# [SciPy-User] point-curve distance estimation or calculation

Matthieu Rigal rigal@rapideye...
Wed Jun 2 07:05:36 CDT 2010

```Hi folks,

This is my first message on the scipy-user list. I post it here because I
wanna try do the most out of it using numpy and scipy and I hope it is not
too far from the initial scope. I couldn't finda solution to it on the
Internet.

First I have two sets of data. I am doing several leastsq optimizations.
for linear y=ax+b, I know how to handle the rest, for second order or more,
it is more difficult.

In the y = ax²+bx+c case, I know have a curve. I want to calculate or
estimate the distance between each point (combination of two data sets)
and the curve.

Calculation is doable by applying this formula
http://mathcentral.uregina.ca/QQ/database/QQ.09.07/s/elliot1.php
But then, an estimation of the correct result is required, and it takes a
lot of time for every step, if you have 25 million values in each set.

First, there might be some functions useful to do this calculation quite
fast (up to 5 minutes is quite acceptable), that I may have overseen. That
may basically calculate the following internally

Second, it may be better to get a close estimation of the distance to the
curve. I was thinking about calculating the tangent of the curve at the
(x, y0) point calculated from (x, y).
For this also, I didn't found a direct way of calculating the tangent else
than calculating points very close to y0 and solve the equation. Are there
some direct possibilities ?

Then I would simply calculate a distance from point to line, using one of
following methods
http://www.worsleyschool.net/science/files/linepoint/distance.html

And so get an estimation. But also in this case, it seems quite complicated
and not very efficient, so you may have a fully different idea :-))

Regards,
Matthieu

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