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plotting - Tube with variable color, opacity, and radius


Well, it's "two out of three ain't bad"...


So far I have this:


ParametricPlot3D[{Sin[u], Cos[u], u/10}, {u, 0, 25}, 

  ColorFunction -> (Directive[Opacity[#3/2], Hue[1/2 - 1/5 #3]] &), 
  ColorFunctionScaling -> False, PlotRange -> All] /. 
 Line[pts_, rest___] :> Tube[pts, 0.1, rest]

enter image description here


but now I'd like to vary the tube radius, too. Perhaps as a function of one or a combination of coordinates, or a function of the curve length, etc. I can't figure out how to replace that 0.1 I have with some function that achieves what I want.


I also cobbled this together from this answer, but then I don't know how to vary the opacity the way I want it:


rr = Reap[
  ParametricPlot3D[{Sin[u], Cos[u], u/10}, {u, 0, 25}, 
   ColorFunction -> 

    Function[{x, y, z, t}, Hue[Sow[1/2 - t/50, "tValues"]]], 
   ColorFunctionScaling -> False, 
   PlotStyle -> Directive[Opacity[0.5], CapForm[Round]], 
   PlotRange -> All, MaxRecursion -> 0, PlotPoints -> 300, 
   Method -> {"TubePoints" -> 300}], "tValues"]; 
rr[[1]] /. Line[pts_, rest___] :> Tube[pts, 0.1 - .15 rr[[2]], rest]

enter image description here



Answer



The following code is based on the Reap-Sow approach, and uses for the ColorFunction a pure function, as in your first approach. The pure function is rewritten with Sow and uses the slot #4 for the color variation, rather than #3, to take the values given by u.



rr = Reap[
       ParametricPlot3D[
         {Sin[u], Cos[u], u/10}, {u, 0, 25}, 
          ColorFunction -> (Directive[Opacity[0.5 #3], Hue[Sow[1/2 - #4/50]]] &), 
          ColorFunctionScaling -> False,
          PlotRange -> All,
          MaxRecursion -> 0, PlotPoints -> 300, 
          Method -> {"TubePoints" -> 300}
       ]
];


rr[[1]] /. Line[pts_, rest___] :> Tube[pts, 0.1 - .15 rr[[2]], rest]

enter image description here


Note that since here $z = u /10$, it is equivalent to use instead:


Hue[Sow[1/2 - #3/5]]

which is what you have for the ColorFunction of your first approach (Sow apart).


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