Generalized Euler's Spiral 1-20  21-24

 From: bemfarmer 10 Oct 2011  (1 of 24)
 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 Attachments:

 From: BurrMan 10 Oct 2011  (2 of 24)
 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.

 From: BurrMan 10 Oct 2011  (3 of 24)
 4599.3 In reply to 4599.2 Now if you can do that with the point picker, you have Spiro Curves! :o

 From: bemfarmer 10 Oct 2011  (4 of 24)
 "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. Attachments:

 From: Michael Gibson 10 Oct 2011  (5 of 24)
 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

 From: aixmnu 10 Oct 2011  (6 of 24)
 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

 From: Michael Gibson 10 Oct 2011  (7 of 24)
 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

 From: bemfarmer 10 Oct 2011  (8 of 24)
 And finally, FresnelCurves script. Also does a sine and cosine, for curvature = 1. Attachments:

 From: Michael Gibson 10 Oct 2011  (9 of 24)
 4599.9 In reply to 4599.8 Feels like "The Outer Limits" ... ! :) - Michael

 From: BurrMan 10 Oct 2011  (10 of 24)

 From: Frenchy Pilou (PILOU) 10 Oct 2011  (11 of 24)
 Some SinusoÃ¯ds array + Lineweb will make some cool montains landscapes ;) --- Pilou Is beautiful that please without concept! My Gallery

 From: aixmnu 11 Oct 2011  (12 of 24)
 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

 From: Frenchy Pilou (PILOU) 11 Oct 2011  (13 of 24)

 From: bemfarmer 11 Oct 2011  (14 of 24)
 ++ 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

 From: Michael T. (MICTU_UTCIM) 11 Oct 2011  (15 of 24)
 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

 From: aixmnu 11 Oct 2011  (16 of 24)
 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

 From: Michael Gibson 11 Oct 2011  (17 of 24)
 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