I want to begin by letting you know that my math skills don't go far beyond basic Algebra. I can understand most concepts after a walk-through, but this one is, so far, beyond my capabilities.
What I'd like to know is a) is there a formula for finding the length of x and y control points for a bezier curve based on a specified length of the curve and, if yes, b) can someone please explain it to me in terms I can use and understand with my skill level.
Here's the long version for more context:
I use a program called Seamly to make clothing patterns. The program is open source and uses equations on a grid to produce the drafts. (Please see links for images) Basic Bodice Draft using Seamly
This post explains how to create a curve using the program:
https://wiki.valentinaproject.org/wiki/Creating_Smooth_Curves:_The_Kolson_Method
The problem I run into is that I want to be able to control the length of the curves so that, regardless of the size of the bodice, it will keep the proper circumference around the armhole. Thus, I need to be able to set the length of the curve. The only way to do that in the program would be to use a formula of some sort based on the measurements I know (scye depth, armhole circumference, armhole diameter, etc) to set the control points of the curve.
I was thinking based on the below video from Kahn Academy, that I could use, say, the armhole length and the length of the curve (half the circumference of the arm at the shoulder) and solve for y (the scye depth) to get a length for the control points, but I don't understand how to work back from a given length of curve.
I'm really hoping some kind soul will be able and patient enough to help me. Reading posts with endless Calculus formulas go over my head without real-world context. Thanks!