Locate two neighboring nodes in space so as to divide the matrix into two

I have the coordinates of nodes arranged in space in the shape of 8.

Is there a way to locate the nearest points as marked in the two figures (circled in red)? note: the figures are an example

I need to locate the two nodes to "separate" the coordinates of the nodes in matrix A and matrix B.

plane_new = importdata("plane_new_2_30_jj2.mat");
% OR
plane_new = importdata("plane_new_3_31_jj2.mat");

figure
plot3(plane_new(:,1),plane_new(:,2),plane_new(:,3),'k.','Markersize',20);     
axis equal
grid off

[Matt J]

It's not clear how you choose the pair of separating points in the second case. WHy couldn't they be as marked in yellow below? Why couldn't they be any pair of points on the parallel edges of the neck?

[Matt J]

I'm also not sure why you are giving us example data in 3D form. This is planar data, so you could be mapping this to 2D (as you did here) and working entirely in the 2D domain.

[Alberto Acri]

Hi Matt.

It's not clear how you choose the pair of separating points in the second case. WHy couldn't they be as marked in yellow below? Why couldn't they be any pair of points on the parallel edges of the neck?

Yes, it can also be as you say. I specified in the question that the figures are 'examples'.

I'm also not sure why you are giving us example data in 3D form. This is planar data, so you could be mapping this to 2D (as you did here) and working entirely in the 2D domain.

I hadn't thought about it that I could work in 2D. I will let you know if I reach a solution. Thanks for the advice!

Answer 1

[Matt J]

load xydata xy %Original 3D data mapped to 2D

xy=xy(tspsearch(xy,5),:); %tspsearch is on the file exchange

P=polyshape(xy,'Simplify',0);

pc=regions(rmslivers(subtract( convhull(P) , P),1/100));

[~,is]=maxk(area(pc),2); pc=pc(is);

neck=getNearest(pc(1),pc(2));  %The two points

plot(P); axis equal
hold on
scatter(neck(:,1), neck(:,2),'or','filled')
hold off

function V=getNearest(p1,p2)


   ID=nearestvertex(p1,p2.Vertices);

   Dist=vecnorm(p1.Vertices(ID,:)-p2.Vertices,2,2);

   [~,j]=min(Dist);

   V=[p1.Vertices(ID(j),:);p2.Vertices(j,:)];


end

[Walter Roberson]

regionprops() MinFeretProperties is another potential way to find the distances.

[Matt J]

If you could form an image out of the xy data, then yes.