Wednesday, October 18, 2006

TorusKnots


Having Fun with Torus Knot !

torusknot[a_, b_, c_][p_, q_][t_] := { (a + b Cos[q t]) Cos[p t], (a + b Cos[q t]) Sin[p t], c Sin[q t]}

ParametricPlot3D[torusknot[10, 4, 5][100, 1.5][t] // Evaluate, {t, 0, 120π}, PlotPoints→200 , ViewPoint→ {20, 30, 70}] ; //Timing

[Graphics:HTMLFiles/index_4.gif]


{0.008 Second, Null}

ParametricPlot3D[torusknot[10, 4, 5][100, 1.5][t] // Evaluate, {t, 0, 1π}, PlotPoints→200 , ViewPoint→ {20, 30, 70}] ; //Timing

[Graphics:HTMLFiles/index_7.gif]


{0.008001 Second, Null}

ParametricPlot3D[torusknot[10, 4, 5][100, 1.5][t] // Evaluate, {t, 0, 1π}, PlotPoints→100 , ViewPoint→ {20, 30, 70}] ; //Timing


[Graphics:HTMLFiles/index_10.gif]


{0.004 Second, Null}


ParametricPlot3D[torusknot[10, 4, 5][100, 4π][t] // Evaluate, {t, 0, 1π}, PlotPoints→100 , ViewPoint→ {20, 30, 70}] ; //Timing


[Graphics:HTMLFiles/index_13.gif]


{0.004 Second, Null}

ParametricPlot3D[torusknot[100, 34π, 52][1003, 433π][t] // Evaluate, {t, 0, 10000π}, PlotPoints→100 , ViewPoint→ {20, 30, 70}] ; //Timing


[Graphics:HTMLFiles/index_16.gif]


{0.004 Second, Null}

torusknot[a_, b_, c_][p_, q_][t_] := { (a + b Cos[q t]) Cos[p t], (a + b Cos[q t]) Sin[p t], c Sin[q t]} ;

ParametricPlot3D[torusknot[u, 3, 5][3, u][t], {t, 0, 3}, {u, 0, 3}]



[Graphics:HTMLFiles/index_20.gif]




-Graphics3D -


In[49]:=






[Graphics:HTMLFiles/index_23.gif]




Out[50]=






-Graphics3D -







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