Skip to main content

plotting - ParametricPlot3D: The Mesh shows some unexpected wires to the origin. How to remove them?


In the code below a hexagonal shape is defined and plotted. The ParametricPlot3D shows the hexagonal design almost as intended. However, the mesh makes some strange "wires" to x=y=0. This is unexpected as the function does not exist at these coordinates. Why am I seeing this strange behaviour at the center? How can the plot be improved?


I tried several things: 2nd plot: I also included these coordinates in the Exclusions in the second plot but this didn't help.


3th plot: When the mesh is not plotted the graph looks better, altough some polishing at the edges might improve the graph further.


4th plot. Other problems is encoutered in the 3Dplot.


 Remove["Global`*"];
 func[u0_, v0_] := Module[{u = u0, v = v0},

   {
    u, v,
    If[u == 0 && v == 0,
     Null,
     θ  = ArcTan[v, u];
     θN = Mod[θ, 3.1415/3., -3.1415/6.](*θ w.r.t North*);
     l  = Norm[{u, v}];
     vN = l*Cos[θN ];
     If[.3 < vN < .8, 2 - vN, Null] (*Make parabolic function(vN)*)
     ]

    }
   ]

 func[0., 0.]

 surfacePlot = 
  ParametricPlot3D[func[u, v], {u, -1, 1}, {v, -1, 1}, 
   PlotRange -> All, AxesLabel -> {"x", "y", "z"}, PlotRange -> All]

 surfacePlot = 

  ParametricPlot3D[func[u, v], {u, -1, 1}, {v, -1, 1}, 
   PlotRange -> All, AxesLabel -> {"x", "y", "z"}, PlotRange -> All, 
   Exclusions -> {u == 0, v == 0}, ExclusionsStyle -> {None, Red}]

 surfacePlot = 
  ParametricPlot3D[func[u, v], {u, -1, 1}, {v, -1, 1}, 
   PlotRange -> All, 
   AxesLabel -> {"x", "y", "z"},(*Exclusions\[Rule]{{u\[Equal]0,
   u<.1}},*)PlotPoints -> 80, Mesh -> None]


 surfacePlot = 
  Plot3D[func[u, v][[3]], {u, -1, 1.4}, {v, -1, 1.4}, PlotRange -> All,
    AxesLabel -> {"x", "y", "z"}, PlotRange -> All, 
   PlotPoints -> { 30}]

Plots of strange wires to u=v=x=y=0



Answer



Your mapping is not continuous and the mesh just shows it.


fun1[u_, v_] := 2 - Norm[{u, v}]*Cos[Mod[ArcTan[v, u], Pi/3, -Pi/6]]
ParametricPlot3D[{u, v, fun1[u, v]}, {u, -1, 1}, {v, -1, 1}, 

                 RegionFunction -> (1.2 < fun1[#4, #5] < 1.7 &), PlotPoints -> 50]

Mathematica graphics


Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

plotting - Magnifying Glass on a Plot

Although there is a trick in TEX magnifying glass but I want to know is there any function to magnifying glass on a plot with Mathematica ? For example for a function as Sin[x] and at x=Pi/6 Below, this is just a picture desired from the cited site. the image got huge unfortunately I don't know how can I change the size of an image here! Answer Insetting a magnified part of the original Plot A) by adding a new Plot of the specified range xPos = Pi/6; range = 0.2; f = Sin; xyMinMax = {{xPos - range, xPos + range}, {f[xPos] - range*GoldenRatio^-1, f[xPos] + range*GoldenRatio^-1}}; Plot[f[x], {x, 0, 5}, Epilog -> {Transparent, EdgeForm[Thick], Rectangle[Sequence @@ Transpose[xyMinMax]], Inset[Plot[f[x], {x, xPos - range, xPos + range}, Frame -> True, Axes -> False, PlotRange -> xyMinMax, ImageSize -> 270], {4., 0.5}]}, ImageSize -> 700] B) by adding a new Plot within a Circle mf = RegionMember[Disk[{xPos, f[xPos]}, {range, range/GoldenRatio}]] Show...
Post a Comment
Read more