{"id":91,"date":"2007-10-22T17:31:36","date_gmt":"2007-10-22T09:31:36","guid":{"rendered":"http:\/\/www.cgdev.net\/blog\/?p=91"},"modified":"2013-07-02T17:43:46","modified_gmt":"2013-07-02T09:43:46","slug":"tangent-space-%e5%88%87%e7%a9%ba%e9%97%b4","status":"publish","type":"post","link":"https:\/\/www.cgdev.net\/blog\/91.html","title":{"rendered":"Tangent Space \u5207\u7a7a\u95f4"},"content":{"rendered":"<p>\u4e00: \u6570\u5b66\u4e2d\u7684n\u7ef4\u6b27\u6c0f\u7a7a\u95f4\u7684\u5207\u7a7a\u95f4\u5b9a\u4e49\u4e3a\uff1a\u5982\u679ck\u7ef4\u66f2\u9762S\u5728\u70b9x0\u2208S\u7684\u90bb\u57df\u5185\u80fd\u7528k\u4e2a\u72ec\u7acb\u53c2\u6570t1\uff0ct2\uff0c &#8230; \uff0c tk\u7ed9\u51fa\u7684\u5149\u6ed1\u6620\u5c04t\u2192x\u5373(t1\uff0ct2\uff0c&#8230;\uff0ctk)\u2192(x1\uff0cx2\uff0c&#8230;\uff0cxn)\u7ed9\u51fa\uff0cx0=x(0)\u4e14\u77e9\u9635x'(0)\u7684\u79e9\u4e3ak\uff0c\u90a3\u4e48\u79f0\u5728n\u7ef4\u6b27 \u6c0f\u7a7a\u95f4\u4e2d\u7528\u77e9\u9635\u5f62\u5f0f\u7684\u53c2\u6570\u65b9\u7a0bx-x0=x'(0)t\u7ed9\u51fa\u7684k\u7ef4\u5e73\u9762\u4e3a\u66f2\u9762S\u5728\u70b9x0\u2208S\u7684\u5207\u7a7a\u95f4\u6216\u8005\u5207\u5e73\u9762\u3002<\/p>\n<p>3\u7ef4\u6b27\u6c0f\u7a7a\u95f4\u4e2d\u66f2\u9762\u662f\u4e2a2\u7ef4\u66f2\u9762\uff0c\u66f2\u9762\u4e2d\u67d0\u70b9\u7684\u5207\u7a7a\u95f4\u5c31\u662f\u8be5\u4e0e\u70b9\u7684\u6cd5\u5411\u91cf\u5782\u76f4\u90a3\u4e2a2\u7ef4\u5e73\u9762(\u4e00\u4e2a2\u7ef4\u5411\u91cf\u7a7a\u95f4).<\/p>\n<p>\u4e8c. \u56fe\u5f62\u5b66\u4e2d\u7684\u8ba1\u7b97\u7684Tangent Space \u548c\u4e0a\u9762\u4e00\u81f4\uff0c\u4f46\u4e00\u822c\u8fd8\u8981\u8ba1\u7b97\u51faN, \u6784\u9020\u4e00\u4e2aTBN\u77e9\u9635\u3002T\u5c31\u662fTangent\uff0cN\u5373Normal\uff0cB\u5373 Bitangent\u3002\u56fd\u5916\u5f88\u591a\u8d44\u6599\u5305\u62ecDirectX\u90fd\u79f0B\u4e3aBinormal, \u5b9e\u9645\u4e0aBinormal\u7684\u547d\u540d\u6765\u81ea\u4e8e\u66f2\u7ebf\u8bba\uff0c\u800c\u8fd9\u513f\u6211\u4eec\u8003\u5bdf\u7684\u662f\u66f2\u9762\uff0c\u6240\u4ee5\u79f0\u4e3aBitangent\u66f4\u51c6\u786e\u4e9b\u3002\u4e3a\u4e86\u8fd1\u4f3c\u8ba1\u7b97TBN\u7a7a\u95f4\u7684\u57fa\u5411\u91cf\uff0c\u53ef\u4ee5\u5f15\u5165\u9762\u5207\u7a7a\u95f4\u7684\u6982\u5ff5\uff0c\u5b83\u5c31\u662f\u9876\u70b9\u6240\u5173\u8054\u7684face\u6240\u5728\u5e73\u9762\u51b3\u5b9a\u7684 \u4e00\u4e2a\u4e8c\u7ef4\u5b50\u7a7a\u95f4\u3002\u5411\u91cfT,B\u53ef\u4ee5\u7528\u9762\u5207\u7a7a\u95f4\u57fa\u7684\u52a0\u548c\u6765\u8fd1\u4f3c\u8868\u8fbe\u51fa\u6765\u3002<\/p>\n<p>\u4e09. \u5f53\u4f7f\u7528\u6cd5\u7ebf\u8d34\u56fe\u7b49\u6280\u672f\u65f6, \u5e94\u5c06\u5f97\u5230\u7684\u9876\u70b9\u7684T\u503c\u8c03\u6574\u4e00\u4e0b\uff0c\u4f7f\u4e4b\u548c\u6cd5\u7ebf\u56fe\u4e2d\u7684\u6cd5\u7ebfN\u5782\u76f4\uff0c\u7136\u540e\u518d\u7528\u53c9\u79ef\u5f97\u5230B \u3002\u65b0\u7684[T, B]\u4e0e\u65b0\u9876\u70b9\u6cd5\u7ebf\u6240\u8868\u793a\u7684\u4e00\u7ef4\u5b50\u7a7a\u95f4\u4f5c\u76f4\u548c\u5c31\u6784\u6210\u4e86\u6211\u4eec\u6700\u7ec8\u6240\u9700\u8981\u7684\u53d8\u6362\u9635 [T, B, N]\uff0c\u7136\u540e\u5728vertex shader\u4e2d\u9010\u9876\u70b9\u5c06\u5149\u5411\u91cfL\u53d8\u6362\u5230\u8fd9\u4e2a\u7a7a\u95f4\u6210L&#8217;\uff0c\u7136\u540e\u5728pixel shader\u4e2d\u7528\u786c\u4ef6\u63d2\u503c\u5f97\u5230\u7684\u5149\u5411\u91cf\u4e0e\u6cd5\u7ebf\u4f5c\u70b9\u79ef\u5c31\u5f97\u5230\u5149\u5f3a\u5ea6\u4e86\u3002<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e00: \u6570\u5b66\u4e2d\u7684n\u7ef4\u6b27\u6c0f\u7a7a\u95f4\u7684\u5207\u7a7a\u95f4\u5b9a\u4e49\u4e3a\uff1a\u5982\u679ck\u7ef4\u66f2\u9762S\u5728\u70b9x0\u2208S\u7684\u90bb\u57df\u5185\u80fd\u7528k\u4e2a\u72ec\u7acb\u53c2\u6570t1\uff0ct2\uff0c &#8230; \uff0c tk\u7ed9\u51fa\u7684\u5149\u6ed1\u6620\u5c04t\u2192x\u5373(t1\uff0ct2\uff0c&#8230;\uff0ctk)\u2192(x1\uff0cx2\uff0c&#8230;\uff0cxn)\u7ed9\u51fa\uff0cx0=x(0)\u4e14\u77e9\u9635x'(0)\u7684\u79e9\u4e3ak\uff0c\u90a3\u4e48\u79f0\u5728n\u7ef4\u6b27 \u6c0f\u7a7a\u95f4\u4e2d\u7528\u77e9\u9635\u5f62\u5f0f\u7684\u53c2\u6570\u65b9\u7a0bx-x0=x'(0)t\u7ed9\u51fa\u7684k\u7ef4\u5e73\u9762\u4e3a\u66f2\u9762S\u5728\u70b9x0\u2208S\u7684\u5207\u7a7a\u95f4\u6216\u8005\u5207\u5e73\u9762\u3002 3\u7ef4\u6b27\u6c0f\u7a7a\u95f4\u4e2d\u66f2\u9762\u662f\u4e2a2\u7ef4\u66f2\u9762\uff0c\u66f2\u9762\u4e2d\u67d0\u70b9\u7684\u5207\u7a7a\u95f4\u5c31\u662f\u8be5\u4e0e\u70b9\u7684\u6cd5\u5411\u91cf\u5782\u76f4\u90a3\u4e2a2\u7ef4\u5e73\u9762(\u4e00\u4e2a2\u7ef4\u5411\u91cf\u7a7a\u95f4). \u4e8c. \u56fe\u5f62\u5b66\u4e2d\u7684\u8ba1\u7b97\u7684Tangent Space \u548c\u4e0a\u9762\u4e00\u81f4\uff0c\u4f46\u4e00\u822c\u8fd8\u8981\u8ba1\u7b97\u51faN, \u6784\u9020\u4e00\u4e2aTBN\u77e9\u9635\u3002T\u5c31\u662fTangent\uff0cN\u5373Normal\uff0cB\u5373 Bitangent\u3002\u56fd\u5916\u5f88\u591a\u8d44\u6599\u5305\u62ecDirectX\u90fd\u79f0B\u4e3aBinormal, \u5b9e\u9645\u4e0aBinormal\u7684\u547d\u540d\u6765\u81ea\u4e8e\u66f2\u7ebf\u8bba\uff0c\u800c\u8fd9\u513f\u6211\u4eec\u8003\u5bdf\u7684\u662f\u66f2\u9762\uff0c\u6240\u4ee5\u79f0\u4e3aBitangent\u66f4\u51c6\u786e\u4e9b\u3002\u4e3a\u4e86\u8fd1\u4f3c\u8ba1\u7b97TBN\u7a7a\u95f4\u7684\u57fa\u5411\u91cf\uff0c\u53ef\u4ee5\u5f15\u5165\u9762\u5207\u7a7a\u95f4\u7684\u6982\u5ff5\uff0c\u5b83\u5c31\u662f\u9876\u70b9\u6240\u5173\u8054\u7684face\u6240\u5728\u5e73\u9762\u51b3\u5b9a\u7684 \u4e00\u4e2a\u4e8c\u7ef4\u5b50\u7a7a\u95f4\u3002\u5411\u91cfT,B\u53ef\u4ee5\u7528\u9762\u5207\u7a7a\u95f4\u57fa\u7684\u52a0\u548c\u6765\u8fd1\u4f3c\u8868\u8fbe\u51fa\u6765\u3002 \u4e09. \u5f53\u4f7f\u7528\u6cd5\u7ebf\u8d34\u56fe\u7b49\u6280\u672f\u65f6, \u5e94\u5c06\u5f97\u5230\u7684\u9876\u70b9\u7684T\u503c\u8c03\u6574\u4e00\u4e0b\uff0c\u4f7f\u4e4b\u548c\u6cd5\u7ebf\u56fe\u4e2d\u7684\u6cd5\u7ebfN\u5782\u76f4\uff0c\u7136\u540e\u518d\u7528\u53c9\u79ef\u5f97\u5230B \u3002\u65b0\u7684[T, B]\u4e0e\u65b0\u9876\u70b9\u6cd5\u7ebf\u6240\u8868\u793a\u7684\u4e00\u7ef4\u5b50\u7a7a\u95f4\u4f5c\u76f4\u548c\u5c31\u6784\u6210\u4e86\u6211\u4eec\u6700\u7ec8\u6240\u9700\u8981\u7684\u53d8\u6362\u9635 [T, B, N]\uff0c\u7136\u540e\u5728vertex shader\u4e2d\u9010\u9876\u70b9\u5c06\u5149\u5411\u91cfL\u53d8\u6362\u5230\u8fd9\u4e2a\u7a7a\u95f4\u6210L&#8217;\uff0c\u7136\u540e\u5728pixel shader\u4e2d\u7528\u786c\u4ef6\u63d2\u503c\u5f97\u5230\u7684\u5149\u5411\u91cf\u4e0e\u6cd5\u7ebf\u4f5c\u70b9\u79ef\u5c31\u5f97\u5230\u5149\u5f3a\u5ea6\u4e86\u3002 &nbsp;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[15,4],"class_list":["post-91","post","type-post","status-publish","format-standard","hentry","category-graphics","tag-effect","tag-program"],"_links":{"self":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/posts\/91","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/comments?post=91"}],"version-history":[{"count":0,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/posts\/91\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/media?parent=91"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/categories?post=91"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cgdev.net\/blog\/wp-json\/wp\/v2\/tags?post=91"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}