How to recreate the exact same curve using least number of points

query1.3dm (36.6 KB)
Query1.gh (13.8 KB)

Hi ,
I am trying to recreate the exact same curve using minimum or least number of points. I have given a shot but I see I am loosing the geometry as shown in fugure. I am trying to get rid of undesired points using concept of curvature.

How can I recreate the entire curve with min points without loosing the geometry ?