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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 = createIcosahedron()
%CREATEICOSAHEDRON Create a 3D mesh representing an Icosahedron.
%
% MESH = createIcosahedron;
% [V, E, F] = createIcosahedron;
% Create a solid with 12 vertices, and 20 triangular faces. Faces are
% oriented outwards of the mesh.
%
% [V, F] = createIcosahedron;
% Returns only the vertices and the face vertex indices.
%
% MESH = createIcosahedron;
% Returns the data as a mesh structure, with fields 'vertices', 'edges'
% and 'faces'.
%
% Example
% [n, e, f] = createIcosahedron;
% drawMesh(n, f);
%
% See also
% meshes3d, drawMesh
% createCube, createOctahedron, createDodecahedron, createTetrahedron
%
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-03-21
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
%% Initialisations
theta = 2*pi/5;
l = 1/sin(theta/2)/2;
z1 = sqrt(1-l*l);
t1 = (0:2*pi/5:2*pi*(1-1/5))';
x1 = l*cos(t1);
y1 = l*sin(t1);
t2 = t1 + 2*pi/10;
x2 = l*cos(t2);
y2 = l*sin(t2);
h = sqrt(l*l-.5*.5);
z2 = sqrt(3/4 - (l-h)*(l-h));
%% Create mesh data
nodes = [0 0 0;...
[x1 y1 repmat(z1, [5 1])]; ...
[x2 y2 repmat(z1+z2, [5 1])]; ...
0 0 2*z1+z2];
edges = [...
1 2;1 3;1 4;1 5;1 6; ...
2 3;3 4;4 5;5 6;6 2; ...
2 7;7 3;3 8;8 4;4 9;9 5;5 10;10 6;6 11;11 2; ...
7 8;8 9;9 10;10 11;11 7; ...
7 12;8 12;9 12;10 12;11 12];
% faces are ordered to have normals pointing outside of the mesh
faces = [...
1 3 2 ; 1 4 3 ; 1 5 4 ; 1 6 5 ; 1 2 6;...
2 3 7 ; 3 4 8 ; 4 5 9 ; 5 6 10 ; 6 2 11;...
7 3 8 ; 8 4 9 ; 9 5 10 ; 10 6 11 ; 11 2 7;...
7 8 12 ; 8 9 12 ; 9 10 12 ; 10 11 12 ; 11 7 12];
% format output
varargout = formatMeshOutput(nargout, nodes, edges, faces);
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