Identify coordinates of nodes in a matrix above/below the coordinates of a plane

Is there a way to identify the coordinates of nodes (black nodes,'DATA_select') above (green selection) or below (purple selection) the plane formed by the cyan nodes?

circle_new = importdata("circle_new.mat");
DATA_select = [-34.9538764953613	-202.653717041016	-180.064163208008
-34.9621696472168	-202.662780761719	-180.033142089844
-34.9837760925293	-202.684707641602	-179.908370971680
-35.1441574096680	-202.809509277344	-179.447555541992
-35.2035064697266	-202.828262329102	-179.262985229492
-35.2346343994141	-202.842453002930	-179.193283081055
-35.2885208129883	-202.862808227539	-179.072174072266
-35.3297538757324	-202.876464843750	-178.992904663086
-35.3625869750977	-202.889877319336	-178.920135498047
-35.4839859008789	-202.917922973633	-178.627349853516
-35.4883193969727	-202.919113159180	-178.618835449219
-35.5550308227539	-202.943710327148	-178.500549316406];

N = [circle_new(1,:); circle_new(100,:); circle_new(200,:)];

% =======================
figure
plot3(circle_new(:,1),circle_new(:,2),circle_new(:,3),'c.','Markersize',10)
hold on    
plot3(DATA_select(:,1),DATA_select(:,2),DATA_select(:,3),'k.','Markersize',20)

plot3(N(:,1), N(:,2), N(:,3), 'r.', 'Markersize', 30);
patch(N(:,1), N(:,2), N(:,3), 'k'); % Plotting the plane
hold off
axis equal
grid off

I determined the normal vector:

% Calculate the normal vector to the plane
v1 = N(2,:) - N(1,:);
v2 = N(3,:) - N(1,:);
normal_vector = cross(v1, v2);
normalized_normal = normal_vector / norm(normal_vector);

Answer 1

[Matt J]

Yes,

dot(normal,point)>0 %above the plane (the direction the normal is pointing)
dot(normal,point)<0 %below the plane

[Alberto Acri]

Thank you for your reply.

• By 'normal' do you mean 'normal_vector'?
• By 'point' do you mean a node of 'DATA_select'?

dot(normal_vector,DATA_select(1,:))>0;  % result 1 for DATA_select(1:12,:)

Perhaps it is more correct to write it this way?

G_plane_new = [-35.2765495628843	-202.715302315428	-179.169337072340];  % node on plane
A = dot(DATA_select(r,:)-G_plane_new,normal_vector)>0;  % r for 1:12

[Matt J]

I assume you figured it out (since you accepted the answer)?

[Alberto Acri]

yes!