luxodrome

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JohnGardner
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Joined: 18 Jan 2013, 20:37

luxodrome

Post by JohnGardner » 31 Jul 2013, 16:20

Hi,

I am trying to create a luxodrome in Softimage, but I am not having much luck locating a solution. Is anyone aware of an ICE compound that will create a luxodrome/rhumb?

Here are some technical resources...
http://en.wikipedia.org/wiki/Rhumb_line
http://www.mathematische-basteleien.de/spiral.htm (scroll down & look for loxodrome)

Thanks,
John

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Daniel Brassard
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Location: St. Thomas, Ontario

Re: luxodrome

Post by Daniel Brassard » 31 Jul 2013, 18:41

Very easy in ICE. It is a variation of the helical torus compound.

You already have the parametric formula. The loxodrome is a curve on the sphere, which cuts the meridians at a constant angle.

The parametric representation in Softimage is:

x= cos(t) * cos [1 / tan(at)]
y= - sin [1 / tan(at)]
z= sin(t) * cos [1 / tan(at)]

where a is constant of your choice and t the variable parameter.

Just download my ICE Topo Pack and modify the helical torus compound to match the formula above.

http://www.si-community.com/community/v ... =19&t=2269

Not in front of Soft at this time but can post the ICEtree tonight.
$ifndef "Softimage"
set "Softimage" "true"
$endif

JohnGardner
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Joined: 18 Jan 2013, 20:37

Re: luxodrome

Post by JohnGardner » 31 Jul 2013, 20:33

Great, thanks!! :)

Matic
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Joined: 18 Jun 2009, 19:58

Re: luxodrome

Post by Matic » 01 Aug 2013, 03:24

The "phi" emitter I post on my site http://andy.moonbase.net/archives/1128 here also touches on this.

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Daniel Brassard
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Location: St. Thomas, Ontario

Re: luxodrome

Post by Daniel Brassard » 01 Aug 2013, 06:20

Here you go.

I used the equation on Wolfram for this representation.

http://demonstrations.wolfram.com/LoxodromeArt/
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Last edited by Daniel Brassard on 01 Aug 2013, 13:47, edited 1 time in total.
$ifndef "Softimage"
set "Softimage" "true"
$endif

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Daniel Brassard
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Re: luxodrome

Post by Daniel Brassard » 01 Aug 2013, 06:29

The compound
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$ifndef "Softimage"
set "Softimage" "true"
$endif

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Daniel Brassard
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Re: luxodrome

Post by Daniel Brassard » 01 Aug 2013, 07:02

You can also model very quickly the shape using a sphere

first create a sphere with enough subdivisions (24 x 24)

triangulate the sphere

delete every x polygons along the sphere in the Loxodrome pattern

Apply thickness, subdivide, render
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$ifndef "Softimage"
set "Softimage" "true"
$endif

JohnGardner
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Re: luxodrome

Post by JohnGardner » 01 Aug 2013, 15:26

Thanks Daniel!

JohnGardner
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Re: luxodrome

Post by JohnGardner » 01 Aug 2013, 16:07

Thanks Matic!

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Daniel Brassard
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Location: St. Thomas, Ontario

Re: luxodrome

Post by Daniel Brassard » 01 Aug 2013, 20:38

And here is another version, graciously provided by Stephen on xsisupport blog

http://xsisupport.com/2013/07/31/ice-loxodrome/

So many ways to skin that cat! :D (the loxodrome ... not Stephen) =))
$ifndef "Softimage"
set "Softimage" "true"
$endif