Find coordinates inside a matrix with specific conditions

I need to identify 3 nodes (the green ones, but it can also be the blue ones) within a matrix that generates a "circle" in space.

The figure is just an example, the important thing is that one node (A) is above the centre node, node (B) is below, node (C) is to the left.

Any good ideas?

plane_new = importdata("plane_new_ok.mat");
node_new = importdata("node_new_ok.mat");

figure
plot3(plane_new(:,1), plane_new(:,2), plane_new(:,3), 'r.', 'Markersize', 15);
hold on
plot3(node_new(:,1), node_new(:,2), node_new(:,3), 'r.', 'Markersize', 15);
hold off
axis equal
xlabel('x')
ylabel('y')
zlabel('z')

[Matt J]

Are A,B,C to be selected from points actually present in plane_new_ok.mat, even if there is no subset of points that are at perfect 90 degree intervals?

[Alberto Acri]

Hi Matt! The nodes to be searched must be in 'plane_new_ok.mat'. Starting from any node in 'plane_new_ok.mat' (node A), I must find the other two nodes (B and C) arranged at approximately (or ugual) 90°!

Answer 1

[Matt J]

Using this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

plane_new = importdata("plane_new_ok.mat");
node_new = importdata("node_new_ok.mat");

[~,i]=max(plane_new(:,3)); %arbitrarioy choose A

A=plane_new(i,:);
rA=A-node_new;  %A-axis

P=planarFit([plane_new;node_new]');
rn=P.normal*sign(P.normal(3));  %plane normal

rC=cross(rn,rA); %C-axis

C=nearestPoint(node_new,+rC,plane_new);
B=nearestPoint(node_new,-rA,plane_new);

figure
plot3(plane_new(:,1), plane_new(:,2), plane_new(:,3), 'r.', 'Markersize', 15);
hold on
plot3(node_new(:,1), node_new(:,2), node_new(:,3), 'r.', 'Markersize', 15);
plot3(A(1), A(2),A(3), 'b.', 'Markersize', 40);
plot3(C(1), C(2),C(3), 'g.', 'Markersize', 40);
plot3(B(1), B(2),B(3), 'k.', 'Markersize', 40);
hold off
axis equal
xlabel('x')
ylabel('y')
zlabel('z')
legend('Data','Center','A','B','C')

function G=nearestPoint(c,d,xyz)

  d=d/norm(d);

  s=(xyz-c)*d'>0;

  xyz=xyz(s,:);

  Dist=vecnorm(cross(xyz-c,repmat(d,height(xyz),1)),2,2);

  [~,ipos]=min(Dist);

  G=xyz(ipos,:);


end