Calculate the largest, smallest diameter and the centroid of a polyshape (irregula rpolygon) from a set of points

I have a set of points (x,y) for a polyshape (almost 120 coordinates), I want to find the largest, smallest diameter and the centroid of this irregular polygon.

[Matt J]

It is not self-evident how you are defining "largest and smallest diameter". Do you mean the minimum and maximum feret diameter?

Answer 1

[Matt J]

For the centroid, polyshape has a method centroid.

If the min and max feret diameters are what you want, then one approach would be,

pgon=nsidedpoly(4,'Radius',0.5); %input polyshape


fun=@(theta) feretDiam(pgon.Vertices,theta);
Theta=linspace(-pi,pi,1e4);

%Min Diameter

[~,i0]=min(fun(Theta));
[thetamin,minDiam]=fminsearch(@(t)fun(t),Theta(i0));
minDiam

minDiam = 0.7071

 
%Max Diameter
[~,i0]=max(fun(Theta));
[thetamax,maxDiam]=fminsearch(@(t)-fun(t),Theta(i0));
 maxDiam=-maxDiam

maxDiam = 1.0000

function d=feretDiam(V,theta)

   p=V*[cos(theta);sin(theta)];
   d=max(p,[],1)-min(p,[],1);
   
end

[Tesla]

Thank you for your suggestion, Yes exactly i mean min and max feret diameters.

But I didn't understant on your code, how I can use my inputs? they are a set data like of x= [.....] and y =[....]

[Matt J]

Why then, does your post title mention polyshapes? Creating a polyshape from your x,y data may be done with,

pgon = polyshape(x,y);

[Tesla]

Okey, I see Thank you.

If I want to plot the bounding box of the min and max feret diameters like in this picture please?

[Matt J]

In general, the min and max diameters are not always perpendicular, which would be necessary to define a box.

[Tesla]

Isee, but is there a way to plot at least those diameters ? to make them visible

[Walter Roberson]

https://www.mathworks.com/help/images/ref/bwferet.html#mw_770f4e84-6fe1-4250-ade5-45cedae841c6 shows how the maximum and minimum feret angle are calculated by bwferet . They will not necessarily be perpendicular.

If you had the coordinates for the largest feret distance, then you could calculate the maximum distance from each boundary coordinate to the line joining the coordinates; divide that into "above" or "below" the line, take the largest distance in each case, and you have arrived at the width of a box needed parallel to the line joining the largest feret distance to enclose all points.

[Tesla]

Thanks that's a nice explaination, but I see here is that just for images. in my case I have x,y coordinates

[Matt J]

You could just draw lines to mark the diameters:

pgon=nsidedpoly(4,'Radius',0.5); %input polyshape


fun=@(theta) feretDiam(pgon.Vertices,theta);

  [~,xmin,ymin]=fun(thetamin);
  [~,xmax,ymax]=fun(thetamax);
 
 plot(pgon);
 line(xmin,ymin,'LineStyle','--');
 line(xmax,ymax,'LineStyle','--');

 
 function [d,xb,yb]=feretDiam(V,theta)

   udir=[cos(theta);sin(theta)];
   p=V*udir;
   umax=max(p,[],1);
   umin=min(p,[],1);
   d=umax-umin;

   if nargout>1
         umax=udir.*umax;
         umin=udir.*umin;

         xb=[umin(1,:);umax(1,:)];
         yb=[umin(2,:);umax(2,:)];
   end
   
end

[Tesla]

I got an error in this line

[~,xmin,ymin]=fun(thetamin);
[~,xmax,ymax]=fun(thetamax);

Unrecognized function or variable.

[Walter Roberson]

poly2mask can create an image from a list of polygon coordinates.

[Matt J]

An alternative would be to draw 2 boxes, one based on the min diameter and one based on the max. The implementation below requires:

https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-convex-polyhedra

close all


pgon=nsidedpoly(4,'Radius',0.5); %input polyshape


fun=@(theta) feretDiam(pgon.Vertices,theta);
Theta=linspace(-pi,pi,1e4);

%Min Diameter

[~,i0]=min(fun(Theta));
[thetamin,minDiam]=fminsearch(@(t)fun(t),Theta(i0));

%Max Diameter
[~,i0]=max(fun(Theta));
[thetamax,maxDiam]=fminsearch(@(t)-fun(t),Theta(i0));

 
  [~,pmin]=fun([thetamin, thetamin+pi/2]);

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

  [~,pmax]=fun([thetamax, thetamax+pi/2]);

Warning: Polyshape has duplicate vertices, intersections, or other inconsistencies that may produce inaccurate or unexpected results. Input data has been modified to create a well-defined polyshape.

 

 plot(pgon); hold on
 args={'FaceColor','none','EdgeColor','r','LineWidth',3,'LineStyle','--'};
 plot(pmin,args{:});
 plot(pmax,args{:});

 axis equal

 function [d,pgon]=feretDiam(V,theta)

   udir=[cos(theta);sin(theta)];
   p=V*udir;
   umax=max(p,[],1);
   umin=min(p,[],1);
   d=umax-umin;

   if nargout>1

    A=[udir';-udir']; b=[umax';-umin'];
    pgon=convhull(polyshape(lcon2vert(A,b)));

   end
   
end

[Tesla]

Thats working Thank you very much

[Tesla]

Can you please tell me what the problem in this code:

pgon=nsidedpoly(4,'Radius',0.5); %input polyshape


fun=@(theta) feretDiam(pgon.Vertices,theta);

  [~,xmin,ymin]=fun(thetamin);

Unrecognized function or variable 'thetamin'.

  [~,xmax,ymax]=fun(thetamax);
 
 plot(pgon);
 line(xmin,ymin,'LineStyle','--');
 line(xmax,ymax,'LineStyle','--');
 
 function [d,xb,yb]=feretDiam(V,theta)

   udir=[cos(theta);sin(theta)];
   p=V*udir;
   umax=max(p,[],1);
   umin=min(p,[],1);
   d=umax-umin;

   if nargout>1
         umax=udir.*umax;
         umin=udir.*umin;

         xb=[umin(1,:);umax(1,:)];
         yb=[umin(2,:);umax(2,:)];
   end
   
 end
 

[Matt J]

Can you please tell me what the problem in this code:

The code doesn't include the lines that compute thetamin and thetamax.