creating a 3D hexahedral grid from coordinates

Hey ,

I am trying to create a 3D grid for a finite element problem. I have the x, y and z coordinates of the nodes of a body, and I want to connect them , so that I have hexahedral elements.

In the picture you can see the scatter plot of 12 coordinates, and how I want them to be connected. But I would like to have an alorithm for an arbitray number of coordinates.

Maybe there is someone who can help me.

Answer 1

[charan]

Hello Katharina,

As per my understanding you are trying to create a grid from given set of coordinates.

This can be achieved by connecting the points in such a way that each point is connected to a fixed number of nearest neighbours.

You can iteratively run through the co-ordinates and using distance formula find the 3 nearest neighbours of every point and join them.

%Generating example points
n = 16;
angl_step = 2*pi/n;
alpha = 0:angl_step:2*pi-angl_step;
X = cos(alpha)';
Y = sin(alpha)';
R = sqrt(X.^2 + Y.^2);
X = X + (0.2*R.*sin(3*alpha)'.*cos(3*alpha)');
Y = Y + (0.2*R.*sin(3*alpha)'.*sin(3*alpha)');
Z = sqrt(X.^2 + Y.^2);
p=[X,Y,Z];
%changing order
p = p([end,end-1,1,2:end-2],:);
%algorithm 
for i=1:length(p)
    dis_array=[];
    for j=i+1:length(p)
    dis_array=[dis_array,dist(p(i,:),p(j,:))];
    end
    [~,idx]=sort(dis_array);
    hold on
    if(~isempty(idx))
    a=[p(i,:);p(i+idx(1),:)];
    
plot3(a(:,1)',a(:,2)',a(:,3)','Marker','o',Color=[0,1,0],LineWidth=2);
    end
    if(length(idx)>1)
       b=[p(i,:);p(i+idx(2),:)];
       plot3(b(:,1)',b(:,2)',b(:,3)','Marker','o',Color=[0,1,0],LineWidth=2);
    end
     if(length(idx)>2)
       c=[p(i,:);p(i+idx(3),:)];
       plot3(c(:,1)',c(:,2)',c(:,3)','Marker','o',Color=[0,1,0],LineWidth=2);
    end

end
hold off

%distance function
function out = dist(p1,p2)
    out=sqrt((p1(1)-p2(1))^2+(p1(2)-p2(2))^2+(p1(3)-p2(3))^2);
end

Please refer to the following reference to know about joining the nearest neighbours in 2D space:

• https://www.mathworks.com/matlabcentral/fileexchange/35488-connect-randomly-ordered-2d-points-into-a-minimal-nearest-neighbor-closed-contour?s_tid=srchtitle_support_results_1_connecting%20a%20point%20to%20its%20nearest%20neighbours

Please refer to the following files from file exchange for code like your requirement:

• https://www.mathworks.com/matlabcentral/fileexchange/78901-discrete-contour-mesh-patch-2d-3d?s_tid=srchtitle_support_results_9_3d%20contour%20from%20points)
• https://www.mathworks.com/matlabcentral/fileexchange/69437-polyplot3?s_tid=srchtitle_support_results_3_polyplot

I hope this resolves the issue you were facing.