Re: Getting 3d printable models out of 3d graphics in Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg121003] Re: Getting 3d printable models out of 3d graphics in Mathematica
• From: Yves Klett <yves.klett at googlemail.com>
• Date: Sun, 21 Aug 2011 05:32:33 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j2o22h\$50p\$1@smc.vnet.net>

```Complex topic.

For one, your face normals are not directed uniformly. Try

a := 10;
b = 2;
c = 3;
Clear[f, g]
f[t_] = Cos[t];
g[t_] = Sin[t];
gr = ParametricPlot3D[{f[t] f[p/b] - (a + g[t])*
g[p/c], ((a + g[t])*f[p/c] + f[t] g[p/b]) f[
p/b], ((a + g[t])*f[p/c] + f[t] g[p/b]) g[p/b]}, {t, 0,
2 Pi}, {p, 0, 12 Pi}, PlotPoints -> 100, Axes -> None,
Mesh -> None, Boxed -> False];
Graphics3D[{FaceForm[Blue, Yellow], gr[[1]]}]

which shows by means of FaceForm the normal direction of the polygons.
If they face the wrong way, they are ignored by some interpreters and
this messes up your file. I had also an instance where non-convex
polygons were not triangulated as expected by Export, although this
would probably not happen with standard 3D plots and convex polygons.

Regards,
Yves

Am 20.08.2011 12:25, schrieb Roger Bagula:
> Surfaces that appear fine in Mathematica aren't accepted
> to be printed by: ( *.obj,*.dxf,*.stl,...others)
> http://www.shapeways.com/
> or need to be repaired at:
> http://www.sculpteo.com/
> http://www.sculpteo.com/en/gallery/public/user/rlbagulatftn/
> I give an example of one that Mathematica 8 failed on yesterday
> from my old work TFTN:
> (* b=c=1 torus cycloid*)
> (* b=2,c=1 baseball seam *)
> (* by R. L. BAGULA 10 JULY 1997=A9 *)
>
> a:=10;
> b=2;
> c=3;
> Clear[f,g ]
> f[t_]=Cos[t];
> g[t_]=Sin[t] ;
> gr=ParametricPlot3D[{f[t] f[p/b]-(a+g[t])*g[p/c],
> ((a+g[t])*f[p/c]+f[t] g[p/b]) f[p/b],
> ((a+g[t])*f[p/c]+f[t] g[p/b]) g[p/b]},
>     {t,0,2Pi},
> {p,0,12 Pi},
>  PlotPoints->100,PlotStyle->{Orange,Specularity[White,10]},Axes-
>> None,Mesh->None,Boxed->False]
> Export["kleinbottle_angcycloid_2_3.stl", gr]
> But I have many examples.
> I want to know if there is some test I can do on a model using
> Mathematica? Brice and other ray tracing programs which don't have
> "physical" requirements have no trouble with Mathematica model.
> One well known artist has a whole series of work based on one of my
> model fractals.
> (* 128*6128*128 CUBE OF xy,yz,zx  beta triangle 3D *)
> (* BY R. L. BAGULA 30 May 2004=A9*)
> a=64;
> b1 = Beta[Abs[a - Abs[a - x]], Abs[a - Abs[a - y]]]
> b2 = Beta[Abs[a - Abs[a - y]], Abs[a - Abs[a - z]]]
> b3 = Beta[Abs[a - Abs[a - x]], Abs[a - Abs[a - z]]]
> g=Flatten[Table[If[Mod[1/(b1*b2*b3),2]==1,
> Cuboid[0.5*{x,y,z}],{}],
> {x,0,2*a},{y,0,2*a},{z,0,2*a}]];
> gg=Show[Graphics3D[g,Boxed->False,ViewPoint->{-3.059, 8.168, 2.221}]]
> Export["betaholeycube.stl", %]
> And after repair this was accepted for printing at:
> http://www.sculpteo.com/
>
> Roger Bagula
>

```

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