# Defining a curve by a changing curvature

I want to create a curve by providing a list of numbers which define curvature at various parameters (t).

e.g. if I provide a list of params (0, 0.25, 0.75, 1) and a curvature list with constant curvature (10, 10, 10, 10) it should create a circle. If I provide another curvature list like (0, 20, 0, -20) it should produce something like a sine curve.

It’d probably have to do some kind of curvature interpolation - I’m not clear on how that should work.

Is there a way to do this?

Here’s a picture of a graph with the Curvature function showing its curvature. I just want something that works in the opposite direction.

… what?  As it is a close and periodic curve, i guess you meant (0, 0.25, 0.5, 0.75) as parameters, because 0 and 1 would mean the same point.
But then this curve fit your inputs, but is not a circle:

curvature.gh (11.5 KB)

What about the orientation? The starting tangent?
Also, the curve could be 3D… you want a logic that is just 2D?