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_project0001 function [ FV ] = mesh_refine_tri4(FV) 0002 0003 % mesh_refine_tri4 - creates 4 triangle from each triangle of a mesh 0004 % 0005 % [ FV ] = mesh_refine_tri4( FV ) 0006 % 0007 % FV.vertices - mesh vertices (Nx3 matrix) 0008 % FV.faces - faces with indices into 3 rows 0009 % of FV.vertices (Mx3 matrix) 0010 % 0011 % For each face, 3 new vertices are created at the 0012 % triangle edge midpoints. Each face is divided into 4 0013 % faces and returned in FV. 0014 % 0015 % B 0016 % /\ 0017 % / \ 0018 % a/____\b Construct new triangles 0019 % /\ /\ [A,a,c] 0020 % / \ / \ [a,B,b] 0021 % /____\/____\ [c,b,C] 0022 % A c C [a,b,c] 0023 % 0024 % It is assumed that the vertices are listed in clockwise order in 0025 % FV.faces (A,B,C above), as viewed from the outside in a RHS coordinate 0026 % system. 0027 % 0028 % See also: mesh_refine, sphere_tri, sphere_project 0029 % 0030 0031 0032 % ---this method is not implemented, but the idea here remains... 0033 % This can be done until some minimal distance (D) of the mean 0034 % distance between vertices of all triangles is achieved. If 0035 % no D argument is given, the function refines the mesh once. 0036 % Alternatively, it could be done until some minimum mean 0037 % area of faces is achieved. As is, it just refines once. 0038 0039 0040 % $Revision: 1.1 $ $Date: 2004/11/12 01:32:35 $ 0041 0042 % Licence: GNU GPL, no implied or express warranties 0043 % History: 05/2002, Darren.Weber_at_radiology.ucsf.edu, created 0044 % 0045 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0046 0047 tic; 0048 fprintf('...refining mesh (tri4)...') 0049 0050 % NOTE 0051 % The centroid is located one third of the way from each vertex to 0052 % the midpoint of the opposite side. Each median divides the triangle 0053 % into two equal areas; all the medians together divide it into six 0054 % equal parts, and the lines from the median point to the vertices 0055 % divide the whole into three equivalent triangles. 0056 0057 % Each input triangle with vertices labelled [A,B,C] as shown 0058 % below will be turned into four new triangles: 0059 % 0060 % Make new midpoints 0061 % a = (A+B)/2 0062 % b = (B+C)/2 0063 % c = (C+A)/2 0064 % 0065 % B 0066 % /\ 0067 % / \ 0068 % a/____\b Construct new triangles 0069 % /\ /\ [A,a,c] 0070 % / \ / \ [a,B,b] 0071 % /____\/____\ [c,b,C] 0072 % A c C [a,b,c] 0073 % 0074 0075 % Initialise a new vertices and faces matrix 0076 Nvert = size(FV.vertices,1); 0077 Nface = size(FV.faces,1); 0078 V2 = zeros(Nface*3,3); 0079 F2 = zeros(Nface*4,3); 0080 0081 for f = 1:Nface, 0082 0083 % Get the triangle vertex indices 0084 NA = FV.faces(f,1); 0085 NB = FV.faces(f,2); 0086 NC = FV.faces(f,3); 0087 0088 % Get the triangle vertex coordinates 0089 A = FV.vertices(NA,:); 0090 B = FV.vertices(NB,:); 0091 C = FV.vertices(NC,:); 0092 0093 % Now find the midpoints between vertices 0094 a = (A + B) ./ 2; 0095 b = (B + C) ./ 2; 0096 c = (C + A) ./ 2; 0097 0098 % Find the length of each median 0099 %A2blen = sqrt ( sum( (A - b).^2, 2 ) ); 0100 %B2clen = sqrt ( sum( (B - c).^2, 2 ) ); 0101 %C2alen = sqrt ( sum( (C - a).^2, 2 ) ); 0102 0103 % Store the midpoint vertices, while 0104 % checking if midpoint vertex already exists 0105 [FV, Na] = mesh_find_vertex(FV,a); 0106 [FV, Nb] = mesh_find_vertex(FV,b); 0107 [FV, Nc] = mesh_find_vertex(FV,c); 0108 0109 % Create new faces with orig vertices plus midpoints 0110 F2(f*4-3,:) = [ NA, Na, Nc ]; 0111 F2(f*4-2,:) = [ Na, NB, Nb ]; 0112 F2(f*4-1,:) = [ Nc, Nb, NC ]; 0113 F2(f*4-0,:) = [ Na, Nb, Nc ]; 0114 0115 end 0116 0117 % Replace the faces matrix 0118 FV.faces = F2; 0119 0120 t=toc; fprintf('done (%5.2f sec)\n',t); 0121 0122 return 0123 0124 0125 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0126 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0127 function [FV, N] = mesh_find_vertex(FV,vertex) 0128 0129 Vn = size(FV.vertices,1); 0130 Va = repmat(vertex,Vn,1); 0131 Vexist = find( FV.vertices(:,1) == Va(:,1) & ... 0132 FV.vertices(:,2) == Va(:,2) & ... 0133 FV.vertices(:,3) == Va(:,3) ); 0134 if Vexist, 0135 if size(Vexist) == [1,1], 0136 N = Vexist; 0137 else, 0138 msg = sprintf('replicated vertices'); 0139 error(msg); 0140 end 0141 else 0142 FV.vertices(end+1,:) = vertex; 0143 N = size(FV.vertices,1); 0144 end 0145 0146 return