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// ************************************************************************************************
//
// BornAgain: simulate and fit reflection and scattering
//
//! @file Img3D/Mesh/Dodecahedron.cpp
//! @brief Implements utility functions in ba3d namespace.
//!
//! @homepage http://www.bornagainproject.org
//! @license GNU General Public License v3 or higher (see COPYING)
//! @copyright Forschungszentrum Jülich GmbH 2018
//! @authors Scientific Computing Group at MLZ (see CITATION, AUTHORS)
//
// ************************************************************************************************
#include "Base/Util/Assert.h"
#include "Img3D/Model/Geometry.h"
#include <QQuaternion>
namespace Img3D {
Geometry::Mesh Geometry::meshDodecahedron()
{
const float GR = GoldenRatio, G1 = 1 / GR;
Vertices vs_;
vs_.reserve(20);
for (float x : {-1, +1})
for (float y : {-1, +1})
for (float z : {-1, +1})
vs_.append(F3(x, y, z));
for (float g1 : {-G1, +G1})
for (float g : {-GR, +GR}) {
vs_.append(F3(0, g1, g));
vs_.append(F3(g1, g, 0));
vs_.append(F3(g, 0, g1));
}
ASSERT(20 == vs_.count());
// scale to circumscribed sphere
float const F = .5f / vs_.at(0).length();
for (auto& v : vs_)
v = v * F;
// face down
auto q = QQuaternion::rotationTo(
F3(0, 0, -1), F3::crossProduct(vs_.at(8) - vs_.at(0), vs_.at(10) - vs_.at(0)));
for (int i = 0; i < 20; ++i) {
vs_[i] = q.rotatedVector(vs_.at(i));
vs_[i].setZ(vs_[i].z() + 0.5f * std::sqrt(G1));
// shift the bottom of the dodecahedron to z=0 plane
}
Vertices vs;
vs.reserve(180);
auto add5 = [&](unsigned i1, unsigned i2, unsigned i3, unsigned i4, unsigned i5) {
vs.addFan(vs_, {i1, i2, i3, i4, i5, i1});
};
add5(1, 11, 17, 3, 16); // bottom
add5(1, 16, 10, 0, 9);
add5(16, 3, 12, 2, 10);
add5(3, 17, 7, 18, 12);
add5(17, 11, 5, 19, 7);
add5(11, 1, 9, 15, 5);
add5(8, 4, 15, 9, 0);
add5(14, 8, 0, 10, 2);
add5(6, 14, 2, 12, 18);
add5(13, 6, 18, 7, 19);
add5(4, 13, 19, 5, 15);
add5(4, 8, 14, 6, 13); // top
ASSERT(144 == vs.count());
return makeMesh(vs);
}
} // namespace Img3D
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