How to get some coordinate description of DiscreteGeometry Face or Edge?

Question

Locklin George 2021-9-24

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1460179-how-to-get-some-coordinate-description-of-discretegeometry-face-or-edge

回答： Abhinaya Kennedy 2024-6-4

The specific problem I am trying to solve is computing the normal vector for an exterior edge of a pde tet mesh at a point.

I am able to find the associated DiscreteGeometry Edge ID that the point lies on and the adjacent Face IDs, but I have not been able to find a way to map those ID values to the DiscreteGeometry Vertices.

If I could get the associated vertices for a Face ID I could then compute the normal vectors for each adjacent face and average them to get the edge normal at the point. Is there a way to get those Vertex indices from the DiscreteGeometry object and Face/Edge IDs?

function norms = meshnormals(model,contactPoints)
    norms = zeros(size(contactPoints));
    for i = 1:size(contactPoints(1))
        edge = nearestEdge(model.Geometry,contactPoints(i,:))
        faces = facesAttachedToEdges(model.Geometry,edge,'external')
        %get face edges?
        %Turn face edges into coordinate vectors?
        %compute face normals?
        %Average face normals?
    end
end

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Answer 1

Abhinaya Kennedy 2024-6-4

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Hi Locklin,

Here's how you can obtain the vertex indices and compute the normal vector for an exterior edge of a pde tet mesh at a point using "DiscreteGeometry" objects:

1. Accessing Vertices from Face ID:

"DiscreteGeometry" doesn't directly provide a function to get vertex indices from a face ID. However, you can achieve this by

Getting the list of all edges associated with the face ("faceEdges").
For each edge in the face, use "model.Geometry.edges{edgeID}" to access the edge object and then extract the two vertex indices ("vertex1" and "vertex2") from the edge object.

2. Computing Face Normals:

Once you have the vertex indices for each face, you can compute the face normal vector:

Calculate the vector difference between two vertices of the face.
Calculate the cross product of two such vectors (from different edges of the face) to get the normal vector by using the "cross" function.
Normalize the resulting vector to ensure unit length.

function norms = meshnormals(model,contactPoints)
  norms = zeros(size(contactPoints));
  for i = 1:size(contactPoints(1,:))
    edge = nearestEdge(model.Geometry,contactPoints(i,:));
    faces = facesAttachedToEdges(model.Geometry,edge,'external');
    
    % Initialize empty list to store face normals
    faceNormals = [];
    for faceID = faces
      % Get face edges
      faceEdges = model.Geometry.faces{faceID};
      
      % Loop through face edges to get vertex indices and compute face normal
      for edgeID = faceEdges
        edge = model.Geometry.edges{edgeID};
        vertex1 = edge.vertex1;
        vertex2 = edge.vertex2;
        
        % Calculate face normal based on vertex difference and cross product
        faceNormal = cross(model.Geometry.vertices{vertex1} - model.Geometry.vertices{vertex2}, ...
                         model.Geometry.vertices{anotherVertex} - model.Geometry.vertices{vertex2});
        faceNormal = faceNormal / norm(faceNormal);  % Normalize
        
        faceNormals = [faceNormals; faceNormal];  % Add to list
      end
      
      % Average face normals for edge normal
      edgeNormal = mean(faceNormals, 1);
      norms(i,:) = edgeNormal;
    end
  end
end