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[WIP] Integral 2d & 3d Curves

About two months ago I started to develop the method for plotting 2d curves by curvature and/or azimuth, distributed along path ("point attributes" in Houdini). This is an integral method, it based on integrating the curve from it's derivatives: Local Azimuth is the 1'st derivative and Curvature is the 2'nd.
Latter, I decided to extend the method to three dimensions. It required research of the Frenet–Serret frame (the local basis) and it's transformations in 3d space to add Torsion and Roll/Twist.
Trying to create a really long curve, I noticed that in this case it is very difficult using a ramp parameters for derivatives. So, I replaced the ramps with the Animation Curves and sample them by "u" attribute. But this replacement is associated with certain difficulties, in the first place now it is not so ease to animate the derivatives (because it's impossible to animate the animation curve itself, but I have to blend together several curves instead).

These three simple curves (right) completely describe any of the 3d spirals (left)

These three simple curves (right) completely describe any of the 3d spirals (left)

The keys are slightly changed

The keys are slightly changed

The old, ramps-based asset (two passes)

The old, ramps-based asset (two passes)

4 spirals and theirs ramps

4 spirals and theirs ramps

How the two-pass construction work

How the two-pass construction work

Arch-like forms

Arch-like forms

Closed curves with complex forms (two passes)

Closed curves with complex forms (two passes)