3D curve fitting using python

Question

I am trying to reduce the number of data points for a 3D curve, currently I have 20000 points and I would like to reduce this to around 2000 without losing much information.

I am doing this on python.

As a simple example, think of a spiral on the surface of a cylinder.

Are there any built-in functions that will do this?

I've tried using the Ramer–Douglas–Peucker algorithm to simplify the line, but due to the nature of the curve, for every data point ignored the final plot is undershooting. See picture of a 2D example, orange is what using rdp produces, green is what I want.

I would like the output of the program to be an array of ~2000 coordinates that still represent the shape of the 3D curve but they don't necessarily have to be original coordinates, I want some points to overshoot and others to undershoot.

Thank you for your help

UPDATE: In the end I chose to do something quite involved but gave me exactly what I wanted. I started using the rdp algorithm to reduce the number of points. With this new information I then fit a straight line of best fit to the spread of the original points between the new reduced points: ie if the algorithm 'ignored' 13 points, I fit the line from point 0 to point 14, and did the same for the next segment where the algorithm had skipped for example 7 points, so I fit from 14 to 22 etc. Having those lines of best fit, I found the points were the lines intersected or if the lines did not intersect, the closest point on each of the lines to the other line. Due to the nature of my problem, I did not need my data to be continuous, so 2000 "discontinuous" segments were not a problem. Thank you very much for your help!

Answer 1

In the end I chose to do something quite involved but gave me exactly what I wanted. I started using the rdp algorithm to reduce the number of points. With this new information I then fit a straight line of best fit to the spread of the original points between the new reduced points: ie if the algorithm 'ignored' 13 points, I fit the line from point 0 to point 14, and did the same for the next segment where the algorithm had skipped for example 7 points, so I fit from 14 to 22 etc. Having those lines of best fit, I found the points were the lines intersected or if the lines did not intersect, the closest point on each of the lines to the other line. Due to the nature of my problem, I did not need my data to be continuous, so 2000 "discontinuous" segments were not a problem. Thank you very much for your help!