[Master Index] [Index for PublicToolbox/Sphere_Tessellation]

# mesh_refine_tri6

## (PublicToolbox/Sphere_Tessellation/mesh_refine_tri6.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

    [ FV ] = mesh_refine_tri6(FV)

### Help Text

     mesh_refine_tri6 - creates 6 smaller triangles from a triangle mesh

     [ FV ] = mesh_refine_tri6( FV )

     FV.vertices is vertices (Nx3 matrix)
     FV.faces is faces with indices into rows of V (Mx3 matrix)

     For each face of F, 4 new vertices are created at the
     triangle edge midpoints and the triangle centroid.  Each
     face is divided into 6 faces and returned in FV.faces.

            B
           /+\
          / + \
        a/__X__\b       Construct new triangles
        /  +|+  \       [A,a,X], [A,X,c]
       / +  |  + \      [B,X,a], [B,b,X]
      /+___ | ___+\     [C,X,b], [C,c,X]
     A	     c	   C

     It is assumed that the vertices are listed in clockwise order in
     FV.faces (A,B,C above), as viewed from the outside in a RHS coordinate
     system.

     See also: mesh_refine, mesh_refine_tri4,
               sphere_tri, sphere_project

### Cross-Reference Information

This function is called by

    mesh_refine                        C:\BrainStorm_2001\PublicToolbox\Sphere_Tessellation\mesh_refine.m

### Listing of function C:\BrainStorm_2001\PublicToolbox\Sphere_Tessellation\mesh_refine_tri6.m

    function [ FV ] = mesh_refine_tri6(FV)

    % mesh_refine_tri6 - creates 6 smaller triangles from a triangle mesh
    %
    % [ FV ] = mesh_refine_tri6( FV )
    %
    % FV.vertices is vertices (Nx3 matrix)
    % FV.faces is faces with indices into rows of V (Mx3 matrix)
    %
    % For each face of F, 4 new vertices are created at the
    % triangle edge midpoints and the triangle centroid.  Each
    % face is divided into 6 faces and returned in FV.faces.
    %
    %        B
    %       /+\
    %      / + \
    %    a/__X__\b       Construct new triangles
    %    /  +|+  \       [A,a,X], [A,X,c]
    %   / +  |  + \      [B,X,a], [B,b,X]
    %  /+___ | ___+\     [C,X,b], [C,c,X]
    % A         c       C
    %
    % It is assumed that the vertices are listed in clockwise order in
    % FV.faces (A,B,C above), as viewed from the outside in a RHS coordinate
    % system.
    %
    % See also: mesh_refine, mesh_refine_tri4,
    %           sphere_tri, sphere_project
    %

    % This can be done until some minimal distance (D) of the mean
    % distance between vertices of all triangles is achieved.  If
    % no D argument is given, the function refines the mesh once.
    %

    % $Revision: 1 $ $Date: 5/20/04 3:58p $

    % Licence:  GNU GPL, no implied or express warranties
    % History:  05/2002, Darren.Weber_at_radiology.ucsf.edu, created
    %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    tic; fprintf('...refining mesh (tri6)...');

    % NOTE
    % The centroid is located one third of the way from each vertex to
    % the midpoint of the opposite side. Each median divides the triangle
    % into two equal areas; all the medians together divide it into six
    % equal parts, and the lines from the median point to the vertices
    % divide the whole into three equivalent triangles.

    % Each input triangle with vertices labelled [A,B,C] as shown
    % below will be turned into six new triangles:
    %
    % Make new midpoints
    % a = (A+B)/2
    % b = (B+C)/2
    % c = (C+A)/2
    %
    % Make triangle centroid
    % X = b + ( (A - b) ./3 );
    %
    %        B
    %       /+\
    %      / + \
    %    a/__X__\b       Construct new triangles
    %    /  +|+  \       [A,a,X], [A,X,c]
    %   / +  |  + \      [B,X,a], [B,b,X]
    %  /+___ | ___+\     [C,X,b], [C,c,X]
    % A         c       C
    %

    % Initialise a new vertices and faces matrix
    Nvert = size(FV.vertices,1);
    Nface = size(FV.faces,1);
    V2 = zeros(Nface*4,3);
    F2 = zeros(Nface*6,3);

    for f=1:Nface,

        % Get the triangle vertex indices
        NA = FV.faces(f,1);
        NB = FV.faces(f,2);
        NC = FV.faces(f,3);

        % Get the triangle vertex coordinates
        A = FV.vertices(NA,:);
        B = FV.vertices(NB,:);
        C = FV.vertices(NC,:);

        % Now find the midpoint between all vertices
        a = (A + B) ./ 2;
        b = (B + C) ./ 2;
        c = (C + A) ./ 2;

        % Now find the centroid length of the medians
        X = b + ( (A - b) ./3 );
        %Bc = c + ( (B - c) ./3 );  % Bc = X
        %Cc = a + ( (C - a) ./3 );  % Cc = X

        % Store the midpoint and the centroid vertices,
        % checking if vertex already exists
        [FV, Na] = mesh_find_vertex(FV,a);
        [FV, Nb] = mesh_find_vertex(FV,b);
        [FV, Nc] = mesh_find_vertex(FV,c);
        [FV, NX] = mesh_find_vertex(FV,X);

        % Create new faces with centroid
        F2(f*6-5,:) = [NA, Na, NX ];
        F2(f*6-4,:) = [NA, NX, Nc ];
        F2(f*6-3,:) = [NB, NX, Na ];
        F2(f*6-2,:) = [NB, Nb, NX ];
        F2(f*6-1,:) = [NC, NX, Nb ];
        F2(f*6-0,:) = [NC, Nc, NX ];

        %figure; patch('vertices',[A;B;C],'faces',[1 2 3],'facecolor',[.7 .7 .7]); hold on;
        %plot3(A(1),A(2),A(3),'ro');
        %plot3(b(1),b(2),b(3),'ro');
        %plot3(Ac(1),Ac(2),Ac(3),'bo')
        %if isequal(r,2), return; end

    end

    % Replace the faces matrix
    FV.faces = F2;

    t=toc; fprintf('done (%5.2f sec)\n',t);

    return

    % Find the length of each median
    %A2bLength = sqrt ( sum( (A - b).^2, 2 ) );
    %B2cLength = sqrt ( sum( (B - c).^2, 2 ) );
    %C2aLength = sqrt ( sum( (C - a).^2, 2 ) );

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    function [FV, N] = mesh_find_vertex(FV,vertex)

        Vn = size(FV.vertices,1);
        Va = repmat(vertex,Vn,1);
        Vexist = find( FV.vertices(:,1) == Va(:,1) & ...
                       FV.vertices(:,2) == Va(:,2) & ...
                       FV.vertices(:,3) == Va(:,3) );
        if Vexist,
            if size(Vexist) == [1,1],
                N = Vexist;
            else,
                msg = sprintf('replicated vertices');
                error(msg);
            end
        else
            FV.vertices(end+1,:) = vertex;
            N = size(FV.vertices,1);
        end

    return

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