One approach —
nodes = importdata("plane_new_ok.mat");
center = importdata("node_new_ok.mat");
rf = scatteredInterpolant(nodes(:,1),nodes(:,2),nodes(:,3));
a = atan2(nodes(:,2)-center(2), nodes(:,1)-center(1));
r = hypot(nodes(:,2)-center(2), nodes(:,1)-center(1));
rc = r/4*(1:3);
xc3 = rc .* cos(a) + center(1);
yc3 = rc .* sin(a) + center(2);
zc3 = rf(xc3, yc3);
figure
plot3(nodes(:,1),nodes(:,2),nodes(:,3),'b.','Markersize',15)
hold on
plot3(center(:,1),center(:,2),center(:,3),'b.','Markersize',15)
hp3 = plot3(xc3, yc3, zc3, '.', 'Markersize',15);
hp3(1).Color = 'm';
hp3(2).Color = 'g';
hp3(3).Color = 'r';
hold off
grid off
xlabel('x')
ylabel('y')
zlabel('z')
axis equal
view(-30,30)
EDIT — Changed line to marker in added circles.
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