Curve fitting as a combination of straight line segments

Forum|Forum|6 years ago
October 16, 2019
5 replies
8894 views

Hello

I would like to convert a given set of data to a segment of straight lines, rather than a perfect curve. For example, in the attached picture, I would like to convert the data for the sine curve into a set of straight line. Two examples are illustrated in the attachment. One is an approximation connecting the peaks and zeros and the other is more refined approximation. If I use the regression (least square method) on the sine curve, I get a horizontal line.

Question: how to convert the given sine curve data into a set of lines and make them more refined, i.e., with the help of some refining variable.

F

Fred_Kohlhepp

23-Emerald I

If you have the data as matched pairs X and Y, the command is

fn(x) := linterp(X,Y,x)

D

DJF

16-Pearl

I'd do it like this. change spacing variable to control the fit.

D

DJF

16-Pearl

Or for some more sophisticated approaches see this thread

https://community.ptc.com/t5/PTC-Mathcad/Calculating-slope-in-dataset/td-p/498334/page/2

A

adar

Author

1-Visitor

Thanks for the thread. Yes, that is what I was looking for.

L

LucMeekes

23-Emerald IV

What exactly do you need?

Do you just want the graph to be more or less 'refined', like this:

Or do you want the line properties for each of the line segments that make up your curve approximation, like this:

Above is an example with 4 line segments. With 6 line segements you get:

Success!
Luc

1_LM_20191016_LineSegments.zip

A

adar

Author

1-Visitor

Thanks. I am looking for regression analysis for a given data in form of a set of lines with properties of each segment. The sine curve was just an example. Here the 'sine' curve should be treated as unknown. I have tried to explain it better in the attached worksheet. Please see attached.

1_sine-regression.zip

F

Fred_Kohlhepp

23-Emerald I

The challenge with fitting a set of straight lines to a non-linear data set lies in determining where the "break points" are. If you can divide the data into groups that define each line segment (command would be "submatrix"), then either "line," or "intercept," and "slope" will give you the least squares linear fit. But automating the choice of where to split up the data set will be challenging.