Ronaldo Persiano rcmpersiano at gmail.com
Fri Jun 10 13:08:48 EDT 2016

```One more point: Rudolf, who I suppose is German, referred to a minimal
surface created by Schwartz, who I suppose is German too. I would like to
render a minimal surface created by a Brazilian mathematician (I am a
Brazilian too): the Costa surface. But I have not found any implicit form
of it. If someone give me a reference for that I would be very grateful.

Ronaldo

2016-06-10 13:56 GMT-03:00 Ronaldo <rcmpersiano at gmail.com>:

> Parkinbot wrote
> > this looks good and shows that your Frep-stuff is working well, besides
> > that it could profit from some (implicit) grid refining scheme near the
> > borders.
>
> Yes, the borders are a lot rough. I did not implemented any feature
> detection scheme. They are a lot harder to implement. A local refining
> scheme would improve the edges but they would be rough anyway.
>
> > Ok, you use the triple cosine shortcut instead of the minimal surface
> > calculation, but this is another theme.
> > To be able to print it, one would also like to have a skin extruded
> > structure, which was the point where my effort (and time) ended.
>
> I used the approximation I found in Wikipedia. I am not acquainted to the
> minimal surface theory and have not found any exact implicit form of the
> surface.
>
> By changing the code a little and redefining the Schwartz primitive, I got
> the following:
> The upper image represents just the surface and it is not a manyfold. It
> was
> obtained by commenting 4 lines of the f_mesh_evaluation code eliminating
> the
> six bounding box of the mesh.
>
> The lower image seems to be what you wanted. The Schwartz primitive for
> that
> was simply redefined as:
>
> > function Schwartz_p(pt, a,b,c,d) =
> >     let( s = a*cos(pt[0]) + b*cos(pt[1]) + c*cos(pt[2]) )
> >     min( s, - s + d);
>
> So, the inside surface was obtained just by doing an "offset" of the
> original function value and the min() is equivalent to an intersection.
> That
> is one of the marvelous things of the implicit representation of f-reps.
>
> This last run took a longer time to preview: 20min. So, I think we are in
> the wrong thread to discuss this subject :)
>
> > BTW, I used an ordinary R²->R function plot after resolving the implict
> > equation to z and discretrizing it over a domain restricted to the
> partial
> > symmetry. While this gives you a nice border around the top hole, you can
> > use union operations to repeat the rendered chuck for all symmetries with
> > the required orientation.
>
> I have no idea of what you are saying here. But I tip my hat to you.
>
> @jon, I could not say it better.
>
>
>
>
> --
> View this message in context:
> Sent from the OpenSCAD mailing list archive at Nabble.com.
>
> _______________________________________________
>
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