n\n\n\n<p>\u4e0e\u70b9\u79ef\u4e0d\u540c\u7684\u662f\uff0c \u77e2\u91cf\u53c9\u79ef\u7684\u7ed3\u679c\u4ecd\u662f\u4e00\u4e2a\u77e2\u91cf\uff0c \u800c\u975e\u6807\u91cf\u3002<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>a\u0004b = (ax, ay, az)\u0004(bx, by, bz) = (aybz - azby, azbx - axbz, axby - aybx)<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/courtship.top\/wp-content\/uploads\/2022\/11\/\u56fe\u7247-10.png\" alt=\"\" class=\"wp-image-1810\" width=\"450\" height=\"125\"\/><\/figure>\n<\/div>\n\n\n<p>\u9700\u8981\u6ce8\u610f\u7684\u662f\uff0c\u53c9\u79ef\u4e0d\u6ee1\u8db3\u4ea4\u6362\u5f8b a x b != b x a\u3002\u5b9e\u9645\u4e0a\uff0c\u53c9\u79ef\u662f\u6ee1\u8db3\u53cd\u4ea4\u6362\u5f8b\u7684\uff0c\u5373a x b = -(b x a)\u3002\u800c\u4e14\u53c9\u79ef\u4e5f\u4e0d\u6ee1\u8db3\u7ed3\u5408\u5f8b\uff0c\u5373 (a x b) x c != a x (b x c)\u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>\u5bf9\u4e24\u4e2a\u77e2\u91cf\u8fdb\u884c\u53c9\u79ef\u7684\u7ed3\u679c\u4f1a\u5f97\u5230 \u4e2a\u540c\u65f6\u5782\u76f4\u4e8e\u8fd9\u4e24\u4e2a\u77e2\u91cf\u7684\u65b0\u77e2\u91cf\u3002<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/courtship.top\/wp-content\/uploads\/2022\/11\/\u56fe\u7247-11.png\" alt=\"\" class=\"wp-image-1812\" width=\"200\" height=\"218\"\/><\/figure>\n<\/div>\n\n\n<p class=\"has-medium-font-size\"><strong>\u53c9\u79ef\u5230\u5e95\u6709\u4ec0\u4e48\u7528\u5462\uff1f\u6700\u5e38\u89c1\u7684\u4e00\u4e2a\u5e94\u7528\u5c31\u662f\u8ba1\u7b97\u5782\u76f4\u4e8e\u4e00\u4e2a\u5e73\u9762\u3001 \u4e09\u89d2\u5f62\u7684\u77e2\u91cf\u3002\u53e6\u5916\uff0c \u8fd8\u53ef\u4ee5\u7528\u4e8e\u5224\u65ad\u4e09\u89d2\u9762\u7247\u7684\u671d\u5411<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5728\u6e32\u67d3\u4e2d\u6211\u4eec\u65f6\u5e38\u4f1a\u9700\u8981\u5224\u65ad\u4e00\u4e2a\u4e09\u89d2\u9762\u7247\u662f\u6b63\u9762\u8fd8\u662f\u80cc\u9762\uff0c \u8fd9\u53ef\u4ee5\u901a\u8fc7\u5224\u65ad\u4e09\u89d2\u5f62\u76843\u4e2a\u9876\u70b9\u5728\u5f53\u524d\u7a7a\u95f4\u4e2d\u662f\u987a\u65f6\u9488\u8fd8\u662f\u9006\u65f6\u9488\u6392\u5217\u6765\u5f97\u5230\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u77e9\u9635<\/h2>\n\n\n\n<p>\u5728\u4e09\u7ef4\u6570\u5b66\u4e2d\uff0c \u6211\u4eec\u901a\u5e38\u4f1a\u4f7f\u7528\u77e9\u9635\u6765\u8fdb\u884c\u53d8\u6362\u3002 \u4e00\u4e2a\u77e9\u9635\u53ef\u4ee5\u628a\u4e00\u4e2a\u77e2\u91cf\u4ece\u4e00\u4e2a\u5750\u6807\u7a7a\u95f4\u8f6c\u6362\u5230\u53e6\u4e00\u4e2a\u5750\u6807\u7a7a\u95f4\u3002\u5728\u7b2c2\u7ae0 \u6e32\u67d3\u6d41\u6c34\u7ebf\u4e2d\uff0c \u6211\u4eec\u5c31\u770b\u5230\u4e86\u5f88\u591a\u5750\u6807\u53d8\u6362\uff0c \u4f8b\u5982\u5728\u9876\u70b9\u7740\u8272\u5668\u4e2d\u6211\u4eec\u9700\u8981\u628a\u9876\u70b9\u5750\u6807\u4ece\u6a21\u578b\u7a7a\u95f4\u53d8\u6362\u5230\u9f50\u6b21\u88c1\u526a\u5750\u6807\u7cfb\u4e2d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e0e\u77e2\u91cf\u8054\u7cfb<\/h3>\n\n\n\n<p>\u5b9e\u9645\u4e0a\uff0c\u77e2\u91cf\u53ef\u4ee5\u770b\u6210\u662f n x \u5217\u77e9\u9635 (column matrix) \u6216 l x n \u884c\u77e9\u9635 (row matrix), \u5176\u4e2d \u5bf9\u5e94\u4e86\u77e2\u91cf\u7684\u7ef4\u5ea6\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u77e9\u9635\u4e58\u6cd5<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u77e9\u9635\u4e58\u6cd5\u5e76\u4e0d\u6ee1\u8db3\u4ea4\u6362\u5f8b<\/li>\n\n\n\n<li>\u77e9\u9635\u4e58\u6cd5\u6ee1\u8db3\u7ed3\u5408\u5f8b<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7279\u6b8a\u77e9\u9635<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">\u65b9\u5757\u77e9\u9635<\/h4>\n\n\n\n<p>\u65b9\u5757\u77e9\u9635 (square matrix), \u7b80\u79f0\u65b9\u9635\uff0c\u662f\u6307\u90a3\u4e9b\u884c\u548c\u5217\u6570\u76ee\u76f8\u7b49\u7684\u77e9\u9635 \u7ef4\u6e32\u67d3\u91cc\uff0c\u6700\u5e38\u4f7f\u7528\u7684\u5c31\u662f 3X3 4X4 \u7684\u65b9\u9635\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/courtship.top\/wp-content\/uploads\/2022\/11\/\u56fe\u7247-12.png\" alt=\"\" class=\"wp-image-1821\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\">\u5355\u4f4d\u77e9\u9635<\/h4>\n\n\n\n<p>\u4e2a\u7279\u6b8a\u7684\u5bf9\u89d2\u77e9\u9635\u662f\u5355\u4f4d\u77e9\u9635 (identity matrix), \u6765\u8868\u793a\u3002\u4e00 3x3 \u7684\u5355\u4f4d\u77e9\u9635\u5982\u4e0b<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/courtship.top\/wp-content\/uploads\/2022\/11\/\u56fe\u7247-13.png\" alt=\"\" class=\"wp-image-1822\"\/><\/figure>\n<\/div>\n\n\n<h4 class=\"wp-block-heading\">\u8f6c\u7f6e\u77e9\u9635<\/h4>\n\n\n\n<p>\u8f6c\u7f6e\u77e9\u9635 (transposed matrix) \u5b9e\u9645\u662f\u5bf9\u539f\u77e9\u9635\u7684\u4e00\u79cd\u8fd0\u7b97\uff0c\u5373\u8f6c\u7f6e\u8fd0\u7b97 \u7ed9\u5b9a rXc\u7684\u77e9\u9635M\uff0c\u5b83\u53ef\u4ee5\u8868\u793a\u6210Mt\u3002\uff0c\u539f\u77e9\u9635\u7684\u7b2ci\u884c\u53d8\u6210\u4e86\u7b2cj\u5217\uff0c\u800c\u7b2cj\u5217\u53d8\u6210\u4e86\u7b2ci\u884c\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/courtship.top\/wp-content\/uploads\/2022\/11\/\u56fe\u7247-14.png\" alt=\"\" class=\"wp-image-1825\"\/><\/figure>\n<\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>\u77e9\u9635\u8f6c\u7f6e\u7684\u8f6c\u7f6e\u7b49\u4e8e\u539f\u77e9\u9635<\/li>\n\n\n\n<li>\u77e9\u9635\u4e32\u63a5\u7684\u8f6c\u7f6e \u7b49\u4e8e\u53cd\u5411\u4e32\u63a5\u5404\u4e2a\u77e9\u9635\u7684\u8f6c\u7f6e<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u9006\u77e9\u9635<\/h4>\n\n\n\n<p>\u4e0d\u662f\u6240\u6709\u7684\u77e9\u9635\u90fd\u6709\u9006\u77e9\u9635\uff0c\u7b2c\u4e00\u4e2a\u524d\u63d0\u5c31\u662f\uff0c\u8be5\u77e9\u9635\u5fc5\u987b\u662f\u4e00\u4e2a\u65b9\u9635\u3002\u9006\u77e9\u9635\u6700\u91cd\u8981\u7684\u6027\u8d28\u5c31\u662f \u5982\u679c\u6211\u4eec\u628aM\u548cM-1\u76f8\u4e58\uff0c\u90a3\u4e48\u5b83\u7684\u7ed3\u679c\u5c06\u4f1a\u662f\u4e00\u4e2a\u5355\u4f4d\u77e9\u9635\u3002<\/p>\n\n\n\n<p>\u5982\u679c\u4e00\u4e2a\u77e9\u9635\u6709\u5bf9\u5e94\u7684\u9006\u77e9\u9635\uff0c\u6211\u4eec\u5c31\u8bf4\u8fd9\u4e2a\u77e9\u9635\u662f\u53ef\u9006\u7684 (invertible) \u6216\u8005\u8bf4\u662f\u975e\u5947\u5f02\u7684 (nonsingular)\u76f8\u53cd\u7684\uff0c\u5982\u679c \u4e2a\u77e9\u9635\u6ca1\u6709\u5bf9\u5e94\u7684\u9006\u77e9\u9635\uff0c\u6211\u4eec\u5c31\u8bf4\u5b83\u662f\u4e0d\u53ef\u9006\u7684 (noninvertible) \u6216\u8005\u8bf4\u662f\u5947\u5f02\u7684 (singular)\u3002<\/p>\n\n\n\n<p>\u5982\u679c \u4e2a\u77e9\u9635\u7684\u884c\u5217\u5f0f (determinant)\u4e0d\u4e3a0\u90a3\u4e48\u5b83\u5c31\u662f\u53ef\u9006\u7684\u3002<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u9006\u77e9\u9635\u7684\u9006\u77e9\u9635\u662f\u539f\u77e9\u9635\u672c\u8eab<\/li>\n\n\n\n<li>\u5355\u4f4d\u77e9\u9635\u7684\u9006\u77e9\u9635\u662f\u5b83\u672c\u8eab<\/li>\n\n\n\n<li>\u8f6c\u7f6e\u77e9\u9635\u7684\u9006\u77e9\u9635\u662f\u9006\u77e9\u9635\u7684\u8f6c\u7f6e<\/li>\n\n\n\n<li>\u77e9\u9635\u4e32\u63a5\u76f8\u4e58\u540e\u7684\u9006\u77e9\u9635\u7b49\u4e8e\u53cd\u5411\u4e32\u63a5\u5404\u4e2a\u77e9\u9635\u7684\u9006\u77e9\u9635<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u6b63\u4ea4\u77e9\u9635<\/h4>\n\n\n\n<p>\u6b63\u4ea4\u662f\u77e9\u9635\u7684\u4e00\u79cd\u5c5e\u6027\u3002<strong>\u5982\u679c\u4e00\u4e2a\u65b9\u9635\u548c\u5b83\u7684\u8f6c\u7f6e\u77e9\u9635\u7684\u4e58\u79ef\u662f\u5355\u4f4d\u77e9\u9635\u7684\u8bdd\uff0c\u6211\u4eec\u5c31\u8bf4\u8fd9\u4e2a\u77e9\u9635\u662f\u6b63\u4ea4\u7684 (orthogonal) <\/strong>\u3002\u53cd\u8fc7\u6765\u4e5f\u662f\u6210\u7acb\u7684\u3002<\/p>\n\n\n\n<p><strong>\u5982\u679c\u4e00\u4e2a\u77e9\u9635\u662f\u6b63\u4ea4\u7684\uff0c\u90a3\u4e48\u5b83\u7684\u8f6c\u7f6e\u77e9\u9635\u548c\u9006\u77e9\u9635\u662f\u4e00\u6837\u7684<\/strong><\/p>\n\n\n\n<p>\u4e3a\u5728\u4e09\u7ef4\u53d8\u6362\u4e2d\u6211\u4eec\u7ecf\u5e38\u4f1a\u9700\u8981\u4f7f\u7528\u9006\u77e9\u9635\u6765\u6c42\u89e3\u53cd\u5411\u7684\u53d8\u6362\u3002\u800c\u9006\u77e9\u9635\u7684\u6c42\u89e3\u5f80\u5f80\u8ba1\u7b97\u6279\u5f88\u5927\uff0c\u4f46\u8f6c\u7f6e\u77e9\u9635\u5374\u975e\u5e38\u5bb9\u6613\u6c42\u89e3 \u6211\u4eec\u53ea\u9700\u8981\u628a\u77e9\u9635\u7ffb\u8f6c\u4e00\u4e0b\u5c31\u53ef\u4ee5\u4e86\u3002<\/p>\n\n\n\n<p>\u56e0\u6b64\uff0c\u5982\u679c\u8fd9\u4e9b\u57fa\u77e2\u91cf\u662f\u4e00\u7ec4\u6807\u51c6\u6b63\u4ea4\u57fa\u7684\u8bdd\uff08\u4f8b\u5982\u53ea\u5b58\u5728\u65cb\u8f6c\u53d8\u6362\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u8f6c\u7f6e\u77e9\u9635\u6765\u6c42\u5f97\u8be5\u53d8\u6362\u7684\u9006\u53d8\u6362\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u77e9\u9635\u51e0\u4f55\u610f\u4e49\uff1a\u53d8\u6362<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u53d8\u6362<\/h3>\n\n\n\n<p>\u53d8\u6362(transform), \u6307\u7684\u662f\u6211\u4eec\u628a\u4e00\u4e9b\u6570\u636e\uff0c \u5982\u70b9\u3001 \u65b9\u5411\u77e2\u6279\u751a\u81f3\u662f\u989c\u8272\u7b49\uff0c \u901a\u8fc7\u67d0\u79cd\u65b9\u5f0f\u8fdb\u884c\u8f6c\u6362\u7684\u8fc7\u7a0b\u3002<\/p>\n\n\n\n<p><strong>\u7ebf\u6027\u53d8\u6362<\/strong>\u6307\u7684\u662f\u90a3\u4e9b\u53ef\u4ee5\u4fdd\u7559\u77e2\u91cf\u52a0\u548c\u6807\u91cf\u4e58\u7684\u53d8\u6362\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/courtship.top\/wp-content\/uploads\/2022\/11\/\u56fe\u7247-15.png\" alt=\"\" class=\"wp-image-1837\"\/><\/figure>\n<\/div>\n\n\n<ul class=\"wp-block-list\">\n<li>\u7f29\u653e(scale)\u5c31\u662f\u4e00\u79cd\u7ebf\u6027\u53d8\u6362<\/li>\n\n\n\n<li>\u65cb\u8f6c(rotation)\u4e5f\u662f\u4e00\u79cd\u7ebf\u6027\u53d8\u6362<\/li>\n\n\n\n<li>\u7ebf\u6027\u53d8\u6362\u9664\u4e86\u5305\u62ec\u65cb\u8f6c\u548c\u7f29\u653e\u5916\uff0c\u8fd8\u5305\u62ec\u9519\u5207(shear)\u3001\u955c\u50cf(mirroring, \u4e5f\u88ab\u79f0\u4e3areflection)\u3001\u6b63\u4ea4\u6295\u5f71(orthographic projection)\u7b49<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u4eff\u5c04\u53d8\u6362<\/h4>\n\n\n\n<p>\u6211\u4eec\u4e0d\u80fd\u7528 3X3 \u7684\u77e9\u9635\u6765\u8868\u793a\u4e00\u4e2a\u5e73\u79fb\u53d8\u6362\uff0c\u6240\u4ee5\u6709\u4e86\u4eff\u5c04\u53d8\u6362<\/p>\n\n\n\n<p><strong>\u4eff\u5c04\u53d8\u6362<\/strong>\u5c31\u662f\u5408\u5e76\u7ebf\u6027\u53d8\u6362\u548c\u5e73\u79fb\u53d8\u6362\u7684\u53d8\u6362\u7c7b\u578b\u3002\u4eff\u5c04\u53d8\u6362\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e2a 4x4 \u7684\u77e9\u9635(\u9f50\u6b21\u5750\u6807)\u6765\u8868\u793a\uff0c\u4e3a\u6b64\uff0c\u6211\u4eec\u9700\u8981\u628a\u77e2\u91cf\u6269\u5c55\u5230\u56db\u7ef4\u7a7a\u95f4\u4e0b\uff0c\u8fd9\u5c31\u662f<strong>\u9f50\u6b21\u5750\u6807\u7a7a\u95f4<\/strong> (homogeneous space)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/courtship.top\/wp-content\/uploads\/2022\/11\/\u56fe\u7247-16.png\" alt=\"\" class=\"wp-image-1840\"\/><\/figure>\n<\/div>\n\n\n<h2 class=\"wp-block-heading\">\u5750\u6807\u7a7a\u95f4<\/h2>\n\n\n\n<p>\u6211\u4eec\u9700\u8981\u5728\u4e0d\u540c\u7684\u60c5\u51b5\u4e0b\u4f7f\u7528\u4e0d\u540c\u7684\u5750\u6807\u7a7a\u95f4 \u56e0\u4e3a\u4e00\u4e9b\u6982\u5ff5\u53ea\u6709\u5728\u7279\u5b9a\u7684\u5750\u6807\u7a7a\u95f4\u4e0b\u624d\u6709\u610f\u4e49 \u624d\u66f4\u5bb9\u6613\u7406\u89e3\u3002\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u5728\u6e32\u67d3\u4e2d\u6211\u4eec\u8981\u4f7f\u7528\u8fd9\u4e48\u591a\u5750\u6807\u7a7a\u95f4\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5750\u6807\u7a7a\u95f4\u7684\u53d8\u6362<\/h3>\n\n\n\n<p>\u5f53\u7ed9\u5b9a\u4e00\u4e2a\u5750\u6807\u7a7a\u95f4\u4ee5\u53ca\u5176\u4e2d\u4e00\u70b9 \u65f6\uff0c\u6211\u4eec\u662f\u5982\u4f55\u77e5\u9053\u8be5\u70b9\u7684\u4f4d\u7f6e\u7684\u5462\uff1f\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7 \u4e2a\u6b65\u9aa4\u6765\u786e\u5b9a\u5b83\u7684\u4f4d\u7f6e\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u4ece\u5750\u6807\u7a7a\u95f4\u7684\u539f\u70b9\u5f00\u59cb\uff1b<\/li>\n\n\n\n<li>\u5411x\u8f74\u65b9\u5411\u79fb\u52a8a\u4e2a\u5355\u4f4d\u3002<\/li>\n\n\n\n<li>\u5411y\u8f74\u65b9\u5411\u79fb\u52a8b\u4e2a\u5355\u4f4d\u3002<\/li>\n\n\n\n<li>\u5411z\u8f74\u65b9\u5411\u79fb\u52a8c\u4e2a\u5355\u4f4d\u3002<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">\u5bf9\u65b9\u5411\u77e2\u91cf\u7684\u5750\u6807\u7a7a\u95f4\u8f6c\u6362<\/h4>\n\n\n\n<p>\u77e2\u91cf\u662f\u6ca1\u6709\u4f4d\u7f6e\u7684\uff0c\u56e0\u6b64\u5750\u6807\u7a7a\u95f4\u7684\u539f\u70b9\u53d8\u6362\u662f\u53ef\u4ee5\u5ffd\u7565\u7684\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u4ec5\u4ec5\u5e73\u79fb\u5750\u6807\u7cfb\u7684\u539f\u70b9\u662f\u4e0d\u4f1a\u5bf9\u77e2\u91cf\u9020\u6210\u4efb\u4f55\u5f71\u54cd\u7684\u3002\u90a3\u4e48\uff0c\u5bf9\u77e2\u5740\u7684\u5750\u6807\u7a7a\u95f4\u53d8\u6362\u5c31\u53ef\u4ee5\u4f7f\u7528 3X3 \u7684\u77e9\u9635\u6765\u8868\u793a\uff0c\u56e0\u4e3a\u6211\u4eec\u4e0d\u9700\u8981\u8868\u793a\u5e73\u79fb\u53d8\u6362\u3002<\/p>\n\n\n\n<p>\u5728Shader\u4e2d\u7ecf\u5e38\u4f1a\u770b\u5230\u622a\u53d6\u53d8\u6362\u77e9\u9635\u7684\u524d3\u884c\u524d3\u5217\u6765\u5bf9\u6cd5\u7ebf\u65b9\u5411\u3001\u5149\u7167\u65b9\u5411\u6765\u8fdb\u884c\u7a7a\u95f4\u53d8\u6362\uff0c\u8fd9\u6b63\u662f\u539f\u56e0\u6240\u5728<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u9876\u70b9\u7684\u5750\u6807\u7a7a\u95f4\u53d8\u6362\u8fc7\u7a0b<\/h3>\n\n\n\n<p>\u5728\u6e32\u67d3\u6d41\u6c34\u7ebf\u4e2d\uff0c\u4e00\u4e2a\u9876\u70b9\u8981\u7ecf\u8fc7\u591a\u4e2a\u5750\u6807\u7a7a\u95f4\u7684\u53d8\u6362\u624d\u80fd\u6700\u7ec8\u88ab\u753b\u5728\u5c4f\u5668\u4e0a \u3002\u4e00\u4e2a\u9876\u70b9\u6700\u5f00\u59cb\u662f\u5728\u6a21\u578b\u7a7a\u95f4\u4e2d\u5b9a\u4e49\u7684\uff0c\u6700\u540e\u5b83\u5c06\u4f1a\u53d8\u6362\u5230\u5c4f\u5e55\u7a7a\u95f4\u4e2d\uff0c\u5f97\u5230\u771f\u5c4f\u5e55\u50cf\u7d20\u5750\u6807\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6a21\u578b\u7a7a\u95f4<\/h3>\n\n\n\n<p><strong>\u6a21\u578b\u7a7a\u95f4 (model space)<\/strong>, \u5982\u5b83\u7684\u540d\u5b57\u6240\u6697\u793a\u7684\u90a3\u6837\uff0c\u662f\u548c\u67d0\u4e2a\u6a21\u578b\u6216\u8005\u8bf4\u662f\u5bf9\u8c61\u6709\u5173\u7684\u3002\u6709\u65f6\u6a21\u578b\u7a7a\u95f4\u4e5f\u88ab\u79f0\u4e3a \u5bf9\u8c61\u7a7a\u95f4 (1)bject space) \u5c40\u90e8\u7a7a\u95f4 (local space) \u3002<\/p>\n\n\n\n<p>\u5728\u6a21\u578b\u7a7a\u95f4\u4e2d\uff0c\u6211\u4eec\u7ecf\u5e38\u4f7f\u7528\u4e00\u4e9b\u65b9\u5411\u6982\u5ff5\uff0c\u4f8b\u5982\u201c\u524d (forward)\" \"\u540e(back )\" \"\u5de6 (left )\"\u201c\u53f3 (right)\" \"\u4e0a (up)\"\"\u4e0b(down )\" \u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u4e16\u754c\u7a7a\u95f4<\/h3>\n\n\n\n<p>\u4e16\u754c\u7a7a\u95f4 (world space) \u4e2a\u7279\u6b8a\u7684\u5750\u6807\u7cfb\uff0c\u56e0\u4e3a\u5b83\u5efa\u7acb\u4e86\u6211 \u6240\u5173 \u7684\u6700\u5927\u7684\u7a7a\u95f4\u3002<\/p>\n\n\n\n<p>\u4e16\u754c\u7a7a\u95f4\u53ef\u4ee5\u88ab\u7528\u4e8e\u63cf\u8ff0\u7edd\u5bf9\u4f4d\u7f6e\u3002<\/p>\n\n\n\n<p>\u5728Unity\u4e2d\uff0c\u4e16\u754c\u7a7a\u95f4\u540c\u6837\u4f7f\u7528\u4e86\u5de6\u624b\u5750\u6807\u7cfb\u3002\u4f46\u5b83\u7684x\u8f74\uff0cy\u8f74\uff0cz\u8f74\u662f\u56fa\u5b9a\u4e0d\u53d8\u7684\u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>\u9876\u70b9\u53d8\u6362\u7684\u7b2c\u4e00\u6b65\uff0c\u5c31\u662f\u5c06\u9876\u70b9\u5750\u6807\u4ece\u6a21\u578b\u7a7a\u95f4\u53d8\u6362\u5230\u4e16\u754c\u7a7a\u95f4\u4e2d \u8fd9\u4e2a\u53d8\u6362\u901a\u5e38\u53eb\u6a21\u578b\u53d8\u6362<\/strong>\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u89c2\u5bdf\u7a7a\u95f4<\/h3>\n\n\n\n<p><strong>\u89c2\u5bdf\u7a7a\u95f4 (view space) \u4e5f\u88ab\u79f0\u4e3a\u6444\u50cf\u673a\u7a7a\u95f4 (camera space) <\/strong>\u3002\u89c2\u5bdf\u7a7a\u95f4\u53ef\u4ee5\u8ba4\u4e3a\u662f\u6a21\u578b\u95f4\u7684\u4e00\u4e2a\u7279\u4f8b\uff0d\u5728\u6240\u6709\u7684\u6a21\u578b\u4e2d\u6709\u4e00\u4e2a\u975e\u5e38\u7279\u6b8a\u7684\u6a21\u578b\uff0c\u5373\u6444\u50cf\u673a\uff08\u867d\u7136\u901a\u5e38\u6765\u8bf4\u6444\u50cf\u673a\u672c\u8eab\u662f\u4e0d\u53ef\u89c1\u7684\uff09\uff0c\u5b83\u7684\u6a21\u578b\u7a7a\u95f4\u503c\u5f97\u6211\u4eec\u5355\u72ec\u62ff\u51fa\u6765\u8ba8\u8bba \uff0c\u4e5f\u5c31\u662f\u89c2\u5bdf\u7a7a\u95f4\u3002<\/p>\n\n\n\n<p>\u6444\u50cf\u673a\u51b3\u5b9a\u4e86\u6211\u4eec\u6e32\u67d3\u6e38\u620f\u6240\u4f7f\u7528\u7684\u89c6\u89d2\u3002<\/p>\n\n\n\n<p>Unity \u5728\u6a21\u578b\u7a7a\u95f4\u548c\u4e16\u754c\u7a7a\u95f4\u4e2d\u9009\u7528\u7684\u90fd\u662f\u5de6\u624b\u5750\u6807\u7cfb\uff0c\u800c\u5728\u89c2\u5bdf\u7a7a\u95f4\u4e2d\u4f7f\u7528\u7684\u662f\u53f3\u624b\u5750\u6807\u7cfb\u3002\u8fd9\u662f\u7b26\u5408 OpenGL \u4f20\u7edf\u7684\uff0c \u5728\u8fd9\u6837\u7684\u89c2\u5bdf\u7a7a\u95f4\u4e2d \uff0c\u6444\u50cf\u673a\u7684 \u6b63\u524d\u65b9\u6307\u5411\u7684\u662f-z \u65b9\u5411\u3002<\/p>\n\n\n\n<p>\u89c2\u5bdf\u7a7a\u95f4\u548c\u5c4f\u5e55\u7a7a\u95f4\u662f\u4e0d\u540c \u3002\u89c2\u5bdf\u7a7a\u95f4\u662f\u4e00\u4e2a\u4e09\u7ef4\u7a7a\u95f4 \uff0c\u800c\u5c4f\u5e55\u7a7a\u95f4\u662f\u4e00\u4e2a\u4e8c\u7ef4\u7a7a\u95f4\u3002\u4ece\u89c2\u5bdf\u7a7a\u95f4\u5230\u5c4f\u5e55\u7a7a\u95f4\u7684\u8f6c\u6362\u9700\u8981\u7ecf\u8fc7\u4e00\u4e2a\u64cd\u4f5c\uff0c\u90a3\u5c31<strong>\u6295\u5f71 (projection)<\/strong> \u3002<\/p>\n\n\n\n<p class=\"has-medium-font-size\"><strong>\u9876\u70b9\u53d8\u6362\u7684\u7b2c\u4e8c\u6b65 \uff0c\u5c31\u662f\u5c06\u9876\u70b9\u5750\u6807\u4ece\u4e16\u754c\u7a7a\u95f4\u53d8\u6362\u5230\u89c2\u5bdf\u7a7a\u95f4\u4e2d\u3002\u8fd9\u4e2a\u53d8\u6362\u901a\u5e38\u53eb\u505a\u89c2\u5bdf<br \/>\u53d8\u6362 (view transform)<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u88c1\u526a\u7a7a\u95f4<\/h3>\n\n\n\n<p>\u9879\u70b9\u63a5\u4e0b\u6765\u8981\u4ece\u89c2\u5bdf\u7a7a\u95f4\u8f6c\u6362\u5230\u88c1\u526a\u7a7a\u95f4 (clip space, \u4e5f\u88ab\u79f0\u4e3a\u9f50\u6b21\u88c1\u526a\u7a7a\u95f4\uff09 \u8fd9\u4e2a\u7528<br \/>\u4e8e\u53d8\u6362\u7684\u77e9\u9635\u53eb\u505a<strong>\u88c1\u526a\u77e9\u9635 (clip matrix)<\/strong>, \u4e5f\u88ab\u79f0\u4e3a<strong>\u6295\u5f71\u77e9\u9635 (projection matrix)<\/strong><\/p>\n\n\n\n<p>\u88c1\u526a\u7a7a\u95f4\u7684\u76ee\u6807\u662f\u80fd\u591f\u65b9\u4fbf\u5730\u5bf9\u6e32\u67d3\u56fe\u5143\u8fdb\u884c\u88c1\u526a \u5b8c\u5168\u4f4d\u5343\u8fd9\u5757\u7a7a\u95f4\u5185\u90e8\u7684\u56fe\u5143\u5c06\u4f1a\u88ab\u4fdd<br \/>\u7559\uff0c\u5b8c\u5168\u4f4d\u4e8e\u8fd9\u5757\u7a7a\u95f4\u5916\u90e8\u7684\u56fe\u5143\u5c06\u4f1a\u88ab\u5254\u9664\uff0c\u800c\u4e0e\u8fd9\u5757\u7a7a\u95f4\u8fb9\u754c\u76f8\u4ea4\u7684\u56fe\u5143\u5c31\u4f1a\u88ab\u88c1\u526a\u3002<\/p>\n\n\n\n<p><strong>\u89c6\u9525\u4f53(view frustum)<\/strong> \u51b3\u5b9a\u4e86\u88c1\u526a\u7a7a\u95f4\u3002\u89c6\u9525\u4f53\u6307\u7684\u662f\u7a7a\u95f4\u4e2d\u7684\u4e00\u5757\u533a\u57df\uff0c\u8fd9\u5757\u533a\u57df\u51b3\u5b9a\u4e86\u6444\u50cf\u673a\u53ef\u4ee5\u770b\u5230\u7684\u7a7a\u95f4\u3002\u89c6\u9525\u4f53\u7531\u516d\u4e2a\u5e73\u9762\u5305\u56f4\u800c\u6210\uff0c\u8fd9\u4e9b\u5e73\u9762\u4e5f\u88ab\u79f0\u4e3a\u88c1\u526a\u5e73\u9762 (clip planes) \u3002\u89c6\u9525\u4f53\u6709\u4e24\u79cd\u7c7b\u578b\uff0c\u8fd9\u6d89\u53ca\u4e24\u79cd\u6295\u5f71\u7c7b\u578b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6b63\u4ea4\u6295\u5f71 (orthographic projection)<\/li>\n\n\n\n<li>\u900f\u89c6\u6295\u5f71 (perspective projection)<\/li>\n<\/ul>\n\n\n\n<p>\u900f\u89c6\u6295\u5f71\u6a21\u62df\u4e86\u4eba\u773c\u770b\u4e16\u754c\u7684\u65b9\u5f0f\uff0c\u800c\u6b63\u4ea4\u6295\u5f71\u5219\u5b8c\u5168\u4fdd\u7559\u4e86\u7269\u4f53\u7684\u8ddd\u79bb\u548c\u89d2\u5ea6\u3002\u56e0\u6b64\uff0c\u5728\u8ffd\u6c42\u771f\u5b9e\u611f\u7684 \u6e38\u620f\u4e2d\u6211\u4eec\u5f80\u5f80\u4f1a\u4f7f\u7528\u900f\u89c6\u6295\u5f71\uff0c\u800c\u5728 \u6e38\u620f\u6216\u6e32\u67d3\u5c0f\u5730\u56fe\u7b49\u5176\u4ed6HUD \u5143\u7d20\u65f6\uff0c\u6211\u4eec\u4f1a\u4f7f\u7528\u6b63\u4ea4\u6295\u5f71\u3002<\/p>\n\n\n\n<p>\u5728\u89c6\u9525\u4f53\u7684 \u5757\u88c1\u526a\u5e73\u9762\u4e2d \u6709\u4e24\u5757\u88c1\u526a\u5e73\u9762\u6bd4\u8f83\u7279\u6b8a\uff0c\u5b83\u4eec\u5206\u522b\u88ab\u79f0\u4e3a\u8fd1\u526a\u88c1\u5e73\u9762(near clipplane) \u8fdc\u526a\u88c1\u5e73\u9762 (far clip plane) \u3002<strong>\u5b83\u4eec\u51b3\u5b9a\u4e86\u6444\u50cf\u673a\u53ef\u4ee5\u770b\u5230\u7684\u6df1\u5ea6\u8303\u56f4\u3002<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/courtship.top\/wp-content\/uploads\/2022\/11\/\u56fe\u7247-19.png\" alt=\"\" class=\"wp-image-1904\" width=\"559\" height=\"233\"\/><\/figure>\n<\/div>\n\n\n<p>\u6709\u4e00\u79cd\u66f4\u52a0\u901a\u7528 \u3001\u65b9\u4fbf\u548c\u6574\u6d01\u7684\u65b9\u5f0f\u6765\u8fdb\u884c\u88c1\u526a\u7684\u5de5\u4f5c\uff0c\u8fd9\u79cd\u65b9\u5f0f\u5c31\u662f\u901a\u8fc7\u4e00\u4e2a<strong>\u6295\u5f71\u77e9\u9635<\/strong>\u628a\u9876\u70b9\u8f6c\u6362\u5230\u4e00\u4e2a\u88c1\u526a\u7a7a\u95f4\u4e2d\u3002\u6295\u5f71\u77e9\u9635\u6709\u4e24\u4e2a\u76ee\u7684\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u4e3a\u6295\u5f71\u505a\u51c6\u5907\u3002\u4f46\u662f\u5b83\u5e76\u6ca1\u6709\u8fdb\u884c\u771f\u6b63\u7684\u6295\u5f71\u5de5\u4f5c\uff0c\u800c\u662f\u5728\u4e3a\u6295\u5f71\u505a\u51c6\u5907 \u3002\u771f\u6b63 \u7684\u6295\u5f71\u53d1\u751f\u5728\u540e\u9762\u7684\u9f50\u6b21\u9664\u6cd5(homogeneous division) \u8fc7\u7a0b\u4e2d \u800c\u7ecf\u8fc7\u6295\u5f71\u77e9\u9635\u7684\u53d8\u6362\u540e\uff0c\u9876\u70b9\u7684w\u5206\u91cf\u5c06\u4f1a\u5177\u6709\u7279\u6b8a\u7684\u610f\u4e49\u3002<\/li>\n\n\n\n<li>\u5176\u6b21\u662f\u5bf9x y z\u5206\u91cf\u8fdb\u884c\u7f29\u653e<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">\u900f\u89c6\u6295\u5f71<\/h4>\n\n\n\n<p>\u89c6\u9525\u4f53\u7684\u610f\u4e49\u5728\u4e8e\u5b9a\u4e49\u4e86\u573a\u666f\u4e2d\u7684\u4e00\u5757\u4e09\u7ef4\u7a7a\u95f4\u3002\u6240\u6709\u4f4d\u4e8e\u8fd9\u5757\u7a7a\u95f4\u5185\u7684\u7269\u4f53\u5c06\u4f1a\u88ab\u6e32\u67d3\uff0c\u5426\u5219\u5c31\u4f1a\u88ab\u5254\u9664\u6216\u88c1\u526a\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u6295\u5f71\u77e9\u9635\u672c\u8d28\u5c31\u662f\u5bf9 \u5206\u91cf\u8fdb\u884c\u4e86\u4e0d\u540c\u7a0b\u5ea6\u7684\u7f29\u653e\uff08\u5f53\u7136z\u5206\u91cf\u8fd8\u505a\u4e86\u4e00\u4e2a\u5e73\u79fb\uff09\uff0c\u7f29\u653e\u7684\u76ee\u7684\u662f\u4e3a\u4e86\u65b9\u4fbf\u88c1\u526a\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u6b63\u4ea4\u6295\u5f71<\/h4>\n\n\n\n<p>\u6b63\u4ea4\u6295\u5f71\u7684\u89c6\u9525\u4f53\u662f\u4e00\u4e2a\u957f\u65b9\u4f53 \u56e0\u6b64\u8ba1\u7b97\u4e0a\u76f8\u6bd4\u900f\u89c6\u6295\u5f71\u6765\u8bf4\u66f4\u52a0\u7b80\u5355\u3002<\/p>\n\n\n\n<p>\u548c\u900f\u89c6\u6295\u5f71\u4e0d\u540c\u7684\u662f\uff0c\u4f7f\u7528\u6b63\u4ea4\u6295\u5f71\u7684\u6295\u5f71\u77e9\u9635\u5bf9\u9876\u70b9\u8fdb\u884c\u53d8\u6362\u540e\uff0c\u5176w\u5206\u91cf\u4ecd\u7136\u4e3a1\u3002\u672c\u8d28\u662f\u56e0\u4e3a\u6295\u5f71\u77e9\u9635\u6700\u540e\u4e00\u884c\u7684\u4e0d\u540c\uff0c\u900f\u89c6\u6295\u5f71\u7684\u6295\u5f71\u77e9\u9635\u7684\u6700\u540e\u4e00\u884c\u662f[0 0~1 0],\u6b63\u4ea4\u6295\u5f71\u7684\u6295\u5f71\u77e9\u9635\u7684\u6700\u540e \u884c\u662f[0 0 0 1] \u3002\u8fd9\u6837\u7684\u9009\u62e9\u662f\u6709\u539f\u56e0\u7684\uff0c\u662f\u4e3a\u4e86\u4e3a\u9f50\u6b21\u9664\u6cd5\u505a\u51c6\u5907\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5c4f\u5e55\u7a7a\u95f4<\/h3>\n\n\n\n<p>\u5f53\u5b8c\u6210\u4e86\u6240\u6709\u7684\u88c1\u526a\u5de5\u4f5c\u540e\uff0c\u5c31\u9700\u8981\u8fdb\u884c\u771f\u6b63\u7684\u6295\u5f71\u4e86\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u9700\u8981\u628a\u89c6\u9525\u4f53\u6295\u5f71\u5230\u5c4f\u5e55\u7a7a\u95f4(screen space) \u4e2d\u3002\u7ecf\u8fc7\u8fd9\u4e00\u6b65\u53d8\u6362\uff0c\u6211\u4eec\u4f1a\u5f97\u5230\u771f\u6b63\u7684\u50cf\u7d20\u4f4d\u7f6e\uff0c\u800c\u4e0d\u662f\u865a\u62df\u7684\u4e09\u7ef4\u5750\u6807\u3002<\/p>\n\n\n\n<p>\u5c4f\u5e55\u7a7a\u95f4\u662f\u4e00\u4e2a\u4e8c\u7ef4\u7a7a\u95f4\uff0c\u56e0\u6b64\uff0c\u6211\u4eec\u5fc5\u987b\u628a\u9876\u70b9\u4ece\u88c1\u526a\u7a7a\u95f4\u6295\u5f71\u5230\u5c4f\u5e55\u7a7a\u95f4\u4e2d\uff0c\u6765\u751f\u6210\u5bf9<br \/>\u5e94\u768420\u5750\u6807\u3002\u8fd9\u4e2a\u8fc7\u7a0b\u53ef\u4ee5\u7406\u89e3\u6210\u6709\u4e24\u4e2a\u6b65\u9aa4\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u9996\u5148\uff0c\u6211\u4eec\u9700\u8981\u8fdb\u884c\u6807\u51c6\u9f50\u6b21\u9664\u6cd5(homogeneous division), \u4e5f\u88ab\u79f0\u4e3a\u900f\u89c6\u9664\u6cd5(perspective division)\u3002\u7ecf\u8fc7\u8fd9\u4e00\u6b65\uff0c\u6211\u4eec\u53ef\u4ee5\u628a\u5750\u6807\u4ece\u9f50\u6b21\u683d\u526a\u5750\u6807\u7a7a\u95f4\u8f6c\u6362\u5230NDC\u4e2d\u3002\n<ul class=\"wp-block-list\">\n<li>\u6309\u7167OpenGL\u7684\u4f20\u7edf\uff0c\u8fd9\u4e2a\u7acb\u65b9\u4f53\u7684x\u3001 y\u3001 z\u5206\u5740\u7684\u8303\u56f4\u90fd\u662f[-1, l]\u3002\u4f46 \u5728DirectX\u8fd9\u6837\u7684API\u4e2d\uff0cz\u5206\u5669\u7684\u8303\u56f4\u4f1a\u662f[0,1]\u3002\u800cUnity\u9009\u62e9\u4e86 OpenGL\u8fd9\u6837\u7684\u9f50\u6b21\u88c1\u526a\u7a7a\u95f4\u3002<\/li>\n\n\n\n<li>\u800c\u5bf9\u4e8e\u6b63\u4ea4\u6295\u5f71\u6765\u8bf4\uff0c\u5b83\u7684\u88c1\u526a\u7a7a\u95f4\u5b9e\u9645\u5df2\u7ecf\u662f\u4e00\u4e2a\u7acb\u65b9\u4f53\u4e86\uff0c\u800c\u4e14\u7531\u4e8e\u7ecf\u8fc7\u6b63\u4ea4\u6295\u5f71\u77e9\u9635\u53d8\u6362\u540e\u7684\u9876\u70b9\u7684w\u5206\u91cf\u662f 1, \u56e0\u6b64\u9f50\u6b21\u9664\u6cd5\u5e76\u4e0d\u4f1a\u5bf9\u9876\u70b9\u7684x y z\u5750\u6807\u4ea7\u751f\u5f71\u54cd<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7ecf\u8fc7\u9f50\u6b21\u9664\u6cd5\u540e\uff0c\u900f\u89c6\u6295\u5f71\u548c\u6b63\u4ea4\u6295\u5f71\u7684\u89c6\u9525\u4f53\u90fd\u53d8\u6362\u5230\u4e00\u4e2a\u76f8\u540c\u7684\u7acb\u65b9\u4f53\u5185\u3002\u73b0\u5728\uff0c\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u53d8\u6362\u540e\u7684 \u5750\u6807\u6765\u6620\u5c04\u8f93\u51fa\u7a97\u53e3\u7684\u5bf9\u5e94\u50cf\u7d20\u5750\u6807\u3002<\/li>\n<\/ol>\n\n\n\n<p><strong>\u9876\u70b9\u7740\u8272\u5668\u7684\u6700\u57fa\u672c\u7684\u4efb\u52a1\u5c31\u662f\u628a\u9876\u70b9\u5750\u6807\u4ece\u6a21\u578b\u7a7a\u95f4\u8f6c\u6362\u5230\u88c1\u526a\u7a7a\u95f4\u4e2d\u3002<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u6cd5\u7ebf\u53d8\u6362<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">\u6cd5\u7ebf<\/h3>\n\n\n\n<p>\u6cd5\u7ebf\u53d8\u6362\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u53d8\u6362<\/p>\n\n\n\n<p><strong>\u6cd5\u7ebf (normal)<\/strong>, \u4e5f\u88ab\u79f0\u4e3a<strong>\u6cd5\u77e2\u91cf (normal vector)<\/strong> \u3002<\/p>\n\n\n\n<p>\u6cd5\u7ebf\u662f\u9700\u8981\u6211\u4eec\u7279\u6b8a\u5904\u7406\u7684\u4e00\u79cd\u65b9\u5411\u77e2\u91cf\u3002\u5728\u6e38\u620f\u4e2d\uff0c\u6a21\u578b\u7684\u4e00\u4e2a\u9876\u70b9\u5f80\u5f80\u4f1a\u643a\u5e26\u989d\u5916\u7684\u4fe1\u606f\uff0c\u800c\u9876\u70b9\u6cd5\u7ebf\u5c31\u662f\u5176\u4e2d \u79cd\u4fe1\u606f\u3002\u5f53\u6211\u4eec\u53d8\u6362\u4e00\u4e2a\u6a21\u578b\u7684\u65f6\u5019\uff0c\u4e0d\u4ec5\u9700\u8981\u53d8\u6362\u5b83\u7684\u9876\u70b9\uff0c\u8fd8\u9700\u8981\u53d8\u6362\u9876\u70b9\u6cd5\u7ebf\uff0c\u4ee5\u4fbf\u5728\u540e\u7eed\u5904\u7406\uff08\u5982\u7247\u5143\u7740\u8272\u5668\uff09\u4e2d\u8ba1\u7b97\u5149\u7167\u7b49\u3002<\/p>\n\n\n\n<p>\u4e00\u822c\u6765\u8bf4\uff0c\u70b9\u548c\u7edd\u5927\u90e8\u5206\u65b9\u5411\u77e2\u91cf\u90fd\u53ef\u4ee5\u4f7f\u7528\u540c\u4e00\u4e2a 4X4 3X3 \u7684\u53d8\u6362\u77e9\u9635 MA \u628a\u5176\u4ece\u5750\u6807\u7a7a\u95f4 \u53d8\u6362\u5230\u5750\u6807\u7a7a\u95f4 \u3002<strong>\u4f46\u5728\u53d8\u6362\u6cd5\u7ebf\u7684\u65f6\u5019\uff0c\u5982\u679c\u4f7f\u7528\u540c\u4e00\u4e2a\u53d8\u6362\u77e9\u9635\uff0c\u53ef\u80fd\u5c31\u65e0\u6cd5\u786e\u4fdd\u7ef4\u6301\u6cd5\u7ebf\u7684\u5782\u76f4\u6027\u3002<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u5207\u7ebf<\/h3>\n\n\n\n<p><strong>\u5207\u7ebf(tangent)<\/strong>, \u4e5f\u88ab\u79f0\u4e3a<strong>\u5207\u77e2\u91cf (ta ngent vector) <\/strong>\u3002\u4e0e\u6cd5\u7ebf\u7c7b\u4f3c\uff0c\u5207\u7ebf\u5f80\u5f80\u4e5f\u662f\u6a21\u578b\u9876\u70b9\u643a\u5e26\u7684\u4e00\u79cd\u4fe1<br \/>\u606f\u3002\u5b83\u901a\u5e38\u4e0e\u7eb9\u7406\u7a7a\u95f4\u5bf9\u9f50\uff0c\u800c\u4e14\u4e0e\u6cd5\u7ebf\u65b9\u5411\u5782\u76f4\u3002\u7531\u4e8e\u5207\u7ebf\u662f\u7531\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u7684\u5dee\u503c\u8ba1\u7b97\u5f97\u5230\u7684\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u7528\u4e8e\u53d8\u6362\u9876\u70b9\u7684\u53d8\u6362\u77e9\u9635\u6765\u53d8\u6362\u5207\u7ebf\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/courtship.top\/wp-content\/uploads\/2022\/11\/\u56fe\u7247-20.png\" alt=\"\" class=\"wp-image-1943\" width=\"450\" 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