Enneper Surface Script  1-20  21-26

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 From:  bemfarmer
6521.1 
Here is a script to create Enneper minimal surfaces.

The nearly identical parametric equations come from:
https://sites.google.com/site/workofap/surface
or http://rhino3.de/_develop/__v3_plugins/math/library.shtml
The rhino math library is kind of like _FxGraph.

Setting the Min Radius to a small value like 0.25 creates a hole in the middle.
The Max Radius can be set a little more than 1.0.

Network works to create a surface, when the radius is 1.0, with the "radial-ish" curves.
Loft works to create a surface, when the radial-ish curves are not present.

- Brian








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 From:  Frenchy Pilou (PILOU)
6521.2 
Flowers before spring !
---
Pilou
Is beautiful that please without concept!
My Gallery
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 From:  wastzzz
6521.3 
Bellissimo!
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 From:  Frenchy Pilou (PILOU)
6521.4 

EDITED: 18 Feb 2014 by PILOU

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 From:  Max Smirnov (SMIRNOV)
6521.5 
Great! Really cool script!
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 From:  TOM (SIRTOM)
6521.6 In reply to 6521.5 
Hi,

I am adding a link here

http://www.indiana.edu/~minimal/maze/figures/planarenneper.jpg

and the question how to achieve a planarenneper - is it generated with another formula or
just a variation of the Bemfarmer-script ?

EDITED: 24 Apr 2016 by SIRTOM

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 From:  bemfarmer
6521.7 In reply to 6521.6 
Hi Tom,

Based upon limited google-ing, apparently the "planar enneper" is a "Richmond_surface" combination of plane and enneper.

for m=2, there is a real parametric expression here, which looks fairly simple:

https://en.wikipedia.org/wiki/Richmond_surface

I have not seen a javascript program for Weierstrass. :-)

https://en.wikipedia.org/wiki/Weierstrass%E2%80%93Enneper_parameterization

- Brian

https://www.math.hmc.edu/~gu/curves_and_surfaces/surfaces/richmond.html

EDITED: 24 Apr 2016 by BEMFARMER

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 From:  TOM (SIRTOM)
6521.8 In reply to 6521.7 
"which looks fairly simple"

Well "simple" is relative ;-)

The simpliest, for me, will be to build it by hand and forget
about this intimitating formulas :-)
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 From:  Ken (OKURO)
6521.9 In reply to 6521.1 
First of all thank you for your fantastic contributions, simply great !

I tried to install the rhino math plugin,, download link:
http://rhino3.de/_develop/__v3_plugins/math/MathForV5.zip
but unfortunately the math library is missing
and may be that also the VBscript libraries are missing ?
I am wondering if you happen to know another source to download?
Very many thanks,

Ken
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 From:  bemfarmer
6521.10 
Here is a draft script of the Richmond surface, which has Enneper end near the center, and Planar end at the periphery.
Order can be increased for more ruffles.
Additional description is in the .js file.

- Brian

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 From:  TOM (SIRTOM)
6521.11 In reply to 6521.10 
Have not been at the forum for a couple of days and coming back - guess what - just discovered that bemfarmer has
come up with a new script !! Awesome Sunday surprise. And THANK YOU so much Mr bemfarmer for wiring up
this nice little tool - I am amazed.
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 From:  TOM (SIRTOM)
6521.12 In reply to 6521.11 
Hi.

The enneper script by default generates curves with dimensions between 0 and around 3mm.
I create lofts from them and these surfaces should fit with others of much larger scale (between 30
and 100 mm) So it would make work more fluid if I were able to create the enneper curves at
a bigger / chosen scale. (increasing the "max" value wont help as this drastically changes the shape
of the generated curve. My question here is :

What do I have to insert in the script to create curves with a bigger radius, example 100 mm ?

EDITED: 2 Jun 2016 by SIRTOM

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 From:  James (JFH)
6521.13 In reply to 6521.12 
Tom,

Not sure if this helps, but attached is a very simple .nod file
for enneper generation that can be scaled.

-James

Attachments:

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 From:  mkdm
6521.14 In reply to 6521.13 
Hi James,

Thank's a lot!

How much can be eclectic the MathArray Node made by Max ?!!

It would be fantastic if almost every plugin written until now for Moi,
could be rewritten for NodeEditor!!!

Nice day,

Marco (mkdm).
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 From:  TOM (SIRTOM)
6521.15 In reply to 6521.13 
Thankyou James. Does the Nodeeitor work for V2 ?
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 From:  James (JFH)
6521.16 In reply to 6521.15 
Tom,

>> Does the Nodeeitor work for V2 ?

I don't know, I'm using V3.
I can't see why it wouldn't.
Give it a go, it's great fun.

Good Luck
-James
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 From:  TOM (SIRTOM)
6521.17 In reply to 6521.16 
Looks like an amazing tool - will have a look and hope to find instructions
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 From:  Frenchy Pilou (PILOU)
6521.18 
About the Node Enneper : Maybe you must limit number of Lobes to 12!
It's freezes and blocks Moi over 12 ! (in reasonable time)

EDITED: 2 Jun 2016 by PILOU

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 From:  TOM (SIRTOM)
6521.19 In reply to 6521.18 
No nodes possible in V2. Thinking about transition to V3 but there are
still lots of secrets for me to unpack in V2 before getting to know all
the new treasures hidden in V3.
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 From:  TOM (SIRTOM)
6521.20 


Hi.

The Enneper script generates curveswith very small dimensions around 1,5 mm.
Is there a way to change some numbers in the script to be able to generate curves with much larger dimension - I am currently curves with MaxRadiis around 170mm.

I achieve this by scaling, of cours, bur would be very helpful toe get the desired size directtly.

TOM

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