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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

## Description

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[ curve + radius Cos[s] unitNormal + radius Sin[s] biNormal //

``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[q0t]; 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[q0t]; 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[pw + (1 - p)w0, {t, -Pi, Pi}, {p, 0, 1}, Axes -> False, Boxed -> False, PlotRange -> All, PlotPoints -> {60, 60}, ColorFunction -> "Pastel", MeshStyle -> {Tube[0.255/4]}, 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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What software did you use to generate this?

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