Osnovni trirob

Krivulja K je podana s parametrizacijo

r[t_]  := {2  Cos[t], 2  Sin[t], t/2}

za  t∈[0, 4π].

gr = ParametricPlot3D[r[t], {t, 0, 4  π}];

Osnovni trirob

T0[t_] = r'[t]/(Sqrt[r'[t] . r'[t]]) // Simplify

b0 = r'[t]\[Cross]r''[t] // 
          Simplify;
n0 = b0\[Cross]r'[t] // Simplify;
N0[t_] = n0/(Sqrt[n0 . n0]) // Simplify

B0[t_] = T0[t]\[Cross]N0[t] // Simplify

\(\(trirob[t_] := 
        Show[gr, 
          Graphics3D[{RGBColor[0, 0, 1], Thickness[0.01], 
              Line[{r[t], r[t] + T0[t]}], 
              Text["T", 
                r[t] + 1.3  T0[t]], 
Line[{r[t], 
                  r[t] + N0[t]}], 
              Text["N", 
                r[t] + 1.3  N0[t]], 
Line[{r[t], 
                  r[t] + B0[t]}], 
              Text["B", 
                r[t] + 1.3 
                     B0[t]]}], 
PlotRange -> {{\(-2.5\), 2.5}, {\(-2.5\), 2.5}, {0, 7.5}}];\)\)

Table[trirob[t], {t, 0, 4  π, 4  π/50}];

Še en primer

r[t_]  := {Sin[t], Cos[t], Sin[2  t]};
gr = 
        ParametricPlot3D[r[t], {t, 0, 2  π}, 
          ViewPoint -> {4.000, - 5.000,  4.000}];

T0[t_] = r'[t]/(Sqrt[r'[t] . r'[t]]) // Simplify

b0 = r'[t]\[Cross]r''[t] // 
          Simplify;
n0 = b0\[Cross]r'[t] // Simplify;
N0[t_] = n0/(Sqrt[n0 . n0]) // Simplify

B0[t_] = T0[t]\[Cross]N0[t] // Simplify

trirob[t_] := 
        Show[gr, 
          Graphics3D[{RGBColor[0, 0, 1], Thickness[0.01], 
              Line[{r[t], r[t] + T0[t]}], 
              Text["T", 
                r[t] + 1.3  T0[t]], 
Line[{r[t], 
                  r[t] + N0[t]}], 
              Text["N", 
                r[t] + 1.3  N0[t]], 
Line[{r[t], 
                  r[t] + B0[t]}], 
              Text["B", 
                r[t] + 1.3  B0[t]]}], 
PlotRange -> 
            1.5 {{-1, 1}, {-1, 1}, {-1, 1}}];

Table[trirob[t], {t, 0, 2  π, 2  π/100}];