求空间曲面的切平面 用matlab求空间曲面的切平面和法线用gui
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x^2+y^2+z^2=1即空间曲面为球面 F(x,y,z)= x^2+y^2+z^2-1=0
F分别对x,y,z偏导,分别为 2x,2y,2z
∴曲面在(x0 , y0 ,z0)( 即a=a0 b=b0时)处得切平面为
2x0(x-x0)+2y0(y-y0)+2z0(z-z0)=0
∴x x0+ y y0+z z0=1
即 x sin(a0)cos(b0) +y sin(a0) sin(b0) +z cos(a0)=1
则此时x=y=z=0
①②化为
dx=du,即(0对三个方程左右两边进行微分,得
dx=e^vdu+u*e^vdv
①
dy=v*e^udu+e^udv
②
dz=du+dv
③
又知u=v=0,得
dz=dx+dy
所以曲面在x=y=z=0,0,0)点的法向量为{-1,dy=dv
带入③
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