Generalized Euler's Spiral  1-20  21-24

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 From:  bemfarmer
4599.1 
Attached is MoI script for generating Euler's Spiral, with curvature factor of 2. It is 2Dimensional.
It was very difficult to do, :) , which is why the script has so many comments.

When the curvature factor is 1, a circle forms.
For fractional curvature factor, another spiral forms. What is it called?

I've also done a script for sine(x*x) and cosine(x*x), if anyone is interested.

May do a quick Fresnel script.

Debug tip of the day, Math.PI is correct. Math.pi is incorrect, and makes factory.update(); very unhappy.
Maybe because the points became text? Used alert("to here4") in script to locate the problem area.

Also attached text file of long, redundant notes, mentioning benefits of Euler's Spiral.
Maybe a tool could be programmed to connect point1 with tangent1, to point2 with tangent2.
Does MoI have any way to say what the tangent is at a point on a curve?













EDITED: 27 Mar 2012 by BEMFARMER


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 From:  BurrMan
4599.2 In reply to 4599.1 
""""""""I've also done a script for sine(x*x) and cosine(x*x), if anyone is interested."""""""""

I am.... Thanks.
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 From:  BurrMan
4599.3 In reply to 4599.2 
Now if you can do that with the point picker, you have Spiro Curves! :o
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 From:  bemfarmer
4599.4 
"Spiro" has a patent application: US Patent Application 20080005212 - METHOD AND APPARATUS FOR INTERACTIVE CURVE GENERATION
so this may limit what can be done?

Clothoids and Euler's spirals have been around for a few hundred years.

Attached are the very simple sine and cosine squared scripts.
The hardest part was figuring out what to square in Michaels sinewave script.

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 From:  Michael Gibson
4599.5 In reply to 4599.4 
I've approached the author of Spiro previously and unfortunately he seems to be too busy with his current work at Google to do anything more with Spiro or offer it for commercial licensing or anything like that.

- Michael
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 From:  aixmnu
4599.6 In reply to 4599.5 
But aren't spiro spirals implemented in Inkscape? How can this be if it is patented?

cheers mnu
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 From:  Michael Gibson
4599.7 In reply to 4599.6 
Hi mnu,

> But aren't spiro spirals implemented in Inkscape? How can
> this be if it is patented?

Spiro is licensed with a GPL license, which means it can be used in open source projects but not in commercial non-open-source applications.

So basically the license restricts how it can be used and the developer does not seem to be interested in other kinds of licensing at this time.

- Michael
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 From:  bemfarmer
4599.8 
And finally, FresnelCurves script.
Also does a sine and cosine, for curvature = 1.



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 From:  Michael Gibson
4599.9 In reply to 4599.8 
Feels like "The Outer Limits" ... ! :)

- Michael
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 From:  BurrMan
4599.10 In reply to 4599.9 
He's in my head!
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 From:  Frenchy Pilou (PILOU)
4599.11 
Some Sinusoïds array + Lineweb will make some cool montains landscapes ;)
---
Pilou
Is beautiful that please without concept!
My Gallery
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 From:  aixmnu
4599.12 In reply to 4599.7 
Hi Michael,

thanx for the clarification. Too bad. Spiros are really very powerful and I have not yet found a 3D implementation in any sofware although his original paper has some thoughts about generalizing the concept to 3 dimensions, too.

Would it be possible to develop this as an open source plugin for MOI with the GPL license then?

Best Manuel
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 From:  Frenchy Pilou (PILOU)
4599.13 

EDITED: 11 Oct 2011 by PILOU

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 From:  bemfarmer
4599.14 
++ on the mountains.

Here is a link to paper "Euler Spiral for Shape Completion" dated 2001. Uses "biarcs" also.
http://www.lems.brown.edu/vision/publications/Kimia's_Publication/Journals/Euler_spiral-IJCV.pdf

Another paper "3D Euler Spirals for 3D curve Completion," 2010:
http://webee.technion.ac.il/~ayellet/Ps/10-HT.pdf
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 From:  Michael T. (MICTU_UTCIM)
4599.15 In reply to 4599.9 
"Outer Limits" and ocsilliscope theater from Ernie Kovacs!

Michael T.
Michael Tuttle a.k.a. mictu http://www.coroflot.com/DesignsByTuttle
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 From:  aixmnu
4599.16 In reply to 4599.13 
yes exactly. I'm using these spiros on a regular basis inside inkscape and cannot live without them anymore. I don't use them for swirls though but in my workflow they pretty much replaced the bezier curves altogether.

cheers mnu
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 From:  Michael Gibson
4599.17 In reply to 4599.12 
Hi Manuel,

> Would it be possible to develop this as an open source plugin
> for MOI with the GPL license then?

That could be possible if someone else wanted to do that. But I myself try to be careful to avoid GPL-dependent code.

- Michael
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 From:  aixmnu
4599.18 In reply to 4599.17 
Ok, that's what I meant. Someone else of course ;-) Thanx for the info Michael
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 From:  bemfarmer
4599.19 
Attached is a slider version of the generalized Euler spiral.
The original was only downloaded 21 times, so not very popular.
This script does nothing more than the original, but does it with a slider option.
See slider post for invaluable slider information.
:-))

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 From:  BurrMan
4599.20 In reply to 4599.19 
Thanks Bem,
Now if you can incorporate a "vertical step" like found in the radial array tool, then you might see a large amount of downloads!!! :o
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