[Plugin] Spherical Helix (Luxodrome) 1.1

Regular Polygon · 9 Sept 2010, 21:18

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.

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.

%(#BF0000)[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.

pilou · 9 Sept 2010, 23:39

Beauty of the simplicity!

Regular Polygon · 10 Sept 2010, 02:31

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

MALAISE · 10 Sept 2010, 05:28

Thanks to give us an easy tool for drawing such objects

MALAISE

Dave R · 10 Sept 2010, 12:23

Thanks for the cool plugin.

shura · 10 Sept 2010, 14:51

Woohoo! Just love your plugins Mr. Polygon, thanks a lot!

boofredlay · 11 Sept 2010, 00:54

Thanks for this.

Dave R · 11 Sept 2010, 01:56

It's kind of fun with Proper Animation.

boofredlay · 11 Sept 2010, 03:29

That is cool Dave. How did you do it?

Dave R · 11 Sept 2010, 03:42

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.

pilou · 11 Sept 2010, 10:02

Soon Christmas

Dave R · 11 Sept 2010, 12:31

@unknownuser said:

Soon Christmas

I was thinking exactly the same thing.

simon le bon · 11 Sept 2010, 19:26

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 said:

../
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

Dave R · 11 Sept 2010, 22:55

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.

mequan · 12 Sept 2010, 00:23

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

Dave R · 12 Sept 2010, 00:54

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.

Dave R · 12 Sept 2010, 01:10

More playing. I should be doing work.

Regular Polygon · 12 Sept 2010, 03:06

A spherical barber pole! That looks great, Dave.

simon le bon · 12 Sept 2010, 12:10

@dave r said:

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.

Regular Polygon · 9 Oct 2010, 19:01

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.