[ 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

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