Question

用MATLAB将这些点用最小二乘法拟合成一条三维曲线并得出一般方程和参数方程还有图像

-103.1723,-12.8022,658.7408
-102.5497,-13.5531,656.9143
-101.5390,-15.0349,653.5468
-100.3376,-16.7742,649.8018
-99.6429,-17.7510,647.5095
-99.2972,-18.3361,646.0282
-97.5190,-20.8063,639.8084
-93.3629,-27.4994,625.5536
-89.3345,-35.4757,610.2544
-87.7093,-39.3748,603.5714
-82.7088,-49.5862,584.5742
-81.3240,-52.2527,579.7221
-81.1609,-52.9732,578.5109
-80.1400,-54.9509,574.9984
-77.8483,-59.1571,567.2563
-75.4654,-64.7954,556.8365
-75.2559,-65.7905,554.8854
-75.6229,-66.3861,553.7428

Answer 1

根据数据判断，三维曲线方程 为 z(x,y)=Ax^2+Bx*y+Cy^2+Dx+Ey+F

用matlab的regress（）函数命令，拟合出A、B、C、D、E、F系数。

拟合结果：

方程系数 A=-0.39445,B=-0.44107,C=-0.12052,D=-88.1778,E=-47.1086,F=-4240.7499

R²=0.99999  %决定系数（拟合精度）

用matlab的plot3或surfc（）函数命令，绘出三维曲线图和三维曲面图。

如需要详细代码可以私信交流。

追问

是这样的，这些点我是从一条曲线上面取下来的，拟合之后的曲线和我原本的曲线相差太大...我想知道为什么.原本的曲线是一条比这个直很多的曲线