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# 52 to 25 torus knot bridge surface

## by rlbagulatftn, published Oct 24, 2012

52 to 25 torus knot bridge surface Oct 24, 2012
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# Summary

TubePlotFrenet[curveList, {var, min, max}, radius_, opts___] :=
Module[{tangent, unitTangent, normal, unitNormal, biNormal},
tangent = D[curve, t];
unitTangent = tangent/Sqrt[tangent.tangent];
normal = D[unitTangent, t];
unitNormal = normal/Sqrt[normal.normal];
biNormal = Cross[unitTangent, unitNormal];
ParametricPlot3D[
Evaluate, {var, min, max}, {s, 0, 2 [Pi]}, opts]]
{p0, q0} = {5, 2};

r = Cos[q0t] + 2;
x = r
Cos[p0t];
y = r
Sin[p0t];
z = Sin[q0
t];
w0 = 8*{x, y, z}
h = TubePlotFrenet[w0, {t, 0, 2 [Pi]}, 2, Axes -> None,
Boxed -> False, PlotPoints -> {64, 16},
ColorFunction -> "CandyColors", MeshFunctions -> {#3 &}]
{p0, q0} = {2, 5};

r = Cos[q0t] + 2;
x = r
Cos[p0t];
y = r
Sin[p0t];
z = Sin[q0
t];
w = 8{x, y, z}
h1 = TubePlotFrenet[w, {t, 0, 2 [Pi]}, 2, Axes -> None,
Boxed -> False, PlotPoints -> {64, 16},
ColorFunction -> "BeachColors", MeshFunctions -> {#3 &}]
Show[{h, h1}, PlotRange -> All, ViewPoint -> {0, 0, 5}]
ga = ParametricPlot3D[p
w + (1 - p)w0, {t, -Pi, Pi}, {p, 0, 1},
Axes -> False, Boxed -> False, PlotRange -> All,
PlotPoints -> {60, 60}, ColorFunction -> "Pastel",
MeshStyle -> {Tube[0.25
5/4]}, PlotStyle -> {Opacity[0.0]},
ViewPoint -> {0, 0, 5}, ImageSize -> {674, 501}, Mesh -> 16]
gw = Show[{h, h1, ga}, PlotRange -> All, ViewPoint -> {0, 0, 5},
ImageSize -> 1000]

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