I'm trying to understand the logic (theory?) behind the offset/parallel curve for the design of a radial diffuser.
I found the equations for a 2D parametrical offset curve on wiki, where the normal unit vector to the original curve is defined as the first derivative of the original curve.
However, in this article , the normal vector is defined as a second drivative of the original curve.
What I'm trying to achieve is: I would like to define the equation of the offset curve and then play around a little bit to make it "progressive" compared to the original curve.
My original curve is:
$a_3=11.482$
$b_3=-10.629$
$c_3=0$
$r_3=81.109$
$x=r_3\cos(t)+a_3$
$y=r_3\sin(t)+b_3$
$z=5t(20^t)+c_3$
Edit: the offset of the curve is in the z direction