Getting information about tetrahedral elements after mesh encryption

I generated the base mesh with existing information including point and tetrahedral element information

But now I marked some of the tetrahedra in the mesh (not all of them) for encryption, applying the method of dividing a face into four faces

The encrypted information is only the previous mesh and the newly added points, and the newly added faces, but I want the information of the tetrahedron, how can I get the encrypted information of the tetrahedral elements？

Answer 1

[Charu]

Hi,

From my understanding, you are trying to obtain the new information for tetrahedral elements in a mesh after marking some tetrahedra for encryption by dividing a face into four faces.

Refer to the following steps to resolve this issue:

1.Begin by identifying the mesh requiring modification. For each marked tetrahedron, divide its faces by adding new nodes at the midpoints, effectively creating smaller faces.

NewNodes = Nodes;
NewElements = [];

% Example indices of tetrahedra to be encrypted
  markedTetrahedra = [1, 5, 10]; 

% Iterate over each tetrahedron
for i = 1:size(Elements, 2)
    % Get the node indices of the current tetrahedron
    n1 = Elements(1, i);
    n2 = Elements(2, i);
    n3 = Elements(3, i);
    n4 = Elements(4, i);
% Calculate midpoints of each edge
    m12 = (Nodes(:, n1) + Nodes(:, n2)) / 2;

2.Incorporate these new nodes into the nodelist and replace the original tetrahedra with newly formed ones using these nodes.

This process ensures that each original tetrahedron is subdivided into smaller, more manageable tetrahedra.

% Add midpoints to NewNodes if not already present
      [NewNodes, idx12] = addNode(NewNodes, m12);
% Create new tetrahedra
      NewElements = [NewElements, ...
        [n1; idx12; idx13; idx14], ...  

3.Once it is reconstructed, store the updated node and element information, ensuring that the new elements are correctly indexed in the elements array.

function [nodes, index] = addNode(nodes, newNode)
    tol = 1e-6; 
    index = find(all(abs(nodes - newNode) < tol, 1), 1);
    if isempty(index)
        nodes = [nodes, newNode];
        index = size(nodes, 2);
    end

4.Finally, verify the integrity of the mesh by checking that the new tetrahedra seamlessly replace the originals without any gaps or overlaps. This ensures a smooth transition from the original mesh to the modified, encrypted version.

% Plot the new mesh 
figure;
tetramesh(NewElements', NewNodes', 'FaceColor', 'red');
title('Encrypted Tetrahedral Mesh');

Hope this helps!

For more information, refer to the following MathWorks Documentation:

“tetramesh” function:

https://www.mathworks.com/help/releases/r2024b/matlab/ref/tetramesh.html