Hello Friends
An exploration, I think quite interesting,
of a fascinating and particular surface in my opinion, Dupin Cyclide Ring -
how many interested people find the file at this link:
http://www.mediafire.com/file/donow69cg61d4i0/-DUPIN_CYCLIDE_RING.zip/file
Good depth to everyone
Have a nice day to all
al

Hi Friends ,
Continuing the most particular knowledge
Polyhedra world , of those interested will find here:
http://www.mediafire.com/file/yir88miie279n5i/M__Pipe_Frame_%2526_Knot_Polyhedron.zip/file
a Macro that I think can be useful ..
at least I hope..
-Pipe Frame and Knot on Polyhedron -

Have a nice weekend everyone
al

I see a rugby ball and a dog bone! :)

Hello Friends
Those interested find here:
http://www.mediafire.com/file/v7wqaaezhxhtr5r/Open_the_Door.zip/file
the file related to the movement of a particular
door (Austrian author-KlemensTorggler),view long ago in the Web....
Have a nice day to all
al

Hi Al et al,

That's very cool. I was impressed by door mechanism video on dezeen: https://www.dezeen.com/2014/02/11/door-reinvented-with-folding-mechanism-by-klemens-torggler/
but even better to see it animated in NE. Great work.


Maybe you can help me with a problem.
I have been trying to get my head around voronoi tessellation.
(I recognise that this may be a redundant exercise if/when Max converts his script to a node)

I have started with a mesh of triangles*, applied planar, extracted edges,
getStframe, generate 3ptCircle and find centers with BoundingBox node.

Now it is a matter of drawing lines between centers.
This involves incrementally taking pointDist for each point with the rest
and drawing the shortest (extract Min - compare - split),
then repeating for new minimum distance (2nd shortest) & again for 3rd shortest.

I have not included the nod file because frankly it is not even close to working as I desire.
Perhaps this is beyond NE as is, but I thought you or someone else might have an idea of how to proceed.

James

*Ideally, what I want to do is input a field of points and apply a Delaunay triangulation as my starting point;
though if that was possible, the same code could probably achieve voronoi meshing as well.

Very cool door!

Hello James
Many Thank you for your appreciation .... -

About Voronoi, I also tried to do something,
but I did not go further than you ...
My problem is that I can not sort with a logic (that is
very special), the points obtained as centers of the Circles
circumscribed to the source triangles, to obtain the ngon poly ...
I saw on the web the creation of the progressive field using
Lloyd's algorithm ... I have to say real poetry, almost magic
but all of this higher mathematica ..... unfortunately very far from my level-
I hope that Max or Karsten can soon give us this Node
Have a nice evening
al

This Delaunay and Voronoi stuff could be interesting in the future imho,
in case you could process also images with that in MoI, based on a point
set.

I played today with some old tools on my Mac and came up with the
idea to laser cut those Delaunay / Voronoi Designs, because i have
found a service which is imho pretty cheap and has lot's of materials
to choose from.


free photo hosting

Regards
Stefan

Hi All,

I deleted my last post because I was getting sidetracked, & the solution was much more obvious.
It is to find circumCircle centre and draw lines to midPts of triangle edges like so.



I will do some further development of this approach, but I think I'm on the right track.
James

Hi James
I think it's the right method ...
divide the sides of each triangle in the middle, join the center
with these points ...(so far I have arrived here too)
but,what is the final method to obtain distinct poly ngon ?
for me this is the obstacle to overcome
al

Hi Al (and others),

I have attached nod file for generating voronoi pattern from field of tessellated triangles (also attached).
This turned out to be far less complicated than originally thought. The real problem to solve now is converting
a field of points to delaunay triangulation.

James

Wow!!!

Thanks Karsten, but it wouldn't be possible without your foundational node contributions.
Have you been working on anything new?
James

Hi James and Friends
I saw your file, ingenious enough to create
a thicker along the edges of the polygons, then working
with the boleans we will get what we want ...
but it still does not work ...
In any cases where we want an integral polygon, we can not do it
because the connecting lines of the centers with the midpoints
the edges of the triangles intersect each other ...
even more if the mesh of the triangles and pretty uneven
here:
http://www.mediafire.com/file/1pf6zo59nkj5uq1/VORONOI.zip/file
you will find files that will better illustrate the problem,
I have also worked on your file, deforming the triangular mesh a little
and trying to lower the size of the line
(Sweept profile) but, under a certain value you can not go,
and so, as you will see, the result is not ,according to me, yet
satisfactory
have a nice day
al

Hello James,
>>Have you been working on anything new?

I'm afraid not. I'm in the middle of divorcing my wife.

Some day I will start again.
Karsten

Hi Karsten,

I'm sorry to hear that. I can only imagine how dispiriting that must be.
Please feel free to PM me if you need to vent to a sympathetic ear.
Perhaps a friend you've never met would be the perfect sounding post.

>> Some day I will start again. <<

For our sake, but mostly yours, I hope that day is soon
All the best
James

Hi Friends
I continue with my research and study of interesting surfaces ,
and now it is the turn of this fairly recent geo-mathematical form
due to the genius and research of Paul Schatz ,
it was born only in 1939 and therefore relatively young ...
and In my opinion it is a charming, elegant shape that leaves
with open mouth......
how many interested will find here:
http://www.mediafire.com/file/9ftdpaksnr1mn2e/Oloid.zip/file
the math construction file of the form (relatively simple, I must say)
and a small simulation of movement ...
The Oloid is the only three-dimensional shape that can rotate over its entire surface.
and put in oscillating produces a movement of great charm,
on the web you will find news about the use of this shape to reproduce in the water
a wave similar to the natural one
Have a nice evening to all
al

Hi all,

sorry for being off-topic, but i like to show you my aluminium sign,
from schildermaxe.de (excellent quality) from my previous post
here. Hope you like!



P.S. i did not went for laser engraving, because the price was to high.
Instead i used a sign maker service.

Regards
Stefan