
Most ideal straight line through points [MATH] 
Ariesnl
Member #2,902
November 2002

I'm looking for a way to get a set of the most ideal straight lines "through" a set of points that not necessarily ly ON that line... Any ideas ? Douglass Peucker reduction does the job almost, but not quite.. Any ideas ? Perhaps one day we will find that the human factor is more complicated than space and time 
BitCruncher
Member #11,279
August 2009

Sounds like you're looking for the line of best fit

torhu
Member #2,727
September 2002

Linear regression? 
Polybios
Member #12,293
October 2010

I don't know what you want to do in particular, but this sounds like a good start: https://en.wikipedia.org/wiki/Simple_linear_regression Basically, take the sum of the squared residuals as an objective function and minimize it. 
Ariesnl
Member #2,902
November 2002

I need to detect the best straight lines over the "almost straight" slopes of a "wave like" pattern of points.. Like this : {"name":"611156","src":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/d\/8\/d88bb0ac8fd01ea1f7ed8b6b5bd02d8f.png","w":1484,"h":769,"tn":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/d\/8\/d88bb0ac8fd01ea1f7ed8b6b5bd02d8f"} ...And that "wave pattern" can be in ANY direction ! ! ! The red lines are the most important.. I have a working algorithm using douglass peucker reduction , but it is far from perfect, so I was wondering what other ways there might be. Perhaps one day we will find that the human factor is more complicated than space and time 
Chris Katko
Member #1,881
January 2002

That sounds like you just want a spline (/ bcurve / etc), and then you just take the tangents. {"name":"1200pxParametic_Cubic_Spline.svg.png","src":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/8\/b\/8bceabb0eb78b6af527d48549428d8ca.png","w":1200,"h":818,"tn":"\/\/djungxnpq2nug.cloudfront.net\/image\/cache\/8\/b\/8bceabb0eb78b6af527d48549428d8ca"} sig: 
SiegeLord
Member #7,827
October 2006

I'd approach it as an optimization problem. I'd parametrize the solution as a set of line segments, defined by the coordinates of their end points. Then I'd define the loss function, which would be the minimum sum of distances between the segments and the data points. This can be implemented by computing the distance from each data point to each segment, and then picking the smallest such distance. I'd also maybe penalize the total length of line segments. Then I'd follow this algorithm 1. Start with a single line segment, two end points. "For in much wisdom is much grief: and he that increases knowledge increases sorrow."Ecclesiastes 1:18 
