Improving the interpolation of nodes arranged in a circle on a plane

I am using this code to improve the interpolation of nodes arranged in a circle on a plane.

As input I have the nodes 'outermost_nodes_sel'.

outermost_nodes_sel = importdata("outermost_nodes_sel.txt");
figure
plot3(outermost_nodes_sel(:,1), outermost_nodes_sel(:,2), outermost_nodes_sel(:,3), 'r.', 'Markersize', 15);
hold off
axis equal
xlabel('x')
ylabel('y')
zlabel('z')

% Interpolation
Nt = size(outermost_nodes_sel,1);
t = 1:Nt;
t_new = linspace(1,Nt,3*Nt-1);
line_new = interp1(t,outermost_nodes_sel,t_new);

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

It generates this space for me. How do I insert nodes there too?

Also, is it possible to keep the coordinates of the nodes 'outermost_nodes_sel' fixed?

Answer 1

[Matt J]

You could fit a circle to the given points and then resample it using this FEX download,

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

load('outermost_nodes_sel.mat')

P=planarFit(outermost_nodes_sel');

  xy0=P.project2D(outermost_nodes_sel'); %Map measured 3D samples to 2D

c=circularFit(xy0); %Perform circular fit in 2D

  XYZ=P.unproject3D(  cell2mat(c.sample(0:5:360))  ); %Post-sample the ellipse fit and map back to 3D

  
%%Visualize
hold on
scatter3(outermost_nodes_sel(:,1)  , outermost_nodes_sel(:,2),  outermost_nodes_sel(:,3),...
          'b','filled','SizeData',100);
scatter3(XYZ(1,:), XYZ(2,:), XYZ(3,:),'r','filled');
grid on
view(3)
legend Original Interpolated
hold off

Answer 2

[Mathieu NOE]

hello Alberto

try this - I think it's easier once you work in polar coordinates.

I am not sure to understand by "is it possible to keep the coordinates of the nodes 'outermost_nodes_sel' fixed?" ?

you can overlay both sets of data - this will do nothing to the values of outermost_nodes_sel array

% outermost_nodes_sel = importdata("outermost_nodes_sel.txt");
load("outermost_nodes_sel.mat");
figure
plot3(outermost_nodes_sel(:,1), outermost_nodes_sel(:,2), outermost_nodes_sel(:,3), 'r.', 'Markersize', 15);
hold off
axis equal
xlabel('x')
ylabel('y')
zlabel('z')

[TH,R,Z] = cart2pol(outermost_nodes_sel(:,1), outermost_nodes_sel(:,2), outermost_nodes_sel(:,3));

% Interpolation
Nt = size(outermost_nodes_sel,1);
t = 1:Nt;
TH_new = linspace(min(TH),min(TH)+2*pi,3*Nt-1); % make sure the range is 2*pi
line_new = interp1(TH,[R Z],TH_new);
[x,y,z] = pol2cart(TH_new, line_new(:,1), line_new(:,2));

figure
plot3(x, y, z, 'r.', 'Markersize', 15);
hold off
axis equal
xlabel('x')
ylabel('y')
zlabel('z')

[Alberto Acri]

Thank you for your answer! How can I create a rowsx3 matrix of those nodes you see with this line of code?

plot3(x, y, z, 'r.', 'Markersize', 15);

I would like to reproduce it like this:

plot3(node_interp(:,1), node_interp(:,2), node_interp(:,3), 'r.', 'Markersize', 15);

Thanks!

[Mathieu NOE]

hello again

node_interp = [x(:) y(:) z(:)];
plot3(node_interp(:,1), node_interp(:,2), node_interp(:,3), 'r.', 'Markersize', 15);