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A suite of minimal bounding objects


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A suite of minimal bounding objects



25 Jan 2012 (Updated )

Suite of tools to compute minimal bounding circles, rectangles, triangles, spheres, incircles, etc.

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I've written quite a few separate tools to generate a minimal bounding object of some ilk. So if you have a set of points in the plane, and wish to generate the minimal bounding...
- rectangle
- triangle
- general quadrilateral
- circle
- parallelogram
- semi-circle

there is a tool in here to solve your task efficiently. You will also find minboundsphere, for 3-d data. Inscribed objects are also supported, computed by incircle and insphere.

Caveat - if you have only an image, don't expect these tools to work directly. (The image processing toolbox can do much here anyway - look there first.) In order to use these tools, I require a set of extracted points.


This file inspired Polarizability Gui5.

MATLAB release MATLAB 7.5 (R2007b)
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Comments and Ratings (22)
06 Dec 2014 Andrew  
29 Nov 2014 Yuri

convhulln is failing in minboundsphere if there are some points with the same XYZ. I have to run minboundsphere(unique(xyz,'rows')) to avoid convhulln crashing. Here is example:
minboundsphere([ 0.8726 0.4577 -0.1708
0.8761 0.4610 -0.1411
0.8761 0.4610 -0.1411
0.8761 0.4610 -0.1411
0.8761 0.4610 -0.1411

20 Oct 2014 John D'Errico

Hi Tom,

The problem is as you point out, that the insphere code uses a dot product to find the distance to each facet. Then it is a simple call to linprog, with one slack variable for each facet.

A similar idea for edges though trips up becasue each edge has two normals. So then the distance to each edge is now the sqrt of the sum of squares of a pair of dot products. While I can avoid the sqrt, such a formulation would involve quadratic equality constraints for each slack variable. Clearly this is not solvable by linprog, or even quadprog. Fmincon would be needed, so a bit more nasty of a problem using a similar formulation to the one in insphere. Certainly one could use the existing insphere code to find decent starting values for such an iterative solution, but it is still a bit more work.

I'll need to think if there is another scheme that might apply.


20 Oct 2014 Tom Tranter

Hi John,
Thanks for this submission, it's helped me a lot with a problem I'm working on. I was wondering if the insphere function could be adapted to find the largest sphere bound within the edges of the polygon rather than the faces, as if the polygon were a cage with the sphere bulging through the hollow faces. I'm not too sure how to approach this as the edge normals are not defined in 3D.

30 May 2014 Anton Semechko

Hi John, I sent you an e-mail to the electronic address provided on your Matlab profile. In that e-mail I attached a point cloud for which 'minboundsphere' fails almost consistently.

28 May 2014 John D'Errico


Please send me some cases where it fails, and I will fix it.


28 May 2014 Anton Semechko

Hi John, I ran your 'minboundsphere' function a number of times (for 8 different meshes) and observed that occasionally it fails to produce a minimum bounding sphere that encloses all of the points. In some of these cases, the distance for 5% of the points is a factor of 1.1 greater than the computed radius.

27 May 2014 Anton Semechko

Thanks John! Great submission. I found your function to find minimum bounding spheres especially useful.

23 May 2014 John D'Errico


I can't replicate the cycle that you found with those points, but with only 7 digits printed, the numbers I used were not the same as those you used.

Regardless, I used your idea of maintaining a history that should catch any such problem. I need only keep a small subset of the active sets to catch a cycle, so there is no problem. I've posted a new version to appear tomorrow.

22 May 2014 Sebastien Roy

Nice suite, but minboundcircle can hit an infinite loop in the while section. It happens with this set:

X =


Y =


This set results in an oscillation between two wrong solutions.

Maybe the function could track the active sets already considered and jump out of the loop if a repeated state is found. Unfortunately, such solution can lead to a huge stack of past active sets.

05 May 2014 Spigge

Very useful suite John, thanks. Sometimes one would like to exclude outliers, i.e., points far out from the group of interest. If I were to include say only 90% of the total number of points in a bounding circle, what would be the best strategy you recon?

14 Oct 2013 John D'Errico

Why modify any code, a silly thing to do since it is completely unnecessary? You must first identify the points of interest. Once that is done, pass those locations into the code. All of this takes little more than a single call to find on your part.

14 Oct 2013 Tallha Akram


Code works find for the data points. How can i modify current code for image data?

18 Sep 2013 John D'Errico

minboundrect returns a polygon, so the vertices of the bounding rectangle in (x,y) coordinates, as a polygon in the standard form that matlab uses in any tool that works with a polygon (look for example at inpolygon.)

17 Sep 2013 Maayan

Hi, I'm trying to use the miniboundrect file but i don't understand how the vectors of points that i receive from the function define the minimal rectangle.

28 Feb 2013 Sven

John, just a heads-up that MATLAB 2013a pre-release doesn't like calling convhull with those short options any more...

Error using convhull
CONVHULL no longer supports or requires Qhull-specific options.
Please remove these options when calling CONVHULL.

Error in minboundrect (line 102)
edges = convhull(x,y,{'Qt'}); % 'Pp' will silence the warnings

04 Feb 2013 John D'Errico

Sorry, but I may have put a code for a bounding ellipse in there in the past, but I won't leave code in there with which I am not satisfied. This is the case of the bounding ellipse.

04 Feb 2013 Doctor61

Hi John,
Thanks for your share. I agree with Venkat, 'minboundellipse.m' would have helped me a lot with a case I have in hand.

06 Aug 2012 Ben

Hi John,

minboundellipse.m is in the demo but not in the downloaded zip file. Could you add it? Thanks!

07 Jun 2012 Carlos Martinez-Ortiz  
02 May 2012 xiuwei zhang  
01 Mar 2012 Venkat R

Dear John,

A file 'minboundellipse.m' is missing I suppose.


26 Jan 2012

Removed a tool I had been testing, but only accidentally included

23 May 2014

Repair for minboundcircle

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