已知曲率为 $1/5+2sin(s)-9/2sin(s/2)$, 则图形为
转载自 ni_o.
感谢 herbertfederer 指出错误, 并给出了一些 Mathematica 代码 (只是 copy 过来, 我也不会用, 也不想看了, 转载至此):
1 curve[[Kappa]_, [Tau]_, c_, d_, options___] :=
2 Module[{r, s, t, n, b},
3 solution =
4 First@NDSolve[{t'[s] == [Kappa][s] n[s],
5 n'[s] == -[Kappa][s] t[s] + [Tau][s] b[s],
6 b'[s] == -[Tau][s] n[s], r'[s] == t[s], r[0] == {0, 0, 0},
7 t[0] == {1, 0, 0}, n[0] == {0, 1, 0}, b[0] == {0, 0, 1}}, {r, t,
8 n, b}, {s, c, d}];
9 ParametricPlot3D[r[s] /. solution, {s, c, d}, options]]
10 curve[15 Sin[#]^2 &, Cos[#] &, -50, 50,
11 PlotStyle -> {Thickness[0.001], Blue}, Boxed -> False, Axes -> False]
而得到
