freeboundary: indices of elements on the surface?

"elements" represents tetrahedrons, so it is Nx4 and F on the other hand represents triangles, so it is Mx3. Is there a relationship between "elements" and F at all?

I have a data that is mapped to "elements" so it is in Nx1 format, and I am hoping to find a way to make it in Mx1 format while keeping the same order.

TR = triangulation(elements,nodes); 
[F,P] = freeBoundary(TR);

Answer 1

[Hari]

Hi Pelajar,

I understand that you want to transform data associated with tetrahedral elements (Nx1) into data associated with triangular faces (Mx1) using MATLAB. You are also exploring the relationship between tetrahedral elements and triangular faces.

Here are the steps to acheive the same:

Understanding the Relationship: Tetrahedral elements are defined by four nodes, while triangular faces are defined by three nodes. The freeBoundary function helps identify the triangular faces that form the boundary of the 3D mesh.

Using "triangulation" and "freeBoundary": Create a triangulation object using the "triangulation" function with the elements and nodes. Use the "freeBoundary" function to extract the free boundary faces (F) and their corresponding points (P).

% Create a triangulation object
TR = triangulation(elements, nodes);
% Extract free boundary faces and points
[F, P] = freeBoundary(TR);

Mapping Data from Nx1 to Mx1: To map data from tetrahedral elements to triangular faces, you need to determine which tetrahedrons contribute to each face. This might involve checking which element each face belongs to and averaging or selecting data accordingly.

% Initialize Mx1 data array
faceData = zeros(size(F, 1), 1);

% Example: Assigning the data from the first node of the face's first element
for i = 1:size(F, 1)
    % Find the element associated with the face
    faceElementIndex = find(any(ismember(elements, F(i, :)), 2));    
    % Map the data from the element to the face
    % (Example: use data from the first element found
    if ~isempty(faceElementIndex)
        faceData(i) = elementData(faceElementIndex(1));
    end
    
end

Consideration: Ensure that the mapping logic aligns with your specific needs, such as averaging or selecting specific data points. The above loop is a simple example and might need optimization for large datasets.

Refer to the documentation of triangulation for more details: https://www.mathworks.com/help/matlab/ref/triangulation.html

Hope this helps!