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?

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

I am.... Thanks.

Now if you can do that with the point picker, you have Spiro Curves! :o

"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.

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

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

cheers mnu

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

And finally, FresnelCurves script.
Also does a sine and cosine, for curvature = 1.

Feels like "The Outer Limits" ... ! :)

- Michael

He's in my head!

Some Sinusoïds array + Lineweb will make some cool montains landscapes ;)

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

You speak about this?
http://verysimpledesigns.com/vectors/inkscape-tutorial-spiro-swirls.html
by We Design

++ 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

"Outer Limits" and ocsilliscope theater from Ernie Kovacs!

Michael T.

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

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

Ok, that's what I meant. Someone else of course ;-) Thanx for the info Michael

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.
:-))

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