icosahedron.h

/*****************************************************************************
 * VCLib                                                                     *
 * Visual Computing Library                                                  *
 *                                                                           *
 * Copyright(C) 2021-2025                                                    *
 * Visual Computing Lab                                                      *
 * ISTI - Italian National Research Council                                  *
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 * it under the terms of the Mozilla Public License Version 2.0 as published *
 * by the Mozilla Foundation; either version 2 of the License, or            *
 * (at your option) any later version.                                       *
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 * This program is distributed in the hope that it will be useful,           *
 * but WITHOUT ANY WARRANTY; without even the implied warranty of            *
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the              *
 * Mozilla Public License Version 2.0                                        *
 * (https://www.mozilla.org/en-US/MPL/2.0/) for more details.                *
 ****************************************************************************/
 
#ifndef VCL_ALGORITHMS_MESH_CREATE_ICOSAHEDRON_H
#define VCL_ALGORITHMS_MESH_CREATE_ICOSAHEDRON_H
 
#include <vclib/mesh/requirements.h>
 
namespace vcl {
 
template<FaceMeshConcept MeshType>
MeshType createIcosahedron(bool normalizeVertices = false)
{
    using VertexType = MeshType::VertexType;
    using CoordType  = VertexType::CoordType;
 
    MeshType mesh;
 
    const double t = (1.0 + std::sqrt(5.0)) / 2.0;
 
    // Vertices
    mesh.addVertex(CoordType(-1.0, t, 0.0));
    mesh.addVertex(CoordType(1.0, t, 0.0));
    mesh.addVertex(CoordType(-1.0, -t, 0.0));
    mesh.addVertex(CoordType(1.0, -t, 0.0));
    mesh.addVertex(CoordType(0.0, -1.0, t));
    mesh.addVertex(CoordType(0.0, 1.0, t));
    mesh.addVertex(CoordType(0.0, -1.0, -t));
    mesh.addVertex(CoordType(0.0, 1.0, -t));
    mesh.addVertex(CoordType(t, 0.0, -1.0));
    mesh.addVertex(CoordType(t, 0.0, 1.0));
    mesh.addVertex(CoordType(-t, 0.0, -1.0));
    mesh.addVertex(CoordType(-t, 0.0, 1.0));
 
    if (normalizeVertices) {
        for (VertexType& v : mesh.vertices())
            v.coord().normalize();
    }
 
    // Faces
    mesh.addFace(0, 11, 5);
    mesh.addFace(0, 5, 1);
    mesh.addFace(0, 1, 7);
    mesh.addFace(0, 7, 10);
    mesh.addFace(0, 10, 11);
    mesh.addFace(1, 5, 9);
    mesh.addFace(5, 11, 4);
    mesh.addFace(11, 10, 2);
    mesh.addFace(10, 7, 6);
    mesh.addFace(7, 1, 8);
    mesh.addFace(3, 9, 4);
    mesh.addFace(3, 4, 2);
    mesh.addFace(3, 2, 6);
    mesh.addFace(3, 6, 8);
    mesh.addFace(3, 8, 9);
    mesh.addFace(4, 9, 5);
    mesh.addFace(2, 4, 11);
    mesh.addFace(6, 2, 10);
    mesh.addFace(8, 6, 7);
    mesh.addFace(9, 8, 1);
 
    return mesh;
}
 
} // namespace vcl
 
#endif // VCL_ALGORITHMS_MESH_CREATE_ICOSAHEDRON_H