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I have a function in cylindrical co-ordinate with 3 independent coorrdinates, give by:

f[r_, z_, v_] := -(Sqrt[E^(-(r^2/32) - z^2/32) - v^2]/\[Pi]) + 
  45/392 r^2 Sqrt[E^(-(r^2/32) - z^2/32) - v^2] - (
  1.5957691216057308` E^(-(r^2/32) - z^2/
    32) (-1 - E^(r^2/32 + z^2/32) + E^(r^2/32 + z^2/32) v^2))/(1 - 
    2 (-E^(-(r^2/32) - z^2/32) + v^2))^(3/2) - (
  2 Sqrt[E^(-(r^2/32) - z^2/32) - 
    v^2] (1 - 2 Log[-4 (-E^(-(r^2/32) - z^2/32) + v^2)]))/(49 \[Pi])

As this has 3 independent variables, I need to have a 4D plot. Hence I used DensityPlot3D.

[![DensityPlot3D\[ftrGenK\[\[2\]\], {r, -20, 20}, {z, -20, 20}, {v, -1, 1}, 
 AxesLabel -> {"r", "z", "v"}, 
 AxesStyle -> Directive\[Black, FontSize -> 15\], 
 AxesStyle -> Directive\[Black, FontSize -> 15\], 
 ColorFunction -> "Rainbow", LabelStyle -> Directive\[Bold, Black\], 
 TicksStyle -> Directive\[Thick, Black, 15\], PlotLabel -> "\[Kappa\]=2",
  PlotLegends -> 
  BarLegend\[{"Rainbow", {0, 1}}, LegendMarkerSize -> 150, 
   LegendMargins -> {{0, 0}, {20, 0}}\]\]][1]][1]

I got a plot like this:

As my equation is in cylindrical coordinates, is this correct way to do this?? I think the plot have come issue. Can you please help me Thanks in advance

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  • $\begingroup$ First, in cylindrical coordinate we have three variables with specific ranges z(0, infinity), \theta (0,2pi) and r (0, infinity) . You have to define this clearly. Your code is a mess, you did not define ftrGenK[]. Can you revise your code and make it more clear? $\endgroup$ – HD2006 Aug 5 '18 at 13:20
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In Cartesian coordinates, it looks like two eggs in a frying pan

f[r_, z_, v_] := -(Sqrt[E^(-(r^2/32) - z^2/32) - v^2]/\[Pi]) + 
  45/392 r^2 Sqrt[
    E^(-(r^2/32) - z^2/32) - 
     v^2] - (1.5957691216057308` E^(-(r^2/32) - z^2/32) (-1 - 
       E^(r^2/32 + z^2/32) + E^(r^2/32 + z^2/32) v^2))/(1 - 
      2 (-E^(-(r^2/32) - z^2/32) + v^2))^(3/2) - (2 Sqrt[
      E^(-(r^2/32) - z^2/32) - v^2] (1 - 
       2 Log[-4 (-E^(-(r^2/32) - z^2/32) + v^2)]))/(49 \[Pi])
DensityPlot3D[
 f[Sqrt[x^2 + y^2], z, ArcTan[y/x]], {x, 0, 20}, {y, -10, 
  10}, {z, -10, 10}, AxesLabel -> {"x", "y", "z"}, 
 AxesStyle -> Directive[Black, FontSize -> 15], 
 AxesStyle -> Directive[Black, FontSize -> 15], 
 ColorFunction -> "Rainbow", LabelStyle -> Directive[Bold, Black], 
 TicksStyle -> Directive[Thick, Black, 15], PlotLabel -> "\[Kappa]=2",
  PlotLegends -> 
  BarLegend[{"Rainbow", {0, 1}}, LegendMarkerSize -> 150, 
   LegendMargins -> {{0, 0}, {20, 0}}]]

fig1

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  • $\begingroup$ Thanks a lot.. I had to make some changes.. but finally it worked. Thank you for the idea. Thank you $\endgroup$ – Hari Krishnan Aug 7 '18 at 12:26

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