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

 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.


EDITED: 7 Sep 2017 by BEMFARMER