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Mathematics Algebra Graphics and Visualization

3D plotting a function and showing a parameter variation?

KRISHAN SHARMA

Posted 2 years ago

Hello i am trying to plot a function using Plot3D ClearAll["Global`*"]; M0 = 1; M = 3; \[Beta] = Sqrt[(\[Sigma]^2 + M^2)/M0]; ucap[\[Beta]_, r_] := ( 3 \[Beta]^2 ((1 + r \[Beta]^2) BesselI[0, 2 \[Beta]] - (1 + \[Beta]^2) BesselI[0, 2 Sqrt[r] \[Beta]]))/((6 + 9 \[Beta]^2 + 2 \[Beta]^4) BesselI[ 0, 2 \[Beta]] - 6 (1 + \[Beta]^2)^2 Hypergeometric0F1Regularized[2, \[Beta]^2]); Table[ Plot3D[ ucap[\[Beta], r] /. {r -> Norm[{x, y}]}, {x, -1, 1}, {y, -1, 1}, RegionFunction -> (Norm[{#, #2}] <= 1 &), ImageSize -> Large, AxesLabel -> {"Axial velocity"}, PlotStyle -> Thick ], {\[Sigma], {1, 5, 30, 100}} ] Here is one sample from an article . I also want to show the function in animation form for sigma values 0 to 100. Please Help

Hello i am trying to plot a function using Plot3D

ClearAll["Global`*"];
M0 = 1;
M = 3;
\[Beta] = Sqrt[(\[Sigma]^2 + M^2)/M0];
ucap[\[Beta]_, r_] := (
  3 \[Beta]^2 ((1 + r \[Beta]^2) BesselI[0, 
       2 \[Beta]] - (1 + \[Beta]^2) BesselI[0, 
       2 Sqrt[r] \[Beta]]))/((6 + 9 \[Beta]^2 + 2 \[Beta]^4) BesselI[
     0, 2 \[Beta]] - 
   6 (1 + \[Beta]^2)^2 Hypergeometric0F1Regularized[2, \[Beta]^2]);
Table[
 Plot3D[
  ucap[\[Beta], r] /. {r -> Norm[{x, y}]}, {x, -1, 1}, {y, -1, 1},
  RegionFunction -> (Norm[{#, #2}] <= 1 &),
  ImageSize -> Large,
  AxesLabel -> {"Axial velocity"},
  PlotStyle -> Thick
  ],
 {\[Sigma], {1, 5, 30, 100}}
 ]

Here is one sample from an article

enter image description here .

I also want to show the function in animation form for sigma values 0 to 100. Please Help

POSTED BY: KRISHAN SHARMA

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Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 2 years ago

Looking at the sample you provided you probably want `RevolutionPlot3D` instead of `Plot3D`. Try: Table[RevolutionPlot3D[ucap[\[Beta], r], {r, 0, 1}, ImageSize -> Large, AxesLabel -> {"Axial velocity"}, MeshStyle -> Thick, PlotStyle -> None], {\[Sigma], {1, 5, 30, 100}}]