/**
 * \file
 * \author Thomas Fischer
 * \date   2011-03-17
 * \brief  Implementation of the AngleSkewMetric class.
 *
 * \copyright
 * Copyright (c) 2012-2020, OpenGeoSys Community (http://www.opengeosys.org)
 *            Distributed under a Modified BSD License.
 *              See accompanying file LICENSE.txt or
 *              http://www.opengeosys.org/project/license
 *
 */

#include "AngleSkewMetric.h"

#include <cmath>
#include <boost/math/constants/constants.hpp>

#include "MeshLib/Node.h"

#include "MathLib/MathTools.h"

using namespace boost::math::double_constants;

namespace MeshLib
{

namespace
{
template <unsigned long N>
std::tuple<double, double> getMinMaxAngle(
    std::array<MeshLib::Node, N> const& nodes)
{
    double min_angle(two_pi);
    double max_angle(0.0);

    for (decltype(N) i = 0; i < N; ++i)
    {
        const double angle(MathLib::getAngle(nodes[i], nodes[(i + 1) % N],
                                             nodes[(i + 2) % N]));
        min_angle = std::min(angle, min_angle);
        max_angle = std::max(angle, max_angle);
    }
    return {min_angle, max_angle};
}

double checkTriangle(Element const& elem)
{
    std::array const nodes = {*elem.getNode(0), *elem.getNode(1),
                              *elem.getNode(2)};
    auto const& [min_angle, max_angle] = getMinMaxAngle(nodes);
    return std::max((max_angle - third_pi) / two_thirds_pi,
                    (third_pi - min_angle) / third_pi);
}

double checkQuad(Element const& elem)
{
    std::array const nodes = {*elem.getNode(0), *elem.getNode(1),
                              *elem.getNode(2), *elem.getNode(3)};
    auto const& [min_angle, max_angle] = getMinMaxAngle(nodes);

    return std::max((max_angle - half_pi) / half_pi,
                    (half_pi - min_angle) / half_pi);
}

double checkTetrahedron(Element const& elem)
{
    std::array<double, 4> min;
    std::array<double, 4> max;
    for (auto face_number = 0; face_number < 4; ++face_number)
    {
        auto const& face = *elem.getFace(face_number);
        std::array const nodes = {*face.getNode(0), *face.getNode(1),
                                  *face.getNode(2)};
        std::tie(min[face_number], max[face_number]) = getMinMaxAngle(nodes);
    }

    double const min_angle = *std::min_element(min.begin(), min.end());
    double const max_angle = *std::max_element(max.begin(), max.end());

    return std::max((max_angle - third_pi) / two_thirds_pi,
                    (third_pi - min_angle) / third_pi);
}

double checkHexahedron(Element const& elem)
{
    std::array<double, 6> min;
    std::array<double, 6> max;
    for (auto face_number = 0; face_number < 6; ++face_number)
    {
        auto const& face = *elem.getFace(face_number);
        std::array const nodes = {*face.getNode(0), *face.getNode(1),
                                  *face.getNode(2), *face.getNode(3)};
        std::tie(min[face_number], max[face_number]) = getMinMaxAngle(nodes);
    }

    double const min_angle = *std::min_element(min.begin(), min.end());
    double const max_angle = *std::max_element(max.begin(), max.end());

    return std::max((max_angle - half_pi) / half_pi,
                    (half_pi - min_angle) / half_pi);
}

double checkPrism(Element const& elem)
{
    // face 0: triangle (0,1,2)
    auto const& f0 = *elem.getFace(0);
    std::array const nodes_f0 = {*f0.getNode(0), *f0.getNode(1),
                                 *f0.getNode(2)};
    auto const& [min_angle_tri0, max_angle_tri0] = getMinMaxAngle(nodes_f0);

    // face 4: triangle (3,4,5)
    auto const& f4 = *elem.getFace(4);
    std::array const nodes_f4 = {*f4.getNode(0), *f4.getNode(1),
                                 *f4.getNode(2)};
    auto const& [min_angle_tri1, max_angle_tri1] = getMinMaxAngle(nodes_f4);

    auto const min_angle_tri = std::min(min_angle_tri0, min_angle_tri1);
    auto const max_angle_tri = std::max(max_angle_tri0, max_angle_tri1);

    double const tri_criterion(
        std::max((max_angle_tri - third_pi) / two_thirds_pi,
                 (third_pi - min_angle_tri) / third_pi));

    std::array<double, 3> min;
    std::array<double, 3> max;
    for (int i = 1; i < 4; ++i)
    {
        auto const& f = *elem.getFace(i);
        std::array const nodes = {*f.getNode(0), *f.getNode(1), *f.getNode(2),
                                  *f.getNode(3)};
        std::tie(min[i - 1], max[i - 1]) = getMinMaxAngle(nodes);
    }

    double const min_angle_quad = *std::min_element(min.begin(), min.end());
    double const max_angle_quad = *std::max_element(max.begin(), max.end());

    double const quad_criterion(std::max((max_angle_quad - half_pi) / half_pi,
                                         (half_pi - min_angle_quad) / half_pi));

    return std::min(tri_criterion, quad_criterion);
}

}  // end unnamed namespace

AngleSkewMetric::AngleSkewMetric(Mesh const& mesh) :
    ElementQualityMetric(mesh)
{}

void AngleSkewMetric::calculateQuality()
{
    for (auto const e : _mesh.getElements())
    {
        switch (e->getGeomType())
        {
            case MeshElemType::LINE:
                _element_quality_metric[e->getID()] = -1.0;
                break;
            case MeshElemType::TRIANGLE:
                _element_quality_metric[e->getID()] = checkTriangle(*e);
                break;
            case MeshElemType::QUAD:
                _element_quality_metric[e->getID()] = checkQuad(*e);
                break;
            case MeshElemType::TETRAHEDRON:
                _element_quality_metric[e->getID()] = checkTetrahedron(*e);
                break;
            case MeshElemType::HEXAHEDRON:
                _element_quality_metric[e->getID()] = checkHexahedron(*e);
                break;
            case MeshElemType::PRISM:
                _element_quality_metric[e->getID()] = checkPrism(*e);
                break;
            default:
                break;
        }
    }
}

} // end namespace MeshLib