The simplest function that will do something similar is
y = z.sin(x) --- (1)
This is the straight line y=0 when z=0, and becomes a sine wave of
increasing amplitude as z increases.
Of course, (1) is an infinitely thin sheet, and you want a solid of
thickness, t. That requires:
(z.sin(x) - y - t/2 < 0) ^ (z.sin(x) - y + t/2 > 0)
Where ^ is set-theoretic intersection. It _may_ be possible to put
that into OpenSCAD (http://www.openscad.org/), which will output
printable STL files.
You would probably want to print a chunk of that function intersected
with a cuboid, and upside-down. That way it would taper towards the
top from a fat bottom and so be stable when being printed.
If OpenSCAD can't hack that, make a closed 2D profile of the fattest
section using something like QCAD, save it as a .dxf file, then import
it into OpenSCAD and extrude it while applying a taper.
Also this:
http://reprap.org/wiki/Mendel_User_Manual/Converting_a_simple_2D_image_into_a_printed_object
Is generally useful for this sort of thing.
Best wishes
Adrian
On 07/09/12 16:41, Julian Vincent wrote:
> I've been giving a bit of thought (and revealing a lot of ignorance) to the idea of generating the wavy 'pillars' (which is what the vertical membranes between the layers of a phragmocone are called) with the RepRap machine. The shap is quite intrigueing and looks rather fractal. The insertion of the membrane on the sheet which separates the layers is very wavy with lots of tight curves. These curves become less severe further up the membrane until it becomes relatively smoothly curving. I've put some pictures of this on my university site (http://people.bath.ac.uk/ensjfvv/cuttlebone/). The three images 15, 19 and 21 are plan views of the pillars/membrane as just described, image 20 is a side view showing the pillars between the layers.
> It seems to me that the maths for defining such a membrane, going from wiggly to smooth, ought to be fairly easy to do (i.e. not many lines of code) but I don't know how to do it. Do you? the membrane would then need to be sliced so that it could be produced as layers on the RepRap.
>
> Please help!
>
> Julian Vincent
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