by 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.  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.
Last edited by Regular Polygon on Thu Dec 08, 2011 8:42 am, edited 2 times in total.
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by pilou » Fri Sep 10, 2010 12:39 am
Beauty of the simplicity! 
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by 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.
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by MALAISE » Fri Sep 10, 2010 6:28 am
Thanks to give us an easy tool for drawing such objects MALAISE
La Connaissance n'a de valeur que partagée
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by Dave R » Fri Sep 10, 2010 1:23 pm
Thanks for the cool plugin. 
Etaoin Shrdlu
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by shura » Fri Sep 10, 2010 3:51 pm
Woohoo! Just love your plugins Mr. Polygon, thanks a lot!
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by boofredlay » Sat Sep 11, 2010 1:54 am
Thanks for this.
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by Dave R » Sat Sep 11, 2010 2:56 am
It's kind of fun with Proper Animation.  Sphere Ani.gif
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by boofredlay » Sat Sep 11, 2010 4:29 am
That is cool Dave. How did you do it?
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by 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.
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by pilou » Sat Sep 11, 2010 11:02 am
Soon Christmas 
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by Dave R » Sat Sep 11, 2010 1:31 pm
Pilou wrote:Soon Christmas 
I was thinking exactly the same thing. 
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by 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
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by 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.
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by mequan » Sun Sep 12, 2010 1:23 am
I don't download!!! Why????
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by 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.
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by Dave R » Sun Sep 12, 2010 2:10 am

More playing. I should be doing work.
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by Regular Polygon » Sun Sep 12, 2010 4:06 am
A spherical barber pole! That looks great, Dave. 
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by 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.
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by 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.  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.
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by 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
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by 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.
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by 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
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by 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.
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by watkins » Mon Oct 11, 2010 11:03 am
I look forward to being surprised and delighted.
Kind regards, bob
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