【微分几何】怎么绘制空间曲线的密切平面

1、给定曲线的参数方程：r[t_] := {Cos[3 t], Sin[2 t], t}aa = ParametricPlot3D[r[u], {u, -Pi, Pi}]

3、密切平面有两个不平行的向量r'[t]和r''[t]确定，我们画出这两个向量：aa = Show[ParametricPlot3D[r[u], {u, -Pi, Pi}, PlotStyle -> Blue], Graphics3D[{PointSize[0.02], Red, Point[r[Pi/3]], Green, Arrow[{r[Pi/3], r[Pi/3] + r'[Pi/3]}], Orange, Arrow[{r[Pi/3], r[Pi/3] + r''[Pi/3]*0.16}]}]]

5、绘制密切平面：aa = Show[Parametr坡纠课柩icPlot3D[r[u], {u, -Pi, Pi}, PlotStyle -> Blue], ParametricPlot3D[{X, Y, Z} /. sol, {X, -Pi, Pi}, {Y, -Pi, Pi}, PlotStyle -> Opacity[0.2], PlotRange -> 1], Graphics3D[{PointSize[0.02], Red, Point[r[Pi/3]], Green, Arrow[{r[Pi/3], r[Pi/3] + r'[Pi/3]}], Orange, Arrow[{r[Pi/3], r[Pi/3] + r''[Pi/3]*0.16}]}]]