Hi Wayne,
I'll be very busy at work for the next few months, so have not done anything else.
So anything that you want to do is "fair game" :-)
The last thing I was looking into was an end portion of a braid, with a 50% reduction in taper, like the end of a hair braid.
So basically, the scale variable "a", in the braid equation, would not be constant, but would have a "taper" value.
My unfinished, preliminary notes:
Initial problem: Taper a braid by 50%, using arithmetic progression in nodeeditor.
The following link explains taper well, with drawing and formulas:
https://www.mechical.com/2021/02/types-of-taper.html
(They should have put D-d in brackets (D-d))
D is the beginning diameter of the object to be tapered.
d is the ending diameter of the object.
L is the length over which the taper occurs.
K is the Taper Ratio.
DraftAngle is the taper angle. (One side in 2D).
The taper is constant. taper is concerned with diameters.
The +/- sign is + for now.
The taper could be taper up or taper down in diameter size.
In MoI Extrude taper mode, the taper angle is represented by the Draft Angle. (recent James node...)
Taper ratio = K = ( D - d ) / L
theta = DraftAngle = arctan(( D - d ) / 2*L)
The 2 divisor is because the angle is measured on one "side" only.
The taper "revolves" around the axis of symmetry.
*****
using _ for subscript:
The braid equation uses a_i for scale values.
For a reducing braid cross section, (~ diameter),
the scale decreases, and the decrease will be at a constant rate.
The arithmetic progression formula, , is:
a_n = a_1 + (n-1) * factor.
Let a_n = d
Let a_1 = D
For integer values of L: Let n = L+1
Let factor = K = taper ratio, adjusted by step size??? (+/-)
THE ABOVE SECTION IS NOT FINALIZED... (Might be in error, or need modifications?)
(I started to get confused by Integer values, versus ? values...
- Brian
