I have a 2D closed spline and I need to increase its total length by a factor k, without changing its curvature, basically scaling. If this spline was a circle, I would divide the length by 4: w = k/4 and use w as a scaling factor for both axes in a 2D transformation matrix.
Am I wrong in thinking I can use the same approach for a more irregular/complex spline?
Thanks
If you want to change the arclength of any curve by a factor $k$, you should use $k$ as the scaling factor for both axes in a 2D transformation matrix. Then, if the original curve's arclength was $s$, the transformed curve's arclength will be $k*s$.
I don't understand what you wrote about scaling a circle. If you scale by $w$, then arclength will be scaled by $w$.
And scaling will always affect curvature. The curvature of a circle of radius $r$ is $1/r$. After scaling by a factor $k$, its radius will be $kr$, so its curvature will be $1/kr$. Maybe you were using the word "curvature" in some loose (non-mathematical) sense.