Transfer points on curve onto straight line: preserving distance

Please could I ask for advice. I'm a biologist so apologies if this is trivial. I have calculated the distances between points on two curved lines (an inner and outer part of my bacterial cell) and now I'd like to plot these distances on a straight line as a bar chart, where the x axis represents points on my outermost curve and the y axis represents the distance from those outer points to my inner points. However, the points on my curve are not evenly spaced and I'd like to keep those distances between the outer points represented on the straight line.

Effectively, I'd like to transfer points on a curve to points on a straight line retaining distance between points.

My first thought was a kind of dimensionality reduction such as PCA but I'm not sure this does what I want it to? I'm really wondering if anyone has names of techniques which might help which I could look into further please?

Image of Curve

• Do you have a way to describe your curve, like a (smooth) function? Can it be assumed to be a perfect circle? – Dirk May 13 at 12:35
• It's a catmull rom curve, so not easily but it's possible. – Emily May 13 at 12:38