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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 = createOctahedron()
%CREATEOCTAHEDRON Create a 3D mesh representing an octahedron.
%
% [V, E, F] = createOctahedron;
% Create a 3D mesh representing an octahedron
% V is a 6-by-3 array with vertices coordinate, E is a 12-by-2 array
% containing indices of neighbour vertices, and F is a 8-by-3 array
% containing array of vertex index for each face.
%
% [V, F] = createOctahedron;
% Returns only the vertices and the face vertex indices.
%
% MESH = createOctahedron;
% Returns the data as a mesh structure, with fields 'vertices', 'edges'
% and 'faces'.
%
% Vertices are located on grid vertices:
% ( ±1, 0, 0 )
% ( 0, ±1, 0 )
% ( 0, 0, ±1 )
%
% Edge length of returned octahedron is sqrt(2).
% Surface area of octahedron is 2*sqrt(3)*a^2, approximately 6.9282 in
% this case.
% Volume of octahedron is sqrt(2)/3*a^3, approximately 1.3333 in this
% case.
%
% Example
% [v, e, f] = createOctahedron;
% drawMesh(v, f);
%
% See also
% meshes3d, drawMesh
% createCube, createIcosahedron, createDodecahedron, createTetrahedron
% createCubeOctahedron
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-10
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
nodes = [1 0 0;0 1 0;-1 0 0;0 -1 0;0 0 1;0 0 -1];
edges = [1 2;1 4;1 5; 1 6;2 3;2 5;2 6;3 4;3 5;3 6;4 5;4 6];
faces = [1 2 5;2 3 5;3 4 5;4 1 5;1 6 2;2 6 3;3 6 4;1 4 6];
% format output
varargout = formatMeshOutput(nargout, nodes, edges, faces);
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