[Master Index] [Index for PublicToolbox/Sphere_Tessellation]

# mesh_refine_tri4

## (PublicToolbox/Sphere_Tessellation/mesh_refine_tri4.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

    [ FV ] = mesh_refine_tri4(FV)

### Help Text

     mesh_refine_tri4 - creates 4 triangle from each triangle of a mesh

     [ FV ] = mesh_refine_tri4( FV )

     FV.vertices   - mesh vertices (Nx3 matrix)
     FV.faces      - faces with indices into 3 rows
                     of FV.vertices (Mx3 matrix)

     For each face, 3 new vertices are created at the
     triangle edge midpoints.  Each face is divided into 4
     faces and returned in FV.

            B
           /\
          /  \
        a/____\b       Construct new triangles
        /\    /\       [A,a,c]
       /  \  /  \      [a,B,b]
      /____\/____\     [c,b,C]
     A	     c	   C    [a,b,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, sphere_tri, sphere_project

### Cross-Reference Information

This function is called by

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

### Listing of function C:\BrainStorm_2001\PublicToolbox\Sphere_Tessellation\mesh_refine_tri4.m

    function [ FV ] = mesh_refine_tri4(FV)

    % mesh_refine_tri4 - creates 4 triangle from each triangle of a mesh
    %
    % [ FV ] = mesh_refine_tri4( FV )
    %
    % FV.vertices   - mesh vertices (Nx3 matrix)
    % FV.faces      - faces with indices into 3 rows
    %                 of FV.vertices (Mx3 matrix)
    %
    % For each face, 3 new vertices are created at the
    % triangle edge midpoints.  Each face is divided into 4
    % faces and returned in FV.
    %
    %        B
    %       /\
    %      /  \
    %    a/____\b       Construct new triangles
    %    /\    /\       [A,a,c]
    %   /  \  /  \      [a,B,b]
    %  /____\/____\     [c,b,C]
    % A         c       C    [a,b,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, sphere_tri, sphere_project
    %

    % ---this method is not implemented, but the idea here remains...
    % 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.
    % Alternatively, it could be done until some minimum mean
    % area of faces is achieved.  As is, it just refines 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 (tri4)...')

    % 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 four new triangles:
    %
    % Make new midpoints
    % a = (A+B)/2
    % b = (B+C)/2
    % c = (C+A)/2
    %
    %        B
    %       /\
    %      /  \
    %    a/____\b       Construct new triangles
    %    /\    /\       [A,a,c]
    %   /  \  /  \      [a,B,b]
    %  /____\/____\     [c,b,C]
    % A         c       C    [a,b,c]
    %

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

    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 midpoints between vertices
        a = (A + B) ./ 2;
        b = (B + C) ./ 2;
        c = (C + A) ./ 2;

        % Find the length of each median
        %A2blen = sqrt ( sum( (A - b).^2, 2 ) );
        %B2clen = sqrt ( sum( (B - c).^2, 2 ) );
        %C2alen = sqrt ( sum( (C - a).^2, 2 ) );

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

        % Create new faces with orig vertices plus midpoints
        F2(f*4-3,:) = [ NA, Na, Nc ];
        F2(f*4-2,:) = [ Na, NB, Nb ];
        F2(f*4-1,:) = [ Nc, Nb, NC ];
        F2(f*4-0,:) = [ Na, Nb, Nc ];

    end

    % Replace the faces matrix
    FV.faces = F2;

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

    return

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    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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