// Examples to demonstrate Algoim's methods for computing high-order accurate quadrature schemes
// for implicitly defined domains in hyperrectangles. The file contains a single main() routine;
// compile it as you would for any .cpp file with a main() entry point.

#include <iostream>
#include <iomanip>
#include <fstream>
#include "quadrature_general.hpp"

template <int N>
struct Ellipsoid {
    template <typename T>
    T operator()(const algoim::uvector<T, N>& x) const
    {
        if constexpr (N == 2)
            return x(0) * x(0) + 4.0 * x(1) * x(1) - 1.0;
        else
            return x(0) * x(0) + 4.0 * x(1) * x(1) + 9.0 * x(2) * x(2) - 1.0;
    }

    template <typename T>
    algoim::uvector<T, N> grad(const algoim::uvector<T, N>& x) const
    {
        if constexpr (N == 2)
            return algoim::uvector<T, N>(2.0 * x(0), 8.0 * x(1));
        else
            return algoim::uvector<T, N>(2.0 * x(0), 8.0 * x(1), 18.0 * x(2));
    }
};

#if ALGOIM_EXAMPLES_DRIVER == 0 || ALGOIM_EXAMPLES_DRIVER == 1
int main(int argc, char* argv[])
{
    std::cout << "Algoim Examples - High-order quadrature algorithms for implicitly defined domains\n\n";
    std::cout << std::fixed << std::setprecision(16);

    // Area of a 2D ellipse using automatic subdivision
    {
        std::cout << "Area of a 2D ellipse using automatic subdivision:\n";
        Ellipsoid<2> phi;
        auto         q    = algoim::quadGen<2>(phi, algoim::HyperRectangle<double, 2>(-1.1, 1.1), -1, -1, 4);
        double       area = q([](const auto& x) { return 1.0; });
        std::cout << "  computed area = " << area << "\n";
        std::cout << "    (exact area = 1.5707963267948966)\n\n";
    }

    // Volume of a 3D ellipsoid using automatic subdivision
    {
        std::cout << "Volume of a 3D ellipsoid using automatic subdivision:\n";
        Ellipsoid<3> phi;
        auto         q      = algoim::quadGen<3>(phi, algoim::HyperRectangle<double, 3>(-1.1, 1.1), -1, -1, 4);
        double       volume = q([](const auto& x) { return 1.0; });
        std::cout << "  computed volume = " << volume << "\n";
        std::cout << "    (exact volume = 0.6981317007977318)\n\n";
    }

    // Area of a 2D ellipse, computed via the cells of a Cartesian grid
    {
        int n = 16;
        std::cout << "Area of a 2D ellipse, computed via the cells of a " << n << " by " << n << " Cartesian grid:\n";
        double       dx = 2.2 / n;
        Ellipsoid<2> phi;
        double       area = 0.0;
        for (int i = 0; i < n; ++i)
            for (int j = 0; j < n; ++j) {
                algoim::uvector<double, 2> xmin{-1.1 + i * dx, -1.1 + j * dx};
                algoim::uvector<double, 2> xmax{-1.1 + i * dx + dx, -1.1 + j * dx + dx};
                area += algoim::quadGen<2>(phi, algoim::HyperRectangle<double, 2>(xmin, xmax), -1, -1, 4).sumWeights();
            }
        std::cout << "  computed area = " << area << "\n";
        std::cout << "    (exact area = 1.5707963267948966)\n\n";
    }

    // Surface area of a 3D ellipsoid using automatic subdivision
    {
        std::cout << "Surface area of a 3D ellipsoid using automatic subdivision:\n";
        Ellipsoid<3> phi;
        auto         q            = algoim::quadGen<3>(phi, algoim::HyperRectangle<double, 3>(-1.1, 1.1), 3, -1, 4);
        double       surface_area = q.sumWeights();
        std::cout << "  computed surface area = " << surface_area << "\n";
        std::cout << "    (exact surface area = 4.4008095646649703)\n\n";
    }

    // Visualisation of a quadrature scheme in ParaView via XML VTP file
    {
        std::cout << "Visualisation of a quadrature scheme in ParaView via XML VTP file:\n";
        Ellipsoid<3>  phi;
        auto          q = algoim::quadGen<3>(phi, algoim::HyperRectangle<double, 3>(-1.1, 1.1), -1, -1, 2);
        std::ofstream f("scheme.vtp");
        algoim::outputQuadratureRuleAsVtpXML(q, f);
        std::cout << "  scheme.vtp file written, containing " << q.nodes.size() << " quadrature points\n";
    }

    return 0;
}
#endif