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

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Alberto Acri
Alberto Acri 2024-2-8
评论： Alberto Acri 2024-2-9
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);

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采纳的回答

Matt J
Matt J 2024-2-8
编辑：Matt J 2024-2-8
Yes,
dot(normal,point)>0 %above the plane (the direction the normal is pointing)
dot(normal,point)<0 %below the plane
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