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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 = createDodecahedron()
%CREATEDODECAHEDRON Create a 3D mesh representing a dodecahedron.
%
% [V, E, F] = createDodecahedron;
% Create a 3D mesh representing a dodecahedron
% V is the 20-by-3 array of vertex coordinates
% E is the 30-by-2 array of edge vertex indices
% F is the 12-by-5 array of face vertex indices
%
% [V, F] = createDodecahedron;
% Returns only the vertices and the face vertex indices.
%
% MESH = createDodecahedron;
% Returns the data as a mesh structure, with fields 'vertices', 'edges'
% and 'faces'.
%
% Example
% [v, e, f] = createDodecahedron;
% drawMesh(v, f);
%
% Use values given by P. Bourke, see:
% http://local.wasp.uwa.edu.au/~pbourke/geometry/platonic/
% faces are re-oriented to have normals pointing outwards.
%
% See also
% meshes3d, drawMesh
% createCube, createOctahedron, createIcosahedron, createTetrahedron
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2010-07-29
% Copyright 2010-2023 INRA - TPV URPOI - BIA IMASTE
% golden ratio
phi = (1+sqrt(5))/2;
% coordinates pre-computations
b = 1 / phi ;
c = 2 - phi ;
% use values given by P. Bourke, see:
% http://local.wasp.uwa.edu.au/~pbourke/geometry/platonic/
tmp = [ ...
c 0 1 ; b b b ; 0 1 c ; -b b b ; -c 0 1 ; ...
-c 0 1 ; -b -b b ; 0 -1 c ; b -b b ; c 0 1 ; ...
c 0 -1 ; b -b -b ; 0 -1 -c ; -b -b -b ; -c 0 -1 ; ...
-c 0 -1 ; -b b -b ; 0 1 -c ; b b -b ; c 0 -1 ; ...
0 1 -c ; 0 1 c ; b b b ; 1 c 0 ; b b -b ; ...
0 1 c ; 0 1 -c ; -b b -b ; -1 c 0 ; -b b b ; ...
0 -1 -c ; 0 -1 c ; -b -b b ; -1 -c 0 ; -b -b -b ; ...
0 -1 c ; 0 -1 -c ; b -b -b ; 1 -c 0 ; b -b b ; ...
1 c 0 ; b b b ; c 0 1 ; b -b b ; 1 -c 0 ; ...
1 -c 0 ; b -b -b ; c 0 -1 ; b b -b ; 1 c 0 ; ...
-1 c 0 ; -b b -b ; -c 0 -1 ; -b -b -b ; -1 -c 0 ; ...
-1 -c 0 ; -b -b b ; -c 0 1 ; -b b b ; -1 c 0 ; ...
];
% extract coordinates of unique vertices
[verts, M, N] = unique(tmp, 'rows', 'first'); %#ok<ASGLU>
% compute indices of face vertices, put result in a 12-by-5 index array
ind0 = reshape((1:60), [5 12])';
faces = N(ind0);
% extract edges from faces
edges = [reshape(faces(:, 1:5), [60 1]) reshape(faces(:, [2:5 1]), [60 1])];
edges = unique(sort(edges, 2), 'rows');
% format output
varargout = formatMeshOutput(nargout, verts, edges, faces);
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