Tri.hpp

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#pragma once
 
#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)
    static const t_real __HammerTri_1[3][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 const t_real __HammerTri_3[3][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 const t_real __HammerTri_6[3][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 const t_real __HammerTri_7[3][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 const t_real __HammerTri_12[3][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 DNDS::Geom::Elem