[Plugin] Spherical Helix (Luxodrome) 1.1

[Plugin] Spherical Helix (Luxodrome) 1.1

Postby Regular Polygon » Thu Sep 09, 2010 10:18 pm

This plugin draws spherical helix, also called a luxodrome. It is a spiral curve on the surface of a sphere, which crosses all meridians of longitude at the same angle. It is another type of spherical spiral, other than the Archimedean spherical spiral I posted a week ago.

I like to think of it as the path a ship would trace across the globe if it always pointed in the same direction relative to true north. :geek: The curve below is an example of a course that proceeds slightly north of east, by 5 degrees, at every point.

spherical helix.png


M.C. Escher used this curve in his drawing, Sphere Spirals.



Using a lofting plugin to create a surface between two spirals, and then making 4 copies of the "ribbon", I constructed a crude depiction of Escher’s drawing in SketchUp.

escher.png



CHANGE LOG

*** Version 1.1 - October 7, 2010 ***
More accurate. Computes the exact values for the points on the curve.


The Loxodrome Plugin is at: regularpolygon.org/plugins/loxodrome.php.

Thanks.
0
Last edited by Regular Polygon on Thu Dec 08, 2011 8:42 am, edited 2 times in total.

Regular Polygon 
PluginStore Author
PluginStore Author
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby pilou » Fri Sep 10, 2010 12:39 am

Beauty of the simplicity! :fro:
0
Frenchy Pilou
Is beautiful that please without concept!
Speedy Galerie
User avatar
pilou 
Top SketchUcator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby Regular Polygon » Fri Sep 10, 2010 3:31 am

Yeah, geometry has its own sort of beauty -- one reason why I prefer graphics programming to web development.
0

Regular Polygon 
PluginStore Author
PluginStore Author
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby MALAISE » Fri Sep 10, 2010 6:28 am

Thanks to give us an easy tool for drawing such objects :thumb: :thumb:

MALAISE
0
La Connaissance n'a de valeur que partagée
User avatar
MALAISE 
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby Dave R » Fri Sep 10, 2010 1:23 pm

Thanks for the cool plugin.

0
%

(THERE'S NO PLACE LIKE)

G28 X0.0 Y0.0 Z0.0

M30

%
User avatar
Dave R 
Global Moderator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby shura » Fri Sep 10, 2010 3:51 pm

Woohoo! Just love your plugins Mr. Polygon, thanks a lot!
0
User avatar
shura 
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby boofredlay » Sat Sep 11, 2010 1:54 am

Thanks for this.
0
User avatar
boofredlay 
Global Moderator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby Dave R » Sat Sep 11, 2010 2:56 am

It's kind of fun with Proper Animation. :D
Sphere Ani.gif
0
%

(THERE'S NO PLACE LIKE)

G28 X0.0 Y0.0 Z0.0

M30

%
User avatar
Dave R 
Global Moderator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby boofredlay » Sat Sep 11, 2010 4:29 am

That is cool Dave. How did you do it?
0
User avatar
boofredlay 
Global Moderator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby Dave R » Sat Sep 11, 2010 4:42 am

Hi Eric,

Thank you.

I made a spherical helix, copy, rotated it 60 degrees (I think) and used Chris's Simple Loft to make the ribbon which I copy/rotated to make the other two. Then I set up a pair of scenes and used Proper Animation to get a start and end position. the difference between the two positions is that the ribbons were rotated 180°. The funny thing is that when I switched from scene to scene, I got what you see. I was kind of expecting something like a barber pole but this was cooler.

I made a video screen grab with Snagit and an animated GIF in VirtualDub.
0
%

(THERE'S NO PLACE LIKE)

G28 X0.0 Y0.0 Z0.0

M30

%
User avatar
Dave R 
Global Moderator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby pilou » Sat Sep 11, 2010 11:02 am

Soon Christmas :fro:
0
Frenchy Pilou
Is beautiful that please without concept!
Speedy Galerie
User avatar
pilou 
Top SketchUcator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby Dave R » Sat Sep 11, 2010 1:31 pm

Pilou wrote:Soon Christmas :fro:


I was thinking exactly the same thing. :D
0
%

(THERE'S NO PLACE LIKE)

G28 X0.0 Y0.0 Z0.0

M30

%
User avatar
Dave R 
Global Moderator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby simon le bon » Sat Sep 11, 2010 8:26 pm

Dear Dave,
First I have no idea with the process you have used to produce this rendered luxodrome
But I like it very much.

secondly,
Dave R wrote:../
I made a spherical helix, copy, rotated it 60 degrees (I think) and used Chris's Simple Loft to make the ribbon
have you really used Chris's Simple Loft to make the ribbon? As far as I Know about it we can't skin two joining curves with it!! If there is a way, please be kind to report it.

Dear Regular Polygon,
thank you for this new plugin. I have I think bookmarked each of them.

++simonlebon
0
User avatar
simon le bon 
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby Dave R » Sat Sep 11, 2010 11:55 pm

Simon,

In both cases I used Simple Loft and set the number of segments to 1. The ends of the helices are trimmed off so they are close to in alignment. They actually don't touch each other. It does seem like a long wait for the plugin once you start it but you just wait a little bit and it creates the skin just fine. Your super computer may be much faster than my old dinosaur.

As far as rendering the first one, I used some sketchy line style and rough paper texture style I have (can't remember which) and then exported a JPG. I added some grain, haze and the purplish gradient in Picasa.
0
%

(THERE'S NO PLACE LIKE)

G28 X0.0 Y0.0 Z0.0

M30

%
User avatar
Dave R 
Global Moderator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby mequan » Sun Sep 12, 2010 1:23 am

I don't download!!! Why????
0

mequan 
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby Dave R » Sun Sep 12, 2010 1:54 am

The link at the bottom of the original post should take you to Regular Polygon's blog from which you should be able download the plugin.
0
%

(THERE'S NO PLACE LIKE)

G28 X0.0 Y0.0 Z0.0

M30

%
User avatar
Dave R 
Global Moderator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby Dave R » Sun Sep 12, 2010 2:10 am



More playing. I should be doing work.
0
%

(THERE'S NO PLACE LIKE)

G28 X0.0 Y0.0 Z0.0

M30

%
User avatar
Dave R 
Global Moderator
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby Regular Polygon » Sun Sep 12, 2010 4:06 am

A spherical barber pole! That looks great, Dave. :thumb: :D
0

Regular Polygon 
PluginStore Author
PluginStore Author
 

Re: [Plugin] Spherical Helix (Luxodrome)

Postby simon le bon » Sun Sep 12, 2010 1:10 pm

Dave R wrote:Simon,

In both cases I used Simple Loft.../
.../I added some grain, haze and the purplish gradient in Picasa.



Clever & Simple as usual dear Dave. Thanks a lot ;) , simon.
0
User avatar
simon le bon 
 

Re: [Plugin] Spherical Helix (Luxodrome) 1.1

Postby Regular Polygon » Sat Oct 09, 2010 8:01 pm

Update to Version 1.1.

The original version used an approximation to compute the points on the curve -- unfortunately, I couldn't solve the math for the exact equations. :oops: Since then, I came across the equations that do compute the exact values for the coordinates of each point. They are implemented in Version 1.1.

The difference in the spherical helix between the two versions is not really noticeable. But, if you are doing something that requires accuracy, then it might be worth downloading this latest version.
0

Regular Polygon 
PluginStore Author
PluginStore Author
 

Re: [Plugin] Spherical Helix (Luxodrome) 1.1

Postby watkins » Sat Oct 09, 2010 10:26 pm

Perhaps it is time to bundle your plugins into one folder with a toolbar. I'm sure that CADFather could come up with some pretty good icons.

Thank you for all your hard work.

Kind regards,
bob
0

watkins 
 

Re: [Plugin] Spherical Helix (Luxodrome) 1.1

Postby Regular Polygon » Sat Oct 09, 2010 11:39 pm

Well, I only have 8 or 9 plugins at this point. Once I hit an even dozen, I should release an author-menu type plugin. That would be an option for people who like to organize their plugins by author.
0

Regular Polygon 
PluginStore Author
PluginStore Author
 

Re: [Plugin] Spherical Helix (Luxodrome) 1.1

Postby watkins » Sun Oct 10, 2010 11:49 am

That would be good, but a toolbar would be better (well, for me anyway).

What new plugins do you have in the pipeline?

Kind regards,
Bob
0

watkins 
 

Re: [Plugin] Spherical Helix (Luxodrome) 1.1

Postby Regular Polygon » Mon Oct 11, 2010 7:18 am

Thanks for your feedback, Bob. I'll think about your toolbar suggestion -- or, at least, let it simmer on the back burner.

So, what is in the pipeline? Well, when I am not distracted with the 3D printed lamp Design Challenge, I am working on a new project. All I can say at this point is that it does not involve geometry creation -- for once. If I don't hit any snags, I should have a lot more to say about it in a couple weeks.
0

Regular Polygon 
PluginStore Author
PluginStore Author
 

Re: [Plugin] Spherical Helix (Luxodrome) 1.1

Postby watkins » Mon Oct 11, 2010 11:03 am

I look forward to being surprised and delighted.

Kind regards,
bob
0

watkins 
 

SketchUcation One-Liner Adverts

by Ad Machine » 5 minutes ago



Ad Machine 
Robot
 



 

Return to Plugins

Who is online

Users browsing this forum: Jakcy, makelldyan and 11 guests

Visit our sponsors: