DNDSR/doxygen/Pyramid14_8hpp_source.html

#pragma once

// Auto-generated by tools/gen_shape_functions -- DO NOT EDIT

// Element: Pyramid14

// Regenerate: /usr/bin/python3 -m tools.gen_shape_functions.generate


#include "DNDS/Defines.hpp"

#include "Geom/Geometric.hpp"

#include "Geom/ElemEnum.hpp"

#include "Geom/ElementTraitsBase.hpp"


namespace DNDS::Geom::Elem

{


    // Forward declaration (primary template is in ElementTraitsBase.hpp)

    template <ElemType>

    struct ShapeFuncImpl;


    // <GEN_SHAPE_FUNCS_BEGIN>

    template <>


    struct ShapeFuncImpl<Pyramid14>

    {

        template <class TPoint, class TArray>


        static void Diff0(const TPoint &p, TArray &&v)

        {

            t_real xi = p[0];

            t_real et = p[1];

            t_real zt = p[2];

            // singularity guard

            if (std::abs(1 - zt) < 1e-15)

                zt -= DNDS::signP(1 - zt) * 1e-15;

            const t_real _t0 = zt - 1;

            const t_real _t1 = _t0 + xi;

            const t_real _t2 = _t0 + et;

            const t_real _t3 = ((0.25)) * _t2;

            const t_real _t4 = _t1 * _t3;

            const t_real _t5 = 2 * zt - 1;

            const t_real _t6 = _t5 / ((_t0) * (_t0) * (_t0));

            const t_real _t7 = _t6 * xi;

            const t_real _t8 = _t7 * et;

            const t_real _t9 = 1 - zt;

            const t_real _t10 = _t9 + xi;

            const t_real _t11 = _t10 * _t7;

            const t_real _t12 = _t11 * et;

            const t_real _t13 = _t9 + et;

            const t_real _t14 = ((0.25)) * _t13;

            const t_real _t15 = _t1 * _t14;

            const t_real _t16 = ((_t0) * (_t0));

            const t_real _t17 = -_t16;

            const t_real _t18 = _t6 * (_t17 + ((xi) * (xi)));

            const t_real _t19 = ((0.5)) * _t18 * et;

            const t_real _t20 = _t17 + ((et) * (et));

            const t_real _t21 = ((0.5)) * _t20;

            const t_real _t22 = (((_t5) * (_t5)) - 1) / _t16;

            const t_real _t23 = _t10 * _t22;

            v(0, 0) = _t4 * _t8;

            v(0, 1) = _t12 * _t3;

            v(0, 2) = _t12 * _t14;

            v(0, 3) = _t15 * _t8;

            v(0, 4) = _t5 * zt;

            v(0, 5) = -_t19 * _t2;

            v(0, 6) = -_t11 * _t21;

            v(0, 7) = -_t13 * _t19;

            v(0, 8) = -_t1 * _t21 * _t7;

            v(0, 9) = -_t22 * _t4;

            v(0, 10) = _t23 * _t3;

            v(0, 11) = -_t14 * _t23;

            v(0, 12) = _t15 * _t22;

            v(0, 13) = _t18 * _t20;

        }


        template <class TPoint, class TArray>


        static void Diff1(const TPoint &p, TArray &&v)

        {

            t_real xi = p[0];

            t_real et = p[1];

            t_real zt = p[2];

            // singularity guard

            if (std::abs(1 - zt) < 1e-15)

                zt -= DNDS::signP(1 - zt) * 1e-15;

            const t_real _t0 = 2 * xi;

            const t_real _t1 = zt - 1;

            const t_real _t2 = _t0 + _t1;

            const t_real _t3 = _t1 + et;

            const t_real _t4 = 2 * zt - 1;

            const t_real _t5 = (1.0 / ((_t1) * (_t1) * (_t1)));

            const t_real _t6 = _t4 * _t5;

            const t_real _t7 = _t6 * et;

            const t_real _t8 = ((0.25)) * _t7;

            const t_real _t9 = _t3 * _t8;

            const t_real _t10 = 1 - zt;

            const t_real _t11 = _t0 + _t10;

            const t_real _t12 = _t10 + et;

            const t_real _t13 = _t12 * _t8;

            const t_real _t14 = _t3 * xi;

            const t_real _t15 = ((et) * (et));

            const t_real _t16 = ((_t1) * (_t1));

            const t_real _t17 = -_t16;

            const t_real _t18 = _t15 + _t17;

            const t_real _t19 = _t18 * _t6;

            const t_real _t20 = ((0.5)) * _t19;

            const t_real _t21 = _t12 * xi;

            const t_real _t22 = zt / _t1;

            const t_real _t23 = _t1 + xi;

            const t_real _t24 = 2 * et;

            const t_real _t25 = _t1 + _t24;

            const t_real _t26 = _t6 * xi;

            const t_real _t27 = ((0.25)) * _t26;

            const t_real _t28 = _t25 * _t27;

            const t_real _t29 = _t10 + xi;

            const t_real _t30 = _t10 + _t24;

            const t_real _t31 = _t27 * _t30;

            const t_real _t32 = ((xi) * (xi));

            const t_real _t33 = _t17 + _t32;

            const t_real _t34 = _t33 * _t6;

            const t_real _t35 = ((0.5)) * _t34;

            const t_real _t36 = _t29 * et;

            const t_real _t37 = _t23 * et;

            const t_real _t38 = 4 * zt;

            const t_real _t39 = _t38 - 3;

            const t_real _t40 = _t23 * _t3;

            const t_real _t41 = _t14 + _t37;

            const t_real _t42 = (1.0 / ((_t1) * (_t1) * (_t1) * (_t1)));

            const t_real _t43 = ((0.25)) * _t42 * et * xi;

            const t_real _t44 = _t29 * _t3;

            const t_real _t45 = _t14 + _t36;

            const t_real _t46 = _t12 * _t29;

            const t_real _t47 = _t21 + _t36;

            const t_real _t48 = _t12 * _t23;

            const t_real _t49 = _t21 + _t37;

            const t_real _t50 = -_t39;

            const t_real _t51 = _t3 * _t33;

            const t_real _t52 = 2 * _t32;

            const t_real _t53 = _t33 * et;

            const t_real _t54 = ((0.5)) * _t42;

            const t_real _t55 = _t54 * et;

            const t_real _t56 = _t18 * _t29;

            const t_real _t57 = 2 * _t15;

            const t_real _t58 = _t18 * xi;

            const t_real _t59 = _t54 * xi;

            const t_real _t60 = _t12 * _t33;

            const t_real _t61 = _t18 * _t23;

            const t_real _t62 = _t1 * _t4;

            const t_real _t63 = ((_t4) * (_t4)) - 1;

            const t_real _t64 = ((0.25)) * _t63;

            const t_real _t65 = (1.0 / (_t16));

            const t_real _t66 = _t15 * _t32 * _t42;

            v(0, 0) = _t2 * _t9;

            v(0, 1) = _t11 * _t9;

            v(0, 2) = _t11 * _t13;

            v(0, 3) = _t13 * _t2;

            v(0, 5) = -_t14 * _t7;

            v(0, 6) = -_t11 * _t20;

            v(0, 7) = -_t21 * _t7;

            v(0, 8) = -_t2 * _t20;

            v(0, 9) = -_t22 * _t3;

            v(0, 10) = _t22 * _t3;

            v(0, 11) = -_t12 * _t22;

            v(0, 12) = _t12 * _t22;

            v(0, 13) = _t0 * _t19;

            v(1, 0) = _t23 * _t28;

            v(1, 1) = _t28 * _t29;

            v(1, 2) = _t29 * _t31;

            v(1, 3) = _t23 * _t31;

            v(1, 5) = -_t25 * _t35;

            v(1, 6) = -_t26 * _t36;

            v(1, 7) = -_t30 * _t35;

            v(1, 8) = -_t26 * _t37;

            v(1, 9) = -_t22 * _t23;

            v(1, 10) = _t22 * _t29;

            v(1, 11) = -_t22 * _t29;

            v(1, 12) = _t22 * _t23;

            v(1, 13) = _t24 * _t34;

            v(2, 0) = _t43 * (_t23 * _t3 * _t39 - _t4 * (2 * _t40 + _t41));

            v(2, 1) = _t43 * (_t29 * _t3 * _t39 - _t4 * (2 * _t44 + _t45));

            v(2, 2) = _t43 * (_t12 * _t29 * _t39 - _t4 * (2 * _t46 + _t47));

            v(2, 3) = _t43 * (_t12 * _t23 * _t39 - _t4 * (2 * _t48 + _t49));

            v(2, 4) = _t38 - 1;

            v(2, 5) = _t55 * (_t4 * (_t3 * _t52 + _t51 + _t53) + _t50 * _t51);

            v(2, 6) = _t59 * (_t4 * (_t29 * _t57 + _t56 + _t58) + _t50 * _t56);

            v(2, 7) = _t55 * (_t4 * (_t12 * _t52 + _t53 + _t60) + _t50 * _t60);

            v(2, 8) = _t59 * (_t4 * (_t23 * _t57 + _t58 + _t61) + _t50 * _t61);

            v(2, 9) = _t5 * (-_t40 * _t62 + ((0.25)) * _t41 * _t63);

            v(2, 10) = _t5 * (_t44 * _t62 - _t45 * _t64);

            v(2, 11) = _t5 * (-_t46 * _t62 + ((0.25)) * _t47 * _t63);

            v(2, 12) = _t5 * (_t48 * _t62 - _t49 * _t64);

            v(2, 13) = _t15 * _t65 + _t32 * _t65 - _t38 * _t66 + _t39 + _t66;

        }


        template <class TPoint, class TArray>


        static void Diff2(const TPoint &p, TArray &&v)

        {

            t_real xi = p[0];

            t_real et = p[1];

            t_real zt = p[2];

            // singularity guard

            if (std::abs(1 - zt) < 1e-15)

                zt -= DNDS::signP(1 - zt) * 1e-15;

            const t_real _t0 = zt - 1;

            const t_real _t1 = _t0 + et;

            const t_real _t2 = 2 * zt;

            const t_real _t3 = _t2 - 1;

            const t_real _t4 = _t3 / ((_t0) * (_t0) * (_t0));

            const t_real _t5 = _t4 * et;

            const t_real _t6 = _t1 * _t5;

            const t_real _t7 = ((0.5)) * _t6;

            const t_real _t8 = 1 - zt;

            const t_real _t9 = _t8 + et;

            const t_real _t10 = _t5 * _t9;

            const t_real _t11 = ((0.5)) * _t10;

            const t_real _t12 = ((et) * (et));

            const t_real _t13 = ((_t0) * (_t0));

            const t_real _t14 = -_t13;

            const t_real _t15 = _t4 * (_t12 + _t14);

            const t_real _t16 = -_t15;

            const t_real _t17 = _t0 + xi;

            const t_real _t18 = _t4 * xi;

            const t_real _t19 = _t17 * _t18;

            const t_real _t20 = ((0.5)) * _t19;

            const t_real _t21 = _t8 + xi;

            const t_real _t22 = _t18 * _t21;

            const t_real _t23 = ((0.5)) * _t22;

            const t_real _t24 = ((xi) * (xi));

            const t_real _t25 = _t4 * (_t14 + _t24);

            const t_real _t26 = -_t25;

            const t_real _t27 = ((zt) * (zt));

            const t_real _t28 = _t27 * xi;

            const t_real _t29 = 2 * _t28;

            const t_real _t30 = -_t2 + _t27 + 1;

            const t_real _t31 = _t29 + _t30;

            const t_real _t32 = -xi;

            const t_real _t33 = xi * zt;

            const t_real _t34 = et * zt;

            const t_real _t35 = 6 * _t34;

            const t_real _t36 = _t35 * xi;

            const t_real _t37 = _t32 - _t33 + _t36;

            const t_real _t38 = -et;

            const t_real _t39 = _t27 * et;

            const t_real _t40 = 2 * _t39;

            const t_real _t41 = -_t34 + _t38 + _t40;

            const t_real _t42 = ((zt) * (zt) * (zt) * (zt) * (zt));

            const t_real _t43 = ((zt) * (zt) * (zt));

            const t_real _t44 = ((zt) * (zt) * (zt) * (zt));

            const t_real _t45 = (1.0 / (-10 * _t27 + _t42 + 10 * _t43 - 5 * _t44 + 5 * zt - 1));

            const t_real _t46 = et * xi;

            const t_real _t47 = ((0.5)) * _t45 * _t46;

            const t_real _t48 = -_t27 + _t3;

            const t_real _t49 = _t48 + et;

            const t_real _t50 = -_t40;

            const t_real _t51 = _t34 + _t50;

            const t_real _t52 = _t30 + xi;

            const t_real _t53 = -_t29;

            const t_real _t54 = _t33 + _t36 + _t53;

            const t_real _t55 = _t48 + xi;

            const t_real _t56 = _t24 * _t35;

            const t_real _t57 = _t24 * zt;

            const t_real _t58 = _t24 * _t27;

            const t_real _t59 = _t24 + _t57 - 2 * _t58;

            const t_real _t60 = _t2 * et;

            const t_real _t61 = -_t60;

            const t_real _t62 = _t39 + _t61 + et;

            const t_real _t63 = _t45 * et;

            const t_real _t64 = 6 * _t12 * _t33;

            const t_real _t65 = _t12 * zt;

            const t_real _t66 = _t12 * _t27;

            const t_real _t67 = _t12 + _t65 - 2 * _t66;

            const t_real _t68 = _t2 * xi;

            const t_real _t69 = -_t28 + _t32 + _t68;

            const t_real _t70 = _t45 * xi;

            const t_real _t71 = _t38 - _t39 + _t60;

            const t_real _t72 = -_t68;

            const t_real _t73 = _t28 + _t72 + xi;

            const t_real _t74 = 3 * zt;

            const t_real _t75 = 3 * _t27;

            const t_real _t76 = _t43 + _t74 - _t75 - 1;

            const t_real _t77 = 2 / _t76;

            const t_real _t78 = _t77 * (-_t46 - _t76);

            const t_real _t79 = -_t74;

            const t_real _t80 = _t77 * (-_t43 + _t46 + _t75 + _t79 + 1);

            const t_real _t81 = _t17 * et;

            const t_real _t82 = _t1 * xi + _t46;

            const t_real _t83 = ((0.25)) * _t4;

            const t_real _t84 = _t21 * et;

            const t_real _t85 = _t46 + _t9 * xi;

            const t_real _t86 = 2 * et;

            const t_real _t87 = 2 * xi;

            const t_real _t88 = zt / _t0;

            const t_real _t89 = -_t88;

            const t_real _t90 = 4 * _t34;

            const t_real _t91 = 4 * _t39;

            const t_real _t92 = -_t90 + _t91;

            const t_real _t93 = 8 * _t34;

            const t_real _t94 = _t93 * xi;

            const t_real _t95 = _t94 - 2 * et * xi;

            const t_real _t96 = _t31 + _t72;

            const t_real _t97 = 4 * zt;

            const t_real _t98 = 6 * _t27 - 4 * _t43 + _t44 - _t97 + 1;

            const t_real _t99 = (1.0 / (_t98));

            const t_real _t100 = ((0.25)) * _t99;

            const t_real _t101 = _t100 * xi;

            const t_real _t102 = 2 * _t46 - _t94;

            const t_real _t103 = _t30 + _t53 + _t68;

            const t_real _t104 = _t90 - _t91;

            const t_real _t105 = _t24 * et;

            const t_real _t106 = -_t57 + _t58 + _t98;

            const t_real _t107 = 3 - _t97;

            const t_real _t108 = 4 * xi;

            const t_real _t109 = _t79 + 3;

            const t_real _t110 = (1.0 / ((_t0) * (_t0) * (_t0) * (_t0)));

            const t_real _t111 = _t110 * _t46;

            const t_real _t112 = _t74 - 3;

            const t_real _t113 = (1.0 / (_t30));

            const t_real _t114 = (1.0 / (_t13));

            const t_real _t115 = _t110 * _t24;

            const t_real _t116 = _t30 + _t95;

            const t_real _t117 = _t40 + _t61;

            const t_real _t118 = 4 * _t33;

            const t_real _t119 = 4 * _t28;

            const t_real _t120 = -_t118 + _t119;

            const t_real _t121 = _t100 * et;

            const t_real _t122 = _t118 - _t119;

            const t_real _t123 = _t102 + _t30;

            const t_real _t124 = _t50 + _t60;

            const t_real _t125 = 4 * et;

            const t_real _t126 = _t12 * xi;

            const t_real _t127 = -_t65 + _t66 + _t98;

            const t_real _t128 = _t30 + et;

            const t_real _t129 = _t110 * _t12;

            v(0, 0) = _t7;

            v(0, 1) = _t7;

            v(0, 2) = _t11;

            v(0, 3) = _t11;

            v(0, 5) = -_t6;

            v(0, 6) = _t16;

            v(0, 7) = -_t10;

            v(0, 8) = _t16;

            v(0, 13) = 2 * _t15;

            v(1, 0) = _t20;

            v(1, 1) = _t23;

            v(1, 2) = _t23;

            v(1, 3) = _t20;

            v(1, 5) = _t26;

            v(1, 6) = -_t22;

            v(1, 7) = _t26;

            v(1, 8) = -_t19;

            v(1, 13) = 2 * _t25;

            v(2, 0) = _t47 * (_t31 + _t37 + _t41);

            v(2, 1) = _t47 * (_t29 + _t37 + _t49 + _t51);

            v(2, 2) = _t47 * (_t51 + _t52 + _t54 + et);

            v(2, 3) = _t47 * (_t41 + _t54 + _t55);

            v(2, 4) = 4;

            v(2, 5) = _t63 * (-_t56 + _t59 + _t62);

            v(2, 6) = _t70 * (-_t64 - _t67 - _t69);

            v(2, 7) = _t63 * (-_t56 - _t59 - _t71);

            v(2, 8) = _t70 * (-_t64 + _t67 + _t73);

            v(2, 9) = _t78;

            v(2, 10) = _t80;

            v(2, 11) = _t78;

            v(2, 12) = _t80;

            v(2, 13) = 2 * _t45 * (6 * _t12 * _t24 * zt + 2 * _t12 * zt - _t12 + 2 * _t24 * zt - _t24 - 20 * _t27 + 2 * _t42 + 20 * _t43 - 10 * _t44 - _t58 - _t66 + 10 * zt - 2);

            v(3, 0) = _t83 * (_t1 * _t17 + _t81 + _t82);

            v(3, 1) = _t83 * (_t1 * _t21 + _t82 + _t84);

            v(3, 2) = _t83 * (_t21 * _t9 + _t84 + _t85);

            v(3, 3) = _t83 * (_t17 * _t9 + _t81 + _t85);

            v(3, 5) = _t18 * (-_t0 - _t86);

            v(3, 6) = _t5 * (-_t8 - _t87);

            v(3, 7) = _t18 * (-_t8 - _t86);

            v(3, 8) = _t5 * (-_t0 - _t87);

            v(3, 9) = _t89;

            v(3, 10) = _t88;

            v(3, 11) = _t89;

            v(3, 12) = _t88;

            v(3, 13) = 4 * _t4 * _t46;

            v(4, 0) = _t101 * (-_t92 - _t95 - _t96);

            v(4, 1) = _t101 * (_t102 + _t103 + _t92);

            v(4, 2) = _t101 * (-_t103 - _t104 - _t95);

            v(4, 3) = _t101 * (_t102 + _t104 + _t96);

            v(4, 5) = _t99 * (-_t105 + _t106 + _t24 * _t90 + _t71);

            v(4, 6) = _t111 * (_t107 * _t21 + _t3 * (_t108 + _t109));

            v(4, 7) = _t99 * (-_t105 - _t106 + 4 * _t24 * et * zt - _t62);

            v(4, 8) = _t111 * (_t107 * _t17 + _t3 * (_t108 + _t112));

            v(4, 9) = _t113 * _t55;

            v(4, 10) = -_t113 * _t52;

            v(4, 11) = _t113 * _t52;

            v(4, 12) = -_t113 * _t55;

            v(4, 13) = _t114 * _t86 + _t115 * _t86 - _t115 * _t93;

            v(5, 0) = _t121 * (-_t116 - _t117 - _t120);

            v(5, 1) = _t121 * (_t117 + _t122 + _t123);

            v(5, 2) = _t121 * (-_t116 - _t122 - _t124);

            v(5, 3) = _t121 * (_t120 + _t123 + _t124);

            v(5, 5) = _t111 * (_t1 * _t107 + _t3 * (_t112 + _t125));

            v(5, 6) = _t99 * (4 * _t12 * xi * zt - _t126 - _t127 - _t73);

            v(5, 7) = _t111 * (_t107 * _t9 + _t3 * (_t109 + _t125));

            v(5, 8) = _t99 * (_t118 * _t12 - _t126 + _t127 + _t69);

            v(5, 9) = _t113 * _t49;

            v(5, 10) = -_t113 * _t49;

            v(5, 11) = _t113 * _t128;

            v(5, 12) = -_t113 * _t128;

            v(5, 13) = _t114 * _t87 - 8 * _t129 * _t33 + _t129 * _t87;

        }


        template <class TPoint, class TArray>


        static void Diff3(const TPoint &p, TArray &&v)

        {

            t_real xi = p[0];

            t_real et = p[1];

            t_real zt = p[2];

            // singularity guard

            if (std::abs(1 - zt) < 1e-15)

                zt -= DNDS::signP(1 - zt) * 1e-15;

            const t_real _t0 = 2 * et;

            const t_real _t1 = _t0 * xi;

            const t_real _t2 = xi * zt;

            const t_real _t3 = 8 * et;

            const t_real _t4 = _t2 * _t3;

            const t_real _t5 = 2 * zt;

            const t_real _t6 = ((zt) * (zt));

            const t_real _t7 = -_t5 + _t6 + 1;

            const t_real _t8 = _t1 + _t4 + _t7;

            const t_real _t9 = -_t0;

            const t_real _t10 = 2 * xi;

            const t_real _t11 = _t10 * _t6;

            const t_real _t12 = _t11 + _t9;

            const t_real _t13 = _t0 * _t6;

            const t_real _t14 = -_t10;

            const t_real _t15 = _t13 + _t14;

            const t_real _t16 = 6 * zt;

            const t_real _t17 = ((zt) * (zt) * (zt));

            const t_real _t18 = ((zt) * (zt) * (zt) * (zt));

            const t_real _t19 = ((zt) * (zt) * (zt) * (zt) * (zt));

            const t_real _t20 = (1.0 / (-_t16 - 20 * _t17 + 15 * _t18 - 6 * _t19 + 15 * _t6 + ((zt) * (zt) * (zt) * (zt) * (zt) * (zt)) + 1));

            const t_real _t21 = et * xi;

            const t_real _t22 = ((1.5)) * _t20 * _t21;

            const t_real _t23 = -_t13;

            const t_real _t24 = _t0 + _t23;

            const t_real _t25 = -_t6;

            const t_real _t26 = _t5 - 1;

            const t_real _t27 = _t25 + _t26;

            const t_real _t28 = _t1 + _t27 + _t4;

            const t_real _t29 = -_t11;

            const t_real _t30 = _t10 + _t29;

            const t_real _t31 = ((xi) * (xi));

            const t_real _t32 = 2 * _t31;

            const t_real _t33 = _t32 * _t6;

            const t_real _t34 = -et;

            const t_real _t35 = _t6 * et;

            const t_real _t36 = -_t35;

            const t_real _t37 = _t0 * zt;

            const t_real _t38 = _t31 * zt;

            const t_real _t39 = _t0 * _t31 + _t3 * _t38 + _t34 + _t36 + _t37;

            const t_real _t40 = 3 * _t20;

            const t_real _t41 = _t40 * et;

            const t_real _t42 = ((et) * (et));

            const t_real _t43 = 2 * _t42;

            const t_real _t44 = _t43 * _t6;

            const t_real _t45 = -_t44;

            const t_real _t46 = -xi;

            const t_real _t47 = _t6 * xi;

            const t_real _t48 = -_t47;

            const t_real _t49 = _t10 * zt;

            const t_real _t50 = 8 * _t42;

            const t_real _t51 = _t10 * _t42 + _t2 * _t50 + _t46 + _t48 + _t49;

            const t_real _t52 = _t40 * xi;

            const t_real _t53 = -_t33;

            const t_real _t54 = 4 * zt;

            const t_real _t55 = (1.0 / (-4 * _t17 + _t18 - _t54 + 6 * _t6 + 1));

            const t_real _t56 = 6 * _t21 * _t55;

            const t_real _t57 = -_t56;

            const t_real _t58 = zt - 1;

            const t_real _t59 = _t0 + _t58;

            const t_real _t60 = _t26 / ((_t58) * (_t58) * (_t58));

            const t_real _t61 = ((0.5)) * _t60;

            const t_real _t62 = _t59 * _t61;

            const t_real _t63 = -zt;

            const t_real _t64 = _t63 + 1;

            const t_real _t65 = _t0 + _t64;

            const t_real _t66 = _t61 * _t65;

            const t_real _t67 = -_t0 * _t60;

            const t_real _t68 = 4 * et;

            const t_real _t69 = _t10 + _t58;

            const t_real _t70 = _t61 * _t69;

            const t_real _t71 = _t10 + _t64;

            const t_real _t72 = _t61 * _t71;

            const t_real _t73 = -_t10 * _t60;

            const t_real _t74 = 4 * xi;

            const t_real _t75 = _t58 + xi;

            const t_real _t76 = _t54 - 3;

            const t_real _t77 = 3 * zt;

            const t_real _t78 = _t77 - 3;

            const t_real _t79 = _t74 + _t78;

            const t_real _t80 = (1.0 / ((_t58) * (_t58) * (_t58) * (_t58)));

            const t_real _t81 = _t80 * xi;

            const t_real _t82 = ((0.5)) * _t81;

            const t_real _t83 = _t82 * (-_t26 * _t79 + _t75 * _t76);

            const t_real _t84 = _t64 + xi;

            const t_real _t85 = 3 - _t77;

            const t_real _t86 = _t74 + _t85;

            const t_real _t87 = _t82 * (-_t26 * _t86 + _t76 * _t84);

            const t_real _t88 = (1.0 / ((_t58) * (_t58)));

            const t_real _t89 = _t31 * _t80;

            const t_real _t90 = 4 * _t31 * _t80 * zt - _t88 - _t89;

            const t_real _t91 = -_t76;

            const t_real _t92 = 2 * _t88;

            const t_real _t93 = 12 * et;

            const t_real _t94 = _t2 * _t93;

            const t_real _t95 = _t7 + _t94;

            const t_real _t96 = -_t2;

            const t_real _t97 = _t46 + _t96;

            const t_real _t98 = 4 * _t35;

            const t_real _t99 = -_t37 + _t98;

            const t_real _t100 = (1.0 / (10 * _t17 - 5 * _t18 + _t19 - 10 * _t6 + 5 * zt - 1));

            const t_real _t101 = ((0.5)) * _t100;

            const t_real _t102 = _t101 * xi;

            const t_real _t103 = _t27 + _t94;

            const t_real _t104 = _t0 + _t37 - _t98;

            const t_real _t105 = _t2 + _t29 + xi;

            const t_real _t106 = _t54 * et;

            const t_real _t107 = _t38 * _t93;

            const t_real _t108 = _t31 + _t38 + _t53;

            const t_real _t109 = _t16 * xi;

            const t_real _t110 = 2 * _t6;

            const t_real _t111 = -_t110 + zt + 1;

            const t_real _t112 = _t1 * _t100;

            const t_real _t113 = _t110 + _t63 - 1;

            const t_real _t114 = (1.0 / (_t17 - 3 * _t6 + _t77 - 1));

            const t_real _t115 = _t10 * _t114;

            const t_real _t116 = -_t115;

            const t_real _t117 = 4 * _t47;

            const t_real _t118 = _t117 - _t49;

            const t_real _t119 = et * zt;

            const t_real _t120 = -_t119;

            const t_real _t121 = _t120 + _t34;

            const t_real _t122 = _t101 * et;

            const t_real _t123 = _t119 + _t23 + et;

            const t_real _t124 = _t10 - _t117 + _t49;

            const t_real _t125 = _t16 * et;

            const t_real _t126 = _t54 * xi;

            const t_real _t127 = 12 * _t2 * _t42;

            const t_real _t128 = _t42 * zt;

            const t_real _t129 = _t128 + _t42 + _t45;

            const t_real _t130 = _t0 * _t114;

            const t_real _t131 = -_t130;

            const t_real _t132 = _t58 + et;

            const t_real _t133 = _t68 + _t78;

            const t_real _t134 = _t80 * et;

            const t_real _t135 = ((0.5)) * _t134;

            const t_real _t136 = _t135 * (_t132 * _t76 - _t133 * _t26);

            const t_real _t137 = _t64 + et;

            const t_real _t138 = _t68 + _t85;

            const t_real _t139 = _t135 * (_t137 * _t76 - _t138 * _t26);

            const t_real _t140 = 4 * _t42 * _t80 * zt - _t42 * _t80 - _t88;

            const t_real _t141 = -(0.5) * zt;

            const t_real _t142 = ((0.25)) * _t6;

            const t_real _t143 = _t120 + _t141 + _t142 + _t35 + (0.25);

            const t_real _t144 = _t21 * _t54;

            const t_real _t145 = _t144 - et * xi;

            const t_real _t146 = _t47 + _t96;

            const t_real _t147 = _t2 + _t48;

            const t_real _t148 = -_t144 + _t21;

            const t_real _t149 = _t119 + _t141 + _t142 + _t36 + (0.25);

            const t_real _t150 = _t106 + _t34;

            const t_real _t151 = _t6 + _t63;

            const t_real _t152 = _t10 * _t55;

            const t_real _t153 = _t25 + zt;

            const t_real _t154 = _t126 + _t46;

            const t_real _t155 = _t0 * _t55;

            const t_real _t156 = (1.0 / (_t7));

            const t_real _t157 = -_t156;

            v(2, 0) = _t22 * (-_t12 - _t15 - _t8);

            v(2, 1) = _t22 * (-_t11 - _t14 - _t24 - _t28);

            v(2, 2) = _t22 * (-_t24 - _t30 - _t8);

            v(2, 3) = _t22 * (-_t13 - _t28 - _t30 - _t9);

            v(2, 5) = _t41 * (-_t32 + _t33 + _t39);

            v(2, 6) = _t52 * (_t43 + _t45 + _t51);

            v(2, 7) = _t41 * (_t32 + _t39 + _t53);

            v(2, 8) = _t52 * (-_t43 + _t44 + _t51);

            v(2, 9) = _t56;

            v(2, 10) = _t57;

            v(2, 11) = _t56;

            v(2, 12) = _t57;

            v(2, 13) = 6 * _t20 * (-_t31 * _t5 + _t31 * _t6 + _t31 - _t32 * _t42 - _t38 * _t50 - _t42 * _t5 + _t42 * _t6 + _t42);

            v(3, 0) = _t62;

            v(3, 1) = _t62;

            v(3, 2) = _t66;

            v(3, 3) = _t66;

            v(3, 5) = -_t59 * _t60;

            v(3, 6) = _t67;

            v(3, 7) = -_t60 * _t65;

            v(3, 8) = _t67;

            v(3, 13) = _t60 * _t68;

            v(4, 0) = _t70;

            v(4, 1) = _t72;

            v(4, 2) = _t72;

            v(4, 3) = _t70;

            v(4, 5) = _t73;

            v(4, 6) = -_t60 * _t71;

            v(4, 7) = _t73;

            v(4, 8) = -_t60 * _t69;

            v(4, 13) = _t60 * _t74;

            v(5, 0) = _t83;

            v(5, 1) = _t87;

            v(5, 2) = _t87;

            v(5, 3) = _t83;

            v(5, 5) = _t90;

            v(5, 6) = _t81 * (_t26 * _t86 + _t84 * _t91);

            v(5, 7) = _t90;

            v(5, 8) = _t81 * (_t26 * _t79 + _t75 * _t91);

            v(5, 13) = _t32 * _t80 - 8 * _t89 * zt + _t92;

            v(6, 0) = _t102 * (_t12 + _t95 + _t97 + _t99);

            v(6, 1) = _t102 * (_t103 + _t104 + _t11 + _t97);

            v(6, 2) = _t102 * (_t104 + _t105 + _t95);

            v(6, 3) = _t102 * (_t103 + _t105 + _t9 + _t99);

            v(6, 5) = _t100 * (_t0 - _t106 - _t107 + _t108 + _t13);

            v(6, 6) = _t112 * (-_t109 - _t111);

            v(6, 7) = _t100 * (-_t106 - _t107 - _t108 - _t23 - _t9);

            v(6, 8) = _t112 * (-_t109 - _t113);

            v(6, 9) = _t116;

            v(6, 10) = _t115;

            v(6, 11) = _t116;

            v(6, 12) = _t115;

            v(6, 13) = _t100 * _t68 * (_t16 * _t31 + _t27);

            v(7, 0) = _t122 * (_t118 + _t121 + _t15 + _t95);

            v(7, 1) = _t122 * (_t103 + _t118 + _t123 + _t14);

            v(7, 2) = _t122 * (_t123 + _t124 + _t95);

            v(7, 3) = _t122 * (_t103 + _t121 + _t124 + _t13);

            v(7, 5) = _t112 * (-_t113 - _t125);

            v(7, 6) = _t100 * (-_t126 - _t127 - _t129 - _t14 - _t29);

            v(7, 7) = _t112 * (-_t111 - _t125);

            v(7, 8) = _t100 * (_t10 + _t11 - _t126 - _t127 + _t129);

            v(7, 9) = _t131;

            v(7, 10) = _t130;

            v(7, 11) = _t131;

            v(7, 12) = _t130;

            v(7, 13) = _t100 * _t74 * (_t16 * _t42 + _t27);

            v(8, 0) = _t136;

            v(8, 1) = _t136;

            v(8, 2) = _t139;

            v(8, 3) = _t139;

            v(8, 5) = _t134 * (_t132 * _t91 + _t133 * _t26);

            v(8, 6) = _t140;

            v(8, 7) = _t134 * (_t137 * _t91 + _t138 * _t26);

            v(8, 8) = _t140;

            v(8, 13) = -8 * _t128 * _t80 + _t43 * _t80 + _t92;

            v(9, 0) = _t55 * (-_t143 - _t145 - _t146);

            v(9, 1) = _t55 * (_t143 + _t147 + _t148);

            v(9, 2) = _t55 * (-_t145 - _t147 - _t149);

            v(9, 3) = _t55 * (_t146 + _t148 + _t149);

            v(9, 5) = _t152 * (_t150 + _t151);

            v(9, 6) = _t155 * (_t153 + _t154);

            v(9, 7) = _t152 * (_t150 + _t153);

            v(9, 8) = _t155 * (_t151 + _t154);

            v(9, 9) = _t156;

            v(9, 10) = _t157;

            v(9, 11) = _t156;

            v(9, 12) = _t157;

            v(9, 13) = _t134 * _t74 * (1 - _t54);

        }


    };


    // <GEN_SHAPE_FUNCS_END>


    // <GEN_ELEM_TRAITS_BEGIN>


    template <>


    struct ElementTraits<Pyramid14>

    {

        static constexpr ElemType elemType = Pyramid14;

        static constexpr int dim = 3;

        static constexpr int order = 2;

        static constexpr int numVertices = 5;

        static constexpr int numNodes = 14;

        static constexpr int numFaces = 5;

        static constexpr int numEdges = 8;

        static constexpr ParamSpace paramSpace = PyramidSpace;

        static constexpr t_real paramSpaceVol = 4.0 / 3.0;

        // 3 * NNodes is a compile-time constant; no overflow possible.

        // NOLINTNEXTLINE(bugprone-implicit-widening-of-multiplication-result)


        static constexpr std::array<t_real, 3 * 14> standardCoords = {

            -1, -1, 0,       // Node 0: vertex

            1, -1, 0,        // Node 1: vertex

            1, 1, 0,         // Node 2: vertex

            -1, 1, 0,        // Node 3: vertex

            0, 0, 1,         // Node 4: vertex

            0, -1, 0,        // Node 5

            1, 0, 0,         // Node 6

            0, 1, 0,         // Node 7

            -1, 0, 0,        // Node 8

            -0.5, -0.5, 0.5, // Node 9

            0.5, -0.5, 0.5,  // Node 10

            0.5, 0.5, 0.5,   // Node 11

            -0.5, 0.5, 0.5,  // Node 12

            0, 0, 0};        // Node 13


        static constexpr ElemType GetFaceType(t_index iFace)

        {

            if (iFace < 1)

                return Quad9;

            return Tri6;

        }


        static constexpr std::array<std::array<t_index, 10>, 5> faceNodes = {{{0, 3, 2, 1, 8, 7, 6, 5, 13},

                                                                              {0, 1, 4, 5, 10, 9},

                                                                              {1, 2, 4, 6, 11, 10},

                                                                              {2, 3, 4, 7, 12, 11},

                                                                              {3, 0, 4, 8, 9, 12}}};


        static constexpr ElemType GetEdgeType(t_index /*iEdge*/) { return Line3; }


        static constexpr std::array<std::array<t_index, 3>, 8> edgeNodes = {{{0, 1, 5},

                                                                             {1, 2, 6},

                                                                             {2, 3, 7},

                                                                             {3, 0, 8},

                                                                             {0, 4, 9},

                                                                             {1, 4, 10},

                                                                             {2, 4, 11},

                                                                             {3, 4, 12}}};


        static constexpr ElemType elevatedType = UnknownElem;

        static constexpr int numElevNodes = 0;


        static constexpr int numBisect = 12;

        static constexpr int numBisectVariants = 2;


        static constexpr ElemType GetBisectElemType(t_index i)

        {

            if (i < 4)

                return Pyramid5;

            return Tet4;

        }


        static constexpr std::array<tBisectSub, 24> bisectElements = {{// Variant 0

                                                                       {0, 5, 13, 8, 9},

                                                                       {5, 1, 6, 13, 10},

                                                                       {8, 13, 7, 3, 12},

                                                                       {13, 6, 2, 7, 11},

                                                                       {12, 9, 8, 13},

                                                                       {9, 10, 5, 13},

                                                                       {10, 11, 6, 13},

                                                                       {11, 12, 7, 13},

                                                                       {9, 11, 12, 4},

                                                                       {9, 10, 11, 4},

                                                                       {9, 11, 10, 13},

                                                                       {9, 12, 11, 13},

                                                                       // Variant 1

                                                                       {0, 5, 13, 8, 9},

                                                                       {5, 1, 6, 13, 10},

                                                                       {8, 13, 7, 3, 12},

                                                                       {13, 6, 2, 7, 11},

                                                                       {12, 9, 8, 13},

                                                                       {9, 10, 5, 13},

                                                                       {10, 11, 6, 13},

                                                                       {11, 12, 7, 13},

                                                                       {10, 12, 9, 4},

                                                                       {10, 11, 12, 4},

                                                                       {10, 12, 11, 13},

                                                                       {10, 9, 12, 13}}};


        static constexpr int vtkCellType = 27;


        static constexpr std::array<int, 14> vtkNodeOrder = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13};

    };


    // <GEN_ELEM_TRAITS_END>


} // namespace DNDS::Geom::Elem

Defines.hpp
Core type aliases, constants, and metaprogramming utilities for the DNDS framework.

ElemEnum.hpp

ElementTraitsBase.hpp

Geometric.hpp

DNDS::Geom::Elem
Definition Elements.cpp:4

DNDS::Geom::Elem::ElemType
ElemType
Definition ElemEnum.hpp:19

DNDS::Geom::Elem::Tri6
@ Tri6
Definition ElemEnum.hpp:25

DNDS::Geom::Elem::Line3
@ Line3
Definition ElemEnum.hpp:22

DNDS::Geom::Elem::Pyramid14
@ Pyramid14
Definition ElemEnum.hpp:36

DNDS::Geom::Elem::Quad9
@ Quad9
Definition ElemEnum.hpp:27

DNDS::Geom::Elem::UnknownElem
@ UnknownElem
Definition ElemEnum.hpp:20

DNDS::Geom::Elem::Tet4
@ Tet4
Definition ElemEnum.hpp:29

DNDS::Geom::Elem::Pyramid5
@ Pyramid5
Definition ElemEnum.hpp:35

DNDS::Geom::Elem::ParamSpace
ParamSpace
Definition ElemEnum.hpp:42

DNDS::Geom::Elem::PyramidSpace
@ PyramidSpace
Definition ElemEnum.hpp:52

DNDS::Geom::t_index
int32_t t_index
Definition Geometric.hpp:6

DNDS::Geom::t_real
double t_real
Definition Geometric.hpp:8

DNDS::signP
constexpr real signP(real a)
"Signum, biased toward +1": treats 0 as positive.
Definition Defines.hpp:549

DNDS::Geom::Elem::ElementTraits< Pyramid14 >::GetBisectElemType
static constexpr ElemType GetBisectElemType(t_index i)
Definition Pyramid14.hpp:722

DNDS::Geom::Elem::ElementTraits< Pyramid14 >::GetFaceType
static constexpr ElemType GetFaceType(t_index iFace)
Definition Pyramid14.hpp:692

DNDS::Geom::Elem::ElementTraits< Pyramid14 >::GetEdgeType
static constexpr ElemType GetEdgeType(t_index)
Definition Pyramid14.hpp:705

DNDS::Geom::Elem::ElementTraits
Definition ElementTraitsBase.hpp:22

DNDS::Geom::Elem::ShapeFuncImpl< Pyramid14 >::Diff2
static void Diff2(const TPoint &p, TArray &&v)
Definition Pyramid14.hpp:190

DNDS::Geom::Elem::ShapeFuncImpl< Pyramid14 >::Diff0
static void Diff0(const TPoint &p, TArray &&v)
Definition Pyramid14.hpp:23

DNDS::Geom::Elem::ShapeFuncImpl< Pyramid14 >::Diff1
static void Diff1(const TPoint &p, TArray &&v)
Definition Pyramid14.hpp:72

DNDS::Geom::Elem::ShapeFuncImpl< Pyramid14 >::Diff3
static void Diff3(const TPoint &p, TArray &&v)
Definition Pyramid14.hpp:402

DNDS::Geom::Elem::ShapeFuncImpl
Definition Elements.hpp:174

v
Eigen::Matrix< real, 5, 1 > v
Definition test_ArrayDOF.cpp:468

i
res i
Definition test_MeshConnectivity_Interpolate.cpp:205

order
double order
Definition test_ODE.cpp:257

p
const tPoint const tPoint const tPoint & p
Definition test_Reconstruction.cpp:484