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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function varargout = createTetrakaidecahedron()
%CREATETETRAKAIDECAHEDRON Create a 3D mesh representing a tetrakaidecahedron.
%
% [V, E, F] = createTetrakaidecahedron;
% Create a mesh structure representing a tetrakaidecahedron, composed of
% both square and hexagonal faces. Tetrakaidecahedron can be used to tile
% the 3D Euclidean space.
%
% V is a 24-by-3 array with vertex coordinates,
% E is a 36-by-2 array containing indices of neighbour vertices,
% F is a 14-by-1 cell array containing vertex indices array of each face.
%
% [V, F] = createTetrakaidecahedron;
% Returns only the vertices and the face vertex indices.
%
% MESH = createTetrakaidecahedron;
% Returns the data as a mesh structure, with fields 'vertices', 'edges'
% and 'faces'.
%
% Example
% [n, e, f] = createTetrakaidecahedron;
% drawMesh(n, f);
%
% See also
% meshes3d, drawMesh
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-10
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
nodes = [...
1 0 2;0 1 2;-1 0 2;0 -1 2;...
2 0 1;0 2 1;-2 0 1;0 -2 1;...
2 1 0;1 2 0;-1 2 0;-2 1 0;-2 -1 0;-1 -2 0;1 -2 0;2 -1 0;...
2 0 -1;0 2 -1;-2 0 -1;0 -2 -1;...
1 0 -2;0 1 -2;-1 0 -2;0 -1 -2];
edges = [...
1 2;1 4;1 5;2 3;2 6;3 4;3 7;4 8;...
5 9;5 16;6 10;6 11;7 12;7 13;8 14;8 15;...
9 10;9 17;10 18;11 12;11 18;12 19;13 14;13 19;14 20;15 16;15 20;16 17;....
17 21;18 22;19 23;20 24;21 22;21 24;22 23;23 24];
faces = {...
[1 2 3 4], ...
[1 4 8 15 16 5], [1 5 9 10 6 2], [2 6 11 12 7 3], [3 7 13 14 8 4],...
[5 16 17 9], [6 10 18 11], [7 12 19 13], [8 14 20 15],...
[9 17 21 22 18 10], [11 18 22 23 19 12], [13 19 23 24 20 14], [15 20 24 21 17 16], ...
[21 24 23 22]};
faces = faces';
% format output
varargout = formatMeshOutput(nargout, nodes, edges, faces);
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