I'm trying to get a curve equation from curve curvature (trying to design a bent air pipe with later boundary layer separation). I should also mention that my math is pretty rusty.
My idea was to have a bend curve that would have a linear decreasing curvature k(s). I checks stackexchange for similar questions (linked bellow) and from my understanding, I would have to define a k(s) function and then integrate it twice.
s - arclength
c(s) - curve equation
k(s) - curvature equation
n(s) - unit normal vector
c''(s) = k(s) * n(s)
How can I get the normal unit vector as a function of arclength s?
Related topics:
Given the curvature, find the equation of any curve in plane