Script for Natural Logarithmic 3d Spiral, Frenet-Serret Frame, Runge-Kutta

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 From:  bemfarmer
4955.1 
Attached is a script for creating 3D curves, with the Frenet-Serret equations.
This script creates 3D logarithmic curves as in "The Natural 3D Spiral" by Gur Harary and Ayellet Tal.
Many other curves can be created, by changing Kappa and Tau.
A 12 page pdf information file is included.
Michaels information on Vectors and Points was essential.
The javascript is a bit slow. The code is not optimized, and is crude.

The new OffsetMultiStep script is helpful in creating circles to sweep.





EDITED: 10 Aug 2013 by BEMFARMER


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 From:  Michael Gibson
4955.2 In reply to 4955.1 
Cool seashell form, Brian!

- Michael
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 From:  fleetfoot
4955.3 In reply to 4955.2 
Err...

I'm just a designer, not a mathematician. Do I need this? I can't even read the PDF without my eyes going crossed.
Thanks a bunch and I'm sure it will be very useful down the line to someone.

I always liked the way you could hear the ocean if you put the sea shell to your ear.

DOH!

-fleetfoot
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 From:  Ambimind
4955.4 In reply to 4955.1 
A very pleasing form and well written paper.
I have a passion for mathematics in computer graphics(in particular shader programming), so this type of thing makes my day :)

Thanks for your efforts,
Kiril
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 From:  bemfarmer
4955.5 
A minor modification to the script creates 3D Euler spirals, also known as 3D Clothoids.

// Reference: "3D Euler Spirals for 3D Curve Completion" by Gur Harary
// and Ayellet Tal. Also "Piecewise 3D Euler Spirals" and "Visualizing 3D Euler Spirals" http://cgm.technion.ac.il/people/Gur/

// Script version 1 just makes a curve. V1 does NOT do the gradient-descent,
// which is described in the reference as, given two points, and their
// associated tangents (x0, T0) , (x1, T1), find the four curvature and
// torsion parameters, and Euler spiral Length, in order to connect the
// two points with a segment of an Euler spiral.

So in conclusion, a useable tool may be possible to create, which is of actual use to a MoI user, besides making seashells or organic forms :-), which would connect two points having tangents, on existing models.



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 From:  bemfarmer
4955.6 In reply to 4955.1 
Per request from James E, Marbleman,
here a these two 4 year old scripts in .zip format.
- Brian

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 From:  Marbleman
4955.7 In reply to 4955.6 
Brian

Thank you for taking the time to do this

James
www.jameselliott.co.uk
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