{"id":676,"date":"2014-01-24T16:58:32","date_gmt":"2014-01-24T15:58:32","guid":{"rendered":"http:\/\/darksun190.cn\/?p=676"},"modified":"2022-12-17T15:53:06","modified_gmt":"2022-12-17T07:53:06","slug":"%e6%9c%80%e5%b0%8f%e4%ba%8c%e4%b9%98%e6%b3%95%e6%8b%9f%e5%90%88%e4%b8%80%e4%ba%9b%e5%9f%ba%e6%9c%ac%e7%a9%ba%e9%97%b4%e5%85%83%e7%b4%a0%e7%9a%84c%e5%ae%9e%e7%8e%b0-%ef%bc%88-2","status":"publish","type":"post","link":"http:\/\/darksun190.cn\/blog\/?p=676","title":{"rendered":"\u6700\u5c0f\u4e8c\u4e58\u6cd5\u62df\u5408\u4e00\u4e9b\u57fa\u672c\u7a7a\u95f4\u5143\u7d20\u7684C#\u5b9e\u73b0 \u2014\u2014 \uff08\u4e8c\uff09\u76f4\u7ebf\u4e0e\u5e73\u9762"},"content":{"rendered":"\n

\u672c\u6587\u8ba8\u8bba\u5e76\u5b9e\u73b0\u7684\u7b97\u6cd5\u4e3b\u8981(99%)\u57fa\u4e8e\u8fd9\u7bc7\u6587\u7ae0<\/a>\uff0c\u66f4\u591a\u53c2\u8003\u8bf7\u9605\u8bfb\u8fd9\u91cc<\/a>\u3002<\/p>\n\n\n\n

\u5927\u90e8\u5206\u80fd\u641c\u7d22\u5230\u7684\u5173\u4e8e\u76f4\u7ebf\u6700\u5c0f\u4e8c\u4e58\u62df\u5408\u7684\u8d44\u6599\u662f\u57fa\u4e8e2\u7ef4\u7a7a\u95f4\u7684\\[y=ax+ b\\]<\/p>\n\n\n\n

\u800c\u4ece\u4e09\u7ef4\u7a7a\u95f4\u7684\u89d2\u5ea6\u4e0a\u6765\u770b\uff0c\u8fd9\u53ea\u662f\u4e00\u79cd\u7279\u4f8b\u3002\u672c\u6587\u4e3b\u8981\u8ba8\u8bba\u4e09\u7ef4\u7a7a\u95f4\u4e0a\u7684\u76f4\u7ebf\u62df\u5408\u3002<\/p>\n\n\n\n

\u53c2\u6570\u5316<\/h3>\n\n\n\n

\u4e09\u7ef4\u76f4\u7ebf\u7684\u8868\u793a\u5982\u4e0b\u3002\\[\\left(x,y,z\\right)=\\left(x_0,y_0,z_0\\right) + t\\left(a,b,c\\right)\\]<\/p>\n\n\n\n

\u5176\u4e2d\\(\\left(x_0,y_0,z_0\\right)\\)\u4e3a\u76f4\u7ebf\u4e0a\u4efb\u4e00\u5df2\u77e5\u70b9\uff0c\\(\\left(a,b,c\\right)\\)\u4e3a\u5411\u91cf\uff0c\u6240\u4ee5\u6240\u6709\u76f4\u7ebf\u90fd\u53ef\u4ee5\u4f7f\u7528\u4e00\u4e2a\u70b9\u5750\u6807\u53ca\u4e00\u4e2a\u5411\u91cf\u6765\u8868\u793a\u3002<\/p>\n\n\n\n

\u5bf9\u4e8e\u6d4b\u91cf\u70b9\\(P_i\\left(x_i,y_i,z_i\\right)\\)\u4e0e\u76f4\u7ebf\u7684\u8ddd\u79bb\u4e3a\\[d_i=\\sqrt{{u_i}^2+{v_i}^2+{w_i}^2}\\]<\/p>\n\n\n\n

\u5176\u4e2d\uff1a\\[u_i=c\\left(y_i-y_0\\right)-b\\left(z_i-z_0\\right)\\]\\[v_i=a\\left(z_i-z_0\\right)-c\\left(x_i-x_0\\right)\\]\\[w_i=b\\left(x_i-x_0\\right)-a\\left(y_i-y_0\\right)\\]<\/p>\n\n\n\n

\u7b97\u6cd5<\/h3>\n\n\n\n

\u6839\u636e\u539f\u6587\uff1a\u62df\u5408\u7684\u76f4\u7ebf\u8fc7\u6240\u6709\u70b9\u7684\u5e73\u5747\u503c\uff0c\u6ca1\u6709\u8bc1\u660e\u2026\u2026<\/p>\n\n\n\n

\u6240\u4ee5\u672a\u77e5\u91cf\u5176\u5b9e\u662f3\u4e2a\uff0c\u6784\u5efa\u4e00\u4e2a\u77e9\u9635\\[A=\\begin{bmatrix}x_1-x_0&y_1-y_0&z_1-z_0\\\\x_2-x_0&y_2-y_0&z_2-z_0\\\\\\vdots & \\vdots & \\vdots \\\\x_i-x_0&y_i-y_0&z_i-z_0\\end{bmatrix}\\]<\/p>\n\n\n\n

\u5c06\u77e9\u9635A\u505a\u5947\u5f02\u503c\u5206\u89e3\uff08SVD\uff09\uff0c\u4ee4\uff1a\\[A=U_1SV^T\\]<\/p>\n\n\n\n

\u77e9\u9635\\(V\\)\u7684\u7b2c\u4e00\u5217\uff08Column\uff09\u5373\u662f\u76f4\u7ebf\u5411\u91cf\\(\\left(a,b,c\\right)\\)\u3002<\/p>\n\n\n\n

\u4ee3\u7801\u5b9e\u73b0\uff1a<\/p>\n\n\n\n

 public override void Estimate(List<Point3D> datas)\n        {\n            double sum_x = 0;\n            double sum_y = 0;\n            double sum_z = 0;\n            foreach (Point3D temp in datas)\n            {\n                sum_x += temp.x;\n                sum_y += temp.y;\n                sum_z += temp.z;\n            }\n            sum_x \/= datas.Count;\n            sum_y \/= datas.Count;\n            sum_z \/= datas.Count;\n\n            DenseMatrix jacobian = new DenseMatrix(datas.Count, 3);\n            foreach (Point3D temp in datas)\n            {\n                Vector<double> gradient = new DenseVector(3);\n                gradient[0] = temp.x - sum_x;\n                gradient[1] = temp.y - sum_y;\n                gradient[2] = temp.z - sum_z;\n                jacobian.SetRow(datas.IndexOf(temp), gradient);\n            }\n            Svd svd = jacobian.Svd(true);\n            \/\/ get matrix of left singular vectors with first n columns of U\n            Matrix<double> U1 = svd.U().SubMatrix(0, datas.Count, 0, 3);\n            \/\/ get matrix of singular values\n            Matrix<double> S = new DiagonalMatrix(3, 3, svd.S().ToArray());\n            \/\/ get matrix of right singular vectors\n            Matrix<double> V = svd.VT().Transpose();\n\n            Vector<double> parameters = new DenseVector(3);\n            parameters = V.Column(0);\n            x = sum_x;\n            y = sum_y;\n            z = sum_z;\n            i = parameters[0];\n            j = parameters[1];\n            k = parameters[2];\n        }<\/code><\/pre>\n\n\n\n
\u5e73\u9762\u7684\u6700\u5c0f\u4e8c\u4e58\u62df\u5408<\/h2>\n\n\n\n
\u653e\u5728\u4e00\u8d77\u7684\u539f\u56e0\u662f\u8fd9\u4e24\u79cd\u5143\u7d20\u7684\u7b97\u6cd5\u662f\u5b8c\u5168\u4e00\u6837\u7684\uff0c\u76f4\u7ebf\u62df\u5408\u6700\u540e\u4e00\u6b65\u5f97\u5230\u7684\u77e9\u9635V\u7b2c\u4e00\u5217\u662f\u76f4\u7ebf\u7684\u5411\u91cf\uff0c\u800c\u7b2c\u4e09\u5217\u5c31\u662f\u5e73\u9762\u7684\u5411\u91cf\u3002<\/p>\n\n\n\n
\u53c2\u6570\u5316<\/h3>\n\n\n\n
\u5e73\u9762\u540c\u6837\u53ef\u4ee5\u7528\u4e00\u4e2a\u70b9\\(\\left(x_0,y_0,z_0\\right)\\)\u548c\u4e00\u4e2a\u5411\u91cf\\(\\left(a,b,c\\right)\\)\u6765\u8868\u793a\uff0c\u53ea\u662f\u5782\u76f4\u4e0e\u8be5\u5411\u91cf\u3002<\/p>\n\n\n\n
\u5e73\u9762\u7684\u516c\u5f0f\u4e3a\\[a\\left(x-x_0\\right)+b\\left(y-y_0\\right)+c\\left(z-z_0\\right)=0\\)<\/p>\n\n\n\n
\u5bf9\u4e8e\u6d4b\u91cf\u70b9\\(P_i\\left(x_i,y_i,z_i\\right)\\)\u76f4\u63a5\u7684\u8ddd\u79bb\u4e3a\\[d_i=a\\left(x-x_0\\right)+b\\left(y-y_0\\right)+c\\left(z-z_0\\right)\\]<\/p>\n\n\n\n
\u7b97\u6cd5<\/h3>\n\n\n\n
\u4e0e\u76f4\u7ebf\u7684\u7b97\u6cd5\u5b8c\u5168\u76f8\u540c\u3002<\/p>\n\n\n\n
\u5305\u542b\u76f4\u7ebf\u3001\u5e73\u9762\u4e0e\u5706\u67f1\u7b97\u6cd5\u7684C#\u5b9e\u4f8b\u4e0e\u8bf4\u660e<\/a><\/p>\n\n\n\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
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