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[?] Plot in 3D a X-zylo ?

Donghwan Roh

Posted 8 years ago

X-zylo is a simple cylindrical object with Sine(Sin[t]) shaped undulation on top. You can find link below. It's a flying gyroscope. https://www.amazon.com/X-Zylo-X-zylo-Flying-Gyroscope/dp/B0069G6CKG How can I make this? (cylindrical parametric function? Just bending/flexing the Sin[t], {t,0,10Pi} in 360 degree) Plot3D ParametricPlot3D RevolutionPlot3D in any form to make it.. Thank in advance!

POSTED BY: Donghwan Roh

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Donghwan Roh

Posted 8 years ago

Yes, ParametricRegion and ImplicitRegion can be an option. ParametricPlot3D function does not support thickness(range function). Mathematica is plotting program, and now it support coming into 3D printing. So I hope Mathematica support CAD like feature by mathematical function or intuitive editing. Upper thickness 1mm and Lower base thickness 3mm(for example rr[x_] if x<0.5, 1<rr[x]<1.3 (3mm), if x>0.5 1<rr[x]<1.1 (1mm))Anyway thanks for intuitive opinion Hans Milton!

POSTED BY: Donghwan Roh

Hans Milton

Posted 8 years ago

Donghwan, I do not know how to control thickness value in plot option PlotTheme->"ThickSurface". There may be other approaches if one wants to use Mathematica. See for example ImplicitRegion and ParametricRegion. However if I myself wanted to construct a tightly controlled model to be 3D printed I would use a dedicated 3D CAD program. My own personal preference would be SolidWorks. But there are many other programs that could be used. In an earlier post you mention three of them. Mathematica is not a 3D CAD program. It is something else.

POSTED BY: Hans Milton

Donghwan Roh

Posted 8 years ago

Thank you Hans Milton! Your reply was really helpful^^ I can now try 3D printing above stl file! Now I have one more question. Can I adjust the thickness of the 3D model by PlotTheme->"ThickSurface"? For example thinner like 1mm thickness or thicker just at the base part? (and thin middle and Cos[6t] part)

POSTED BY: Donghwan Roh

Hans Milton

Posted 8 years ago

Increasing the number of PlotPoints gives a smoother model. In the attached model the number of PlotPoints is 200. It has also been scaled by a factor of 50. r[s_, a_, b_] := 1 + a Exp[-b s^2] example = ParametricPlot3D[ 50 {r[s, .3, 10] Cos[t], r[s, .3, 10] Sin[t], s}, {t, 0, 2 Pi}, {s, 0, 1 + 1/2 Cos[6 t]}, PlotPoints -> 200, Mesh -> False, PlotTheme -> "ThickSurface"] When opened in a CAD program: Attachments:

Increasing the number of PlotPoints gives a smoother model. In the attached model the number of PlotPoints is 200. It has also been scaled by a factor of 50.

r[s_, a_, b_] := 1 + a Exp[-b s^2]
example =
    ParametricPlot3D[
    50 {r[s, .3, 10] Cos[t], r[s, .3, 10] Sin[t], s},
    {t, 0, 2 Pi}, {s, 0, 1 + 1/2 Cos[6 t]},
    PlotPoints -> 200, Mesh -> False, PlotTheme -> "ThickSurface"]

When opened in a CAD program:

enter image description here

POSTED BY: Hans Milton

Hans Milton

Posted 8 years ago

To get a solid STL model from a Mathematica surface plot you could try to use the option PlotTheme -> "ThickSurface" in the plot. Attachments:

POSTED BY: Hans Milton

Hans Dolhaine

Hans Dolhaine, retired

Posted 8 years ago

Hello Donghwan, However, no 3D program(Sketchup, Rhinocerus, Autodesk fusion 360, etc.) can recognize the mathematical plane into 3D printable object! Whatever that means? I don't know Sketchup, Rhinocerus and so on and I have not idea how these programs work. So this model need to have full thickness to be printed into real world And what do you mean by "full thickness"? And what do you mean by "model"? Regards, Hans

POSTED BY: Hans Dolhaine

Donghwan Roh

Posted 8 years ago

Attachments:

POSTED BY: Donghwan Roh

Hans Dolhaine

Hans Dolhaine, retired

Posted 8 years ago

POSTED BY: Hans Dolhaine

Donghwan Roh

Posted 8 years ago

POSTED BY: Donghwan Roh

Donghwan Roh

Posted 8 years ago

[?] Plot in 3D Cycloid curves on Zylo ??

POSTED BY: Donghwan Roh

Hans Dolhaine

Hans Dolhaine, retired

Posted 8 years ago

Last remark concerning self-made zylos xx[a_, h_] := {Cos[a], Sin[a], Min[h, 1 + Cos[5 a]/2]} zz[a_, h_] := {Cos[a], Sin[a], Min[h, 1 + Cos[5 a]/2]} pol[a_, h_, da_, dh_] := Polygon[{xx[a, h], xx[a + da, h], zz[a + da, h + dh], zz[a, h + dh]}] nda = 60; ndh = 20; ffh = .48; da = 2 Pi/nda; dh = 2/ndh; zylo = Table[{Hue[ffh n dh], Table[pol[m da, n dh, da, dh], {m, 0, nda - 1}]}, {n, 0, ndh - 1}]; Graphics3D[zylo] and Animate[ Graphics3D[Rotate[zylo, u, {0, 0, 1}]], {u, 0, 2 Pi}]

Last remark concerning self-made zylos

xx[a_, h_] := {Cos[a], Sin[a], Min[h, 1 + Cos[5 a]/2]}
zz[a_, h_] := {Cos[a], Sin[a], Min[h, 1 + Cos[5 a]/2]}
pol[a_, h_, da_, dh_] := 
 Polygon[{xx[a, h], xx[a + da, h], zz[a + da, h + dh], zz[a, h + dh]}]

nda = 60; ndh = 20; ffh = .48;
da = 2 Pi/nda; dh = 2/ndh;
zylo = Table[{Hue[ffh n dh], 
    Table[pol[m da, n dh, da, dh], {m, 0, nda - 1}]}, {n, 0, ndh - 1}];
Graphics3D[zylo]

and

Animate[
 Graphics3D[Rotate[zylo, u, {0, 0, 1}]],
 {u, 0, 2 Pi}]

POSTED BY: Hans Dolhaine

Hans Dolhaine

Hans Dolhaine, retired

Posted 8 years ago

POSTED BY: Hans Dolhaine

Hans Dolhaine

Hans Dolhaine, retired

Posted 8 years ago

Poor man's solution (so it was done long long ago): execute Do[ Print[ParametricPlot3D[{Cos[t], Sin[t], s}, {t, 0, 2 Pi}, {s, 0, 1 + 1/2 Cos[5 t + u]}, PlotPoints -> 50, PlotRange -> All, Mesh -> False, ColorFunction -> Function[{x, y, z}, Hue[.75 z]]]], {u, 0, 2 Pi, .3}] Double click on the second bracket from the right. All plots below the 1st one should vanish, and the bracket should be highlighted (in blue). Then press ctrl-shift -y

POSTED BY: Hans Dolhaine

Hans Dolhaine

Hans Dolhaine, retired

Posted 8 years ago

Both of these are nice als well ParametricPlot3D[{Cos[t], Sin[t], s}, {t, 0, 2 Pi}, {s, 0,1 + 1/2 Cos[5 t]}, PlotPoints -> 50, PlotRange -> All, Mesh -> False, ColorFunction -> Function[{x, y, z}, Hue[.75 z]]] and Animate[ ParametricPlot3D[{Cos[t], Sin[t], s}, {t, 0, 2 Pi}, {s, 0, 1 + 1/2 Cos[5 t + u]}, PlotPoints -> 50, PlotRange -> All, Mesh -> False], {u, 0, 2 Pi, 0.1}] But when I try to rotate the colored object my system crashes. What is going wrong? Animate[ ParametricPlot3D[{Cos[t], Sin[t], s}, {t, 0, 2 Pi}, {s, 0, + 1/2 Cos[5 t + u]}, PlotPoints -> 50, PlotRange -> All, Mesh -> False, ColorFunction -> Function[{x, y, z}, Hue[.75 z]]], {u, 0, 2 Pi, 0.1}]

Both of these are nice als well

ParametricPlot3D[{Cos[t], Sin[t], s}, {t, 0, 2 Pi}, {s, 0,1 + 1/2 Cos[5 t]}, PlotPoints -> 50, PlotRange -> All, 
Mesh -> False, ColorFunction -> Function[{x, y, z}, Hue[.75 z]]]

and

Animate[
ParametricPlot3D[{Cos[t], Sin[t], s}, {t, 0, 2 Pi}, {s, 0, 1 + 1/2 Cos[5 t + u]}, PlotPoints -> 50, 
PlotRange -> All, Mesh -> False], {u, 0, 2 Pi, 0.1}]

But when I try to rotate the colored object my system crashes. What is going wrong?

Animate[
 ParametricPlot3D[{Cos[t], Sin[t], s}, {t, 0, 2 Pi}, {s, 0,  + 1/2 Cos[5 t + u]}, 
PlotPoints -> 50, PlotRange -> All, 
  Mesh -> False, ColorFunction -> Function[{x, y, z}, Hue[.75 z]]],
 {u, 0, 2 Pi, 0.1}]

POSTED BY: Hans Dolhaine