[R-sig-Geo] Minimum bounding circle from cluster of points (Tina Cormier)

[Adrian Baddeley]

 > Specifically, why we would need to cross through 3 points, rather than 2

Essentially because a circle is uniquely determined by 3 points on the circle, not by 2.

The diagram in Tina's email shows an example where the radius of the minimum bounding circle is greater than half the maximum distance between any two points. Another example is the equilateral triangle.

Adrian

From: Tina Cormier <tcorms at gmail.com<mailto:tcorms at gmail.com>>
Date: Tuesday, 12 July 2016 8:02 pm
To: Adrian Baddeley <Adrian.Baddeley at curtin.edu.au<mailto:Adrian.Baddeley at curtin.edu.au>>
Cc: Michael Sumner <mdsumner at gmail.com<mailto:mdsumner at gmail.com>>, chris english <englishchristophera at gmail.com<mailto:englishchristophera at gmail.com>>, "Bacou, Melanie" <mel at mbacou.com<mailto:mel at mbacou.com>>, "r-sig-geo at r-project.org<mailto:r-sig-geo at r-project.org>" <r-sig-geo at r-project.org<mailto:r-sig-geo at r-project.org>>
Subject: Re: [R-sig-Geo] Minimum bounding circle from cluster of points (Tina Cormier)

Ah, thank you for the correction, Adrian. Admittedly, I'm a little foggy on the geometry. Specifically, why we would need to cross through 3 points, rather than 2 as in the method I described above (which was suggested to me by other posters here and in the QGIS forum). I'm not questioning THAT it works (as I have used the function that you wrote, as well as the one that Robert wrote), and both cross through 3 points and capture the whole cluster, even in a situation where the points are unevenly spaced and there are 12 of them. I know what a circumcircle is; I'm just curious if the other method I described above is incorrect to use. Perhaps the geometry lesson is outside the scope of my original question and of the list, but if not, I'd love to hear the synopsis.

Thank you to Adrian and Robert for sending me functions for this issue!
Tina



 [Inline image 1]

On Mon, Jul 11, 2016 at 9:06 PM, Adrian Baddeley <adrian.baddeley at curtin.edu.au<mailto:adrian.baddeley at curtin.edu.au>> wrote:

Tina Cormier <tinaacormier at gmail.com<mailto:tinaacormier at gmail.com>> writes:


> I have the idea now of what I need to do -

> find the longest distance between two points in the cluster,

> the midpoint of that line is the center of the circle,


Sorry, but that is not right.


The circumcircle of a set of points must pass through 3 of the points (if there are at least 3 points). The circumradius is not equal to the maximum distance between all pairs of points.


Think of an equilateral triangle: three points, each pair separated by the same distance 's'.


The circumcentre (the centre of the minimal circle) is the point at the centre of the triangle.

The circumradius is s/sqrt(3), not s/2.


Adrian


Prof Adrian Baddeley DSc FAA

Department of Mathematics and Statistics

Curtin University, Perth, Western Australia


________________________________
From: Tina Cormier <tinaacormier at gmail.com<mailto:tinaacormier at gmail.com>>
Sent: Monday, 11 July 2016 11:15 PM
To: Michael Sumner
Cc: chris english; Bacou, Melanie; Adrian Baddeley; r-sig-geo at r-project.org<mailto:r-sig-geo at r-project.org>
Subject: Re: [R-sig-Geo] Minimum bounding circle from cluster of points (Tina Cormier)

Wow! I'm humbled that you all took the time to help me out! You had great suggestions and sent along some very handy functions. I have the idea now of what I need to do - find the longest distance between two points in the cluster, the midpoint of that line is the center of the circle, and there are numerous ways to create the circle, but once you have the radius, you can just buffer it. Fantastically simple. Someone also suggested using PostGIS (ST_MinimumBoundingCircle), which I will definitely try. I have a postgreSQL db that I use for some simple stuff, and I'm not a guru by any means, but this will help me gain a little more experience.

Thank you again, and I can't wait to pay if forward the next time someone asks about a topic I know well!

Cheers,
Tina


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