{"id":2358,"date":"2024-05-10T08:24:29","date_gmt":"2024-05-10T00:24:29","guid":{"rendered":"https:\/\/courtship.top\/?p=2358"},"modified":"2024-08-28T10:31:28","modified_gmt":"2024-08-28T02:31:28","slug":"%e6%b8%b8%e6%88%8f%e6%95%b0%e5%ad%a6%e4%b8%93%e9%a1%b9%e6%95%b4%e7%90%86","status":"publish","type":"post","link":"https:\/\/courtship.top\/index.php\/2024\/05\/10\/%e6%b8%b8%e6%88%8f%e6%95%b0%e5%ad%a6%e4%b8%93%e9%a1%b9%e6%95%b4%e7%90%86\/","title":{"rendered":"\u6e38\u620f\u6570\u5b66\u4e13\u9879\u6574\u7406"},"content":{"rendered":"\n

\u6570\u5b66\u6982\u5ff5<\/h2>\n\n\n\n

\u70b9\u4e58 Dot Product<\/h3>\n\n\n\n

\u53c8\u79f0\"\u70b9\u79ef\",\"\u6570\u91cf\u79ef\u201d,\"\u5185\u79ef\"\uff0ca*b = |a||b|Cos(\u03b8)<\/strong><\/p>\n\n\n

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

\u51e0\u4f55\u610f\u4e49\uff1a\u662f\u4e00\u6761\u8fb9\u5411\u53e6\u4e00\u6761\u8fb9\u7684\u6295\u5f71\u4e58\u4ee5\u53e6\u4e00\u6761\u8fb9\u7684\u957f\u5ea6.<\/p>\n\n\n\n

v1<\/strong>\u548cv2<\/strong>\u5411\u91cf\u7684\u70b9\u4e58\u8fd0\u7b97\uff1a<\/p>\n\n\n\n

    \n
  • \u76f8\u5e94\u5143\u7d20\u7684\u4e58\u79ef\u7684\u548c\uff1av1( x1, y1\uff0cz1) * v2(x2, y2,z2) = x1*x2 + y1*y2+z1*z2<\/strong>;<\/li>\n\n\n\n
  • \u5176\u7ed3\u679c\u4e0d\u662f\u4e00\u4e2a\u5411\u91cf\uff0c\u800c\u662f\u6807\u91cf<\/li>\n<\/ul>\n\n\n\n
      \n
    1. \u6839\u636e\u70b9\u4e58\u8ba1\u7b97\u4e24\u4e2a\u5411\u91cf\u7684\u5939\u89d2\u3002= arccos(a\u00b7b \/ (|a|\u00b7|b|))<\/li>\n\n\n\n
    2. \u6839\u636e\u70b9\u4e58\u7684\u6b63\u8d1f\u503c\uff0c\u5f97\u5230\u5939\u89d2\u5927\u5c0f\u8303\u56f4\uff0c>0\uff0c\u5219\u5939\u89d2\uff080,90\uff09<0,\u5219\u5939\u89d2\uff0890,180\uff09\uff0c\u53ef\u4ee5\u5229\u7528\u8fd9\u70b9\u5224\u65ad\u4e00\u4e2a\u591a\u8fb9\u5f62\u662f\u9762\u5411\u6444\u50cf\u673a\u8fd8\u662f\u80cc\u5411\u6444\u50cf\u673a\u3002<\/li>\n\n\n\n
    3. \u6839\u636e\u70b9\u4e58\u7684\u5927\u5c0f\uff0c\u5f97\u5230\u5411\u91cf\u7684\u6295\u5f71\u957f\u5ea6\uff0c\u53cd\u5e94\u4e86\u5411\u91cf\u7684\u957f\u5ea6\u5173\u7cfb<\/strong>\u3002<\/li>\n\n\n\n
    4. \u5411\u91cf\u7684\u70b9\u79ef\u4e0e\u5b83\u4eec\u5939\u89d2\u7684\u4f59\u5f26\u6210\u6b63\u6bd4\uff0c\u56e0\u6b64\u5728\u805a\u5149\u706f\u7684\u6548\u679c\u8ba1\u7b97\u4e2d\uff0c\u53ef\u4ee5\u6839\u636e\u70b9\u79ef\u6765\u5f97\u5230\u5149\u7167\u6548\u679c\uff0c\u5982\u679c\u70b9\u79ef\u8d8a\u5927\uff0c\u8bf4\u660e\u5939\u89d2\u8d8a\u5c0f\uff0c\u5219\u7269\u7406\u79bb\u5149\u7167\u7684\u8f74\u7ebf\u8d8a\u8fd1\uff0c\u5149\u7167\u8d8a\u5f3a\u3002<\/li>\n\n\n\n
    5. \u7269\u7406\u4e2d\uff0c\u70b9\u79ef\u53ef\u4ee5\u7528\u6765\u8ba1\u7b97\u5408\u529b\u548c\u529f\u3002\u82e5b\u4e3a\u5355\u4f4d\u77e2\u91cf\uff0c\u5219\u70b9\u79ef\u5373\u4e3aa\u5728\u65b9\u5411b\u7684\u6295\u5f71\uff0c\u5373\u7ed9\u51fa\u4e86\u529b\u5728\u8fd9\u4e2a\u65b9\u5411\u4e0a\u7684\u5206\u89e3\u3002\u529f\u5373\u662f\u529b\u548c\u4f4d\u79fb\u7684\u70b9\u79ef\u3002<\/li>\n\n\n\n
    6. \u8ba1\u7b97\u673a\u56fe\u5f62\u5b66\u5e38\u7528\u6765\u8fdb\u884c\u65b9\u5411\u6027\u5224\u65ad\uff0c\u5982\u4e24\u77e2\u91cf\u70b9\u79ef\u5927\u4e8e0\uff0c\u5219\u5b83\u4eec\u7684\u65b9\u5411\u671d\u5411\u76f8\u8fd1\uff1b\u5982\u679c\u5c0f\u4e8e0\uff0c\u5219\u65b9\u5411\u76f8\u53cd\u3002\u77e2\u91cf\u5185\u79ef\u662f\u4eba\u5de5\u667a\u80fd\u9886\u57df\u4e2d\u7684\u795e\u7ecf\u7f51\u7edc\u6280\u672f\u7684\u6570\u5b66\u57fa\u7840\u4e4b\u4e00\uff0c\u6b64\u65b9\u6cd5\u8fd8\u88ab\u7528\u4e8e\u52a8\u753b\u6e32\u67d3\uff08Animation-Rendering\uff09\u3002<\/li>\n<\/ol>\n\n\n\n

      \u53c9\u4e58 Cross Product<\/h3>\n\n\n\n

      \u53c8\u79f0\"\u53c9\u79ef\",\"\u5411\u91cf\u79ef\",\"\u5916\u79ef\"\u3002<\/p>\n\n\n\n

      v1<\/strong>\u548cv2<\/strong>\u5411\u91cf\u7684\u53c9\u4e58\u8fd0\u7b97\uff1a\u76f8\u5e94\u5143\u7d20\u7684\u4e58\u79ef\u7684\u548c\uff1av1( x1, y1\uff0cz1) x v2(x2, y2, z2) = (y1*z2 - y2*z1<\/strong>)i+(x2*z1 - x1*z2<\/strong>)j+(x1*y2-x2*y1)k<\/strong>;<\/p>\n\n\n\n

        \n
      • c\u22a5a\uff0cc\u22a5b<\/strong>\uff0c\u5373\u5411\u91cfc<\/strong>\u4e0e\u5411\u91cfa\uff0cb<\/strong>\u6240\u5728\u5e73\u9762\u5782\u76f4<\/li>\n\n\n\n
      • \u6a21\u957f|c| = |a||b| sin<a,b><\/strong><\/li>\n\n\n\n
      • (\u6570\u5b66\u4e0a)\u6ee1\u8db3\u53f3\u624b\u6cd5\u5219<\/strong>, a x b = -b x a<\/strong>\uff0c\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u53c9\u4e58\u7684\u6b63\u8d1f\u503c\u6765\u5224\u65ada\uff0cb\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u5373b\u662f\u5904\u4e8ea\u7684\u987a\u65f6\u9488\u8fd8\u662f\u9006\u65f6\u9488\u65b9\u5411\u3002\u53c9\u4e58\u7684\u53f3\u624b\u5b9a\u5219<\/strong>\u662f\u7528\u6765\u786e\u5b9a\u53c9\u4e58\u79ef\u7684\u65b9\u5411\u7684\u3002<\/li>\n<\/ul>\n\n\n\n
          \n
        1. \u6839\u636e\u53c9\u4e58\u5f97\u5230a\uff0cb\u5411\u91cf\u7684\u76f8\u5bf9\u4f4d\u7f6e\uff0c\u548c\u987a\u65f6\u9488\u6216\u9006\u65f6\u9488\u65b9\u4f4d\u3002<\/li>\n\n\n\n
        2. \u7b80\u5355\u7684\u8bf4: \u70b9\u4e58\u5224\u65ad\u89d2\u5ea6\uff0c\u53c9\u4e58\u5224\u65ad\u65b9\u5411\u3002
          \u5f62\u8c61\u7684\u8bf4: \u5f53\u4e00\u4e2a\u654c\u4eba\u5728\u4f60\u8eab\u540e\u7684\u65f6\u5019\uff0c\u53c9\u4e58\u53ef\u4ee5\u5224\u65ad\u4f60\u662f\u5f80\u5de6\u8f6c\u8fd8\u662f\u5f80\u53f3\u8f6c\u66f4\u597d\u7684\u8f6c\u5411\u654c\u4eba\uff0c\u70b9\u4e58\u5f97\u5230\u4f60\u5f53\u524d\u7684\u9762\u671d\u5411\u7684\u65b9\u5411\u548c\u4f60\u5230\u654c\u4eba\u7684\u65b9\u5411\u7684\u6240\u6210\u7684\u89d2\u5ea6\u5927\u5c0f\u3002<\/li>\n\n\n\n
        3. \u5f97\u5230a\uff0cb\u5939\u89d2\u7684\u6b63\u5f26\u503c\uff0c\u8ba1\u7b97\u5411\u91cf\u7684\u5939\u89d2\uff080,90\uff09\uff0c\u53ef\u4ee5\u914d\u5408\u70b9\u4e58\u548cAngle\u65b9\u6cd5\u8ba1\u7b97\u51fa\u542b\u6b63\u8d1f\u7684\u65b9\u5411\u3002<\/li>\n\n\n\n
        4. \u6839\u636e\u53c9\u4e58\u5927\u5c0f\uff0c\u5f97\u5230a\uff0cb\u5411\u91cf\u6240\u5f62\u6210\u7684\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9762\u79ef\u5927\u5c0f\uff0c\u6839\u636e\u9762\u79ef\u5927\u5c0f\u5f97\u5230\u5411\u91cf\u7684\u76f8\u5bf9\u5927\u5c0f<\/li>\n<\/ol>\n\n\n\n

          \u5b9e\u4f8b<\/h2>\n\n\n\n

          \u5f97\u5230\u4e24\u4eba\u7684\u76f8\u5bf9\u89d2\u5ea6<\/h3>\n\n\n\n
          FVector HeadLocation = A->GetActorLocation();\nFVector HeadForward = A->GetActorForwardVector();\nFVector TargetLocation = B->GetActorLocation();\nFVector TargetDirection = (TargetLocation - HeadLocation);\nTargetDirection.Normalize();\n\nfloat AngleDot = FVector::DotProduct(HeadForward, TargetDirection);\nfloat Angle =  FMath::RadiansToDegrees(FMath::Acos(AngleDot)); <\/code><\/pre>\n\n\n\n
          \u5e73\u9762\u5224\u65ad\u4e00\u4e2a\u70b9\u5728\u4e09\u89d2\u5f62\u5185<\/h3>\n\n\n\n
          \u4f7f\u7528\u540c\u5411\u6cd5\uff0c\u5982\u70b9P\u5728\u4e09\u89d2\u5f62\u5185\uff0c\u5219\u8ba1\u7b97\u5404\u70b9\u548cP\u7684\u5411\u91cf\u4e0e\u4e09\u8fb9\u7684\u53c9\u79ef\uff0c\u5982\u679c\u7ed3\u679c\u4e00\u81f4\u5219\u5728\u4e09\u89d2\u5f62\u5185\u3002<\/p>\n\n\n
          \n
          \"\"<\/figure>\n<\/div>\n\n\n
          \/\/\u7a7a\u95f4\u4e09\u89d2\u5f62\n\/\/\u6309\u7167\u9006\u65f6\u9488\u987a\u5e8f\u63d2\u5165\u503c\u5e76\u8ba1\u7b97\u6cd5\u5411\u91cf\ntemplate <class T>\nclass Triangle\n{\npublic:\n    Vec3<T> v0;\n    Vec3<T> v1;\n    Vec3<T> v2;\n\n    Triangle()\n    {\n\n    }\n\n    Triangle(Vec3<T> v0, Vec3<T> v1, Vec3<T> v2)\n    {\n        this->v0 = v0;\n        this->v1 = v1;\n        this->v2 = v2;     \n    }\n\n    \/\/ v1 = Cross(AB, AC)\n    \/\/ v2 = Cross(AB, AP)\n    \/\/ \u5224\u65ad\u77e2\u91cfv1\u548cv2\u662f\u5426\u540c\u5411\n    bool SameSide(Vec3<T>& A, Vec3<T>& B, Vec3<T>& C, Vec3<T>& P)\n    {\n        Vec3<T> AB = B - A ;\n        Vec3<T> AC = C - A ;\n        Vec3<T> AP = P - A ;\n\n        Vec3<T> v1 = AB ^ AC;\n        Vec3<T> v2 = AB ^ AP;\n\n        \/\/ v1 and v2 should point to the same direction\n        return v1*v2 >= 0 ;\n        \/\/return v1 * v2 > 0 ;\n    }\n\n    \/\/ \u5224\u65ad\u5e73\u9762\u70b9P\u662f\u5426\u5728\u5e73\u9762\u4e09\u89d2\u5f62\u5185\n    bool PointInTriangle2D(Vec3<T>& P)\n    {\n        Vec3<T> A(v0.x(), v0.y(), 0);\n        Vec3<T> B(v1.x(), v1.y(), 0);\n        Vec3<T> C(v2.x(), v2.y(), 0);\n        return SameSide(A, B, C, P) && SameSide(B, C, A, P) && SameSide(C, A, B, P);\n    }\n};<\/code><\/pre>\n\n\n\n
          \u7a7a\u95f4\u6216\u5e73\u9762\u5224\u65ad\u4e24\u7ebf\u6bb5\u76f8\u4ea4<\/h3>\n\n\n\n
          \u540c\u4fa7\u6cd5<\/h4>\n\n\n\n
          \u5982\u679c\u4e24\u6761\u7ebf\u6bb5\u76f8\u4ea4\uff0c\u90a3\u4e48\u4e00\u6761\u7ebf\u6bb5\u7684\u4e24\u7aef\u70b9\u5fc5\u7136\u4f4d\u4e8e\u53e6\u4e00\u6761\u7ebf\u6bb5\u7684\u4e24\u7aef\u70b9\u7684\u5f02\u4fa7\u3002\u90a3\u4e48\u95ee\u9898\u5c31\u53ef\u4ee5\u8f6c\u6362\u6210\u70b9\u662f\u5426\u5728\u4e00\u6761\u7ebf\u6bb5\u7684\u540c\u4fa7\u3002\u540c\u4fa7\u5224\u65ad\u53ef\u4ee5\u901a\u8fc7\u5411\u91cf\u53c9\u4e58\u7684\u65b9\u6cd5\u6765\u5b9e\u73b0\uff0c\u5373\u5224\u65ad\u6700\u540e\u53c9\u4e58\u7684\u65b9\u5411\u662f\u5426\u76f8\u540c\u3002<\/p>\n\n\n\n
          \u4e0d\u8fc7\u8fd9\u4e2a\u7b97\u6cd5\u53ef\u4ee5\u5224\u65ad\u5b9a\u6027\u5224\u65ad\uff0c\u65e0\u6cd5\u5b9a\u91cf\u5224\u65ad\u51c6\u786e\u7684\u4ea4\u70b9\u3002<\/p>\n\n\n\n
          \u5411\u91cf\u65b9\u7a0b\u6cd5<\/h4>\n\n\n\n
          \u5df2\u77e5\u7a7a\u95f4\u4e2d\u7ebf\u6bb5\u7684\u8d77\u70b9O\u548c\u7ec8\u70b9E\uff0c\u90a3\u4e48\u663e\u7136\u65b9\u5411\u5411\u91cfD\u4e3a\uff1a<\/p>\n\n\n\n
          [D = E - O ]<\/p>\n\n\n\n
          \u8fd9\u65f6\uff0c\u53ef\u4ee5\u786e\u5b9a\u7ebf\u6bb5\u4e0a\u67d0\u4e00\u70b9P\u4e3a\uff1a<\/p>\n\n\n\n
          [P = O + tD ]<\/p>\n\n\n\n
          \u5176\u4e2d\uff0ct\u4e3a\u8303\u56f4\u6ee1\u8db3 0<=t<=1\u7684\u6807\u91cf\u3002<\/p>\n\n\n\n
          \u90a3\u4e48\u8fd9\u4e2a\u95ee\u9898\u5c31\u8f6c\u6362\u6210\u4e86\u6c42\u89e32\u884c2\u5217\u7684\u7ebf\u6027\u65b9\u7a0b\u7ec4\uff0c\u5982\u679c\u6709\u89e3\uff0c\u8bf4\u660e\u5b58\u5728\u4ea4\u70b9\u5e76\u76f4\u63a5\u6c42\u51fa\u30022\u884c2\u5217\u7ebf\u6027\u65b9\u7a0b\u7ec4\u76f4\u63a5\u4f7f\u7528\u514b\u83b1\u59c6\u6cd5\u5219\u6c42\u89e3\u5373\u53ef\u3002<\/p>\n\n\n\n
          \/\/\u7a7a\u95f4\u76f4\u7ebf\ntemplate <class T>\nclass LineSegment\n{\npublic:\n    Vec3<T> startPoint;\n    Vec3<T> endPoint;\n    Vec3<T> direction;\n\n    Vec3<T> min;\n    Vec3<T> max;\n\n    LineSegment()\n    {\n    }\n\n    LineSegment(Vec3<T> start, Vec3<T> end)\n    {\n        startPoint = start;\n        endPoint = end;\n        direction = end - start;\n        CalMinMax();\n    }\n\n    inline void Set(Vec3<T> start, Vec3<T> end)\n    {\n        startPoint = start;\n        endPoint = end;\n        direction = end - start;\n        CalMinMax();\n    }\n\n    inline void CalMinMax()\n    {\n        min.x() = std::min<T>(startPoint.x(), endPoint.x());\n        min.y() = std::min<T>(startPoint.y(), endPoint.y());\n        min.z() = std::min<T>(startPoint.z(), endPoint.z());\n\n        max.x() = std::max<T>(startPoint.x(), endPoint.x());\n        max.y() = std::max<T>(startPoint.y(), endPoint.y());\n        max.z() = std::max<T>(startPoint.z(), endPoint.z());\n    }\n\n    \/\/\u4e24\u6761\u7ebf\u6bb5\u76f8\u4ea4\n    inline static bool Intersection2D(LineSegment & line1, LineSegment & line2, Vec3<T>& insPoint)\n    {\n        double D = -line1.direction.x() * line2.direction.y() + line1.direction.y() * line2.direction.x();\n        if(D == 0.0)\n        {\n            return false;\n        }\n\n        auto O12 = line2.startPoint - line1.startPoint;\n        T D1 = -O12.x() * line2.direction.y() + O12.y() * line2.direction.x();\n        T D2 = line1.direction.x() * O12.y() - line1.direction.y() * O12.x();\n\n        T t1 = D1 \/ D;\n        if(t1<0 || t1 > 1)\n        {\n            return false;\n        }\n\n        T t2 = D2 \/ D;\n        if(t2<0 || t2 > 1)\n        {\n            return false;\n        }\n\n        insPoint = line1.startPoint + line1.direction * t1;     \/\/\u8fd9\u6837\u8ba1\u7b97\u5f97\u5230\u7684Z\u503c\u662f\u4e0d\u51c6\u786e\u7684\n\n        return true;\n    }  \n};<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
          \u6570\u5b66\u6982\u5ff5 \u70b9\u4e58 Dot Product \u53c8\u79f0”\u70b9\u79ef”,”\u6570\u91cf\u79ef\u201d,”\u5185\u79ef”\uff0ca*b = |a||b|Cos(\u03b8) \u51e0\u4f55\u610f\u4e49\uff1a\u662f\u4e00\u6761 …<\/p>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[7,17],"tags":[],"class_list":["post-2358","post","type-post","status-publish","format-standard","hentry","category-games","category-17"],"_links":{"self":[{"href":"https:\/\/courtship.top\/index.php\/wp-json\/wp\/v2\/posts\/2358","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courtship.top\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/courtship.top\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/courtship.top\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/courtship.top\/index.php\/wp-json\/wp\/v2\/comments?post=2358"}],"version-history":[{"count":22,"href":"https:\/\/courtship.top\/index.php\/wp-json\/wp\/v2\/posts\/2358\/revisions"}],"predecessor-version":[{"id":2526,"href":"https:\/\/courtship.top\/index.php\/wp-json\/wp\/v2\/posts\/2358\/revisions\/2526"}],"wp:attachment":[{"href":"https:\/\/courtship.top\/index.php\/wp-json\/wp\/v2\/media?parent=2358"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/courtship.top\/index.php\/wp-json\/wp\/v2\/categories?post=2358"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/courtship.top\/index.php\/wp-json\/wp\/v2\/tags?post=2358"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}