Tri.hpp

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#pragma once
 
#include <array>
#include "QuadratureBase.hpp"
 
namespace DNDS::Geom::Elem
{
    // ===================================================================
    // Hammer Quadrature on Reference Triangle
    // ===================================================================
    // Reference triangle: vertices at (0,0), (1,0), (0,1)
    // Area = 1/2
    //
    // Data format: [3][n] array where:
    //   [0][i] = xi coordinate (barycentric coord for vertex 1)
    //   [1][i] = eta coordinate (barycentric coord for vertex 2)
    //   [2][i] = quadrature weight (wi)
    //
    // Note: The third barycentric coordinate is 1 - xi - eta
    // ===================================================================
 
    /// Hammer rule with 1 point: degree 1 exact
    /// Point: centroid (1/3, 1/3), Weight: 1/2 (total area)
    namespace detail
    {
        static constexpr std::array<std::array<t_real, 1>, 3> HammerTri_1{{{{1. / 3.}},
                                                                           {{1. / 3.}},
                                                                           {{1. / 2.}}}};
 
        /// Hammer rule with 3 points: degree 2 exact
        /// Points: (2/3, 1/6), (1/6, 2/3), (1/6, 1/6)
        /// Weights: 1/6 each (sum = 1/2)
        static constexpr std::array<std::array<t_real, 3>, 3> HammerTri_3{{{{2. / 3., 1. / 6., 1. / 6.}},
                                                                           {{1. / 6., 2. / 3., 1. / 6.}},
                                                                           {{1. / 6., 1. / 6., 1. / 6.}}}};
 
        /// Hammer rule with 6 points: degree 4 exact
        /// Points include permutations of (a, a), (b, b), (c, d)
        static constexpr std::array<std::array<t_real, 6>, 3> HammerTri_6{{{{0.09157621350977102, 0.8168475729804585, 0.09157621350977052,
                                                                             0.445948490915965, 0.10810301816807, 0.445948490915965}},
                                                                           {{0.09157621350977102, 0.09157621350977052, 0.8168475729804585,
                                                                             0.445948490915965, 0.445948490915965, 0.10810301816807}},
                                                                           {{0.054975871827661, 0.054975871827661, 0.054975871827661,
                                                                             0.1116907948390057, 0.1116907948390057, 0.1116907948390057}}}};
 
        /// Hammer rule with 7 points: degree 5 exact
        /// Includes centroid + 6 points in 3 pairs
        static constexpr std::array<std::array<t_real, 7>, 3> HammerTri_7{{{{0.3333333333333335, 0.470142064105115, 0.05971587178977, 0.470142064105115,
                                                                             0.1012865073234565, 0.7974269853530875, 0.1012865073234565}},
                                                                           {{0.3333333333333335, 0.470142064105115, 0.470142064105115, 0.05971587178977,
                                                                             0.1012865073234565, 0.1012865073234565, 0.7974269853530875}},
                                                                           {{0.1125, 0.066197076394253, 0.066197076394253, 0.066197076394253,
                                                                             0.0629695902724135, 0.0629695902724135, 0.0629695902724135}}}};
 
        /// Hammer rule with 12 points: degree 6 exact
        static constexpr std::array<std::array<t_real, 12>, 3> HammerTri_12{{{{0.2492867451709105, 0.501426509658179, 0.2492867451709105,
                                                                               0.063089014491502, 0.8738219710169954, 0.063089014491502,
                                                                               0.3103524510337845, 0.05314504984481699, 0.6365024991213986,
                                                                               0.05314504984481699, 0.6365024991213986, 0.3103524510337845}},
                                                                             {{0.2492867451709105, 0.2492867451709105, 0.501426509658179,
                                                                               0.063089014491502, 0.063089014491502, 0.8738219710169954,
                                                                               0.05314504984481699, 0.3103524510337845, 0.05314504984481699,
                                                                               0.6365024991213986, 0.3103524510337845, 0.6365024991213986}},
                                                                             {{0.05839313786318975, 0.05839313786318975, 0.05839313786318975,
                                                                               0.0254224531851035, 0.0254224531851035, 0.0254224531851035,
                                                                               0.04142553780918675, 0.04142553780918675, 0.04142553780918675,
                                                                               0.04142553780918675, 0.04142553780918675, 0.04142553780918675}}}};
 
    } // namespace detail
} // namespace DNDS::Geom::Elem