Tet4.hpp

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#pragma once
// Auto-generated by tools/gen_shape_functions -- DO NOT EDIT
// Element: Tet4
// 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<Tet4>
    {
        template <class TPoint, class TArray>
        DNDS_DEVICE_CALLABLE static inline void Diff0(const TPoint &p, TArray &&v)
        {
            t_real xi = p[0];
            t_real et = p[1];
            t_real zt = p[2];
            v(0, 0) = -et - xi - zt + 1;
            v(0, 1) = xi;
            v(0, 2) = et;
            v(0, 3) = zt;
        }
 
        template <class TPoint, class TArray>
        DNDS_DEVICE_CALLABLE static inline void Diff1(const TPoint &p, TArray &&v)
        {
            t_real xi = p[0];
            t_real et = p[1];
            t_real zt = p[2];
            v(0, 0) = -1;
            v(0, 1) = 1;
            v(1, 0) = -1;
            v(1, 2) = 1;
            v(2, 0) = -1;
            v(2, 3) = 1;
        }
 
        template <class TPoint, class TArray>
        DNDS_DEVICE_CALLABLE static inline void Diff2(const TPoint &p, TArray &&v)
        {
            t_real xi = p[0];
            t_real et = p[1];
            t_real zt = p[2];
            // all zero
        }
 
        template <class TPoint, class TArray>
        DNDS_DEVICE_CALLABLE static inline void Diff3(const TPoint &p, TArray &&v)
        {
            t_real xi = p[0];
            t_real et = p[1];
            t_real zt = p[2];
            // all zero
        }
    };
    // <GEN_SHAPE_FUNCS_END>
 
 
    /**
     * @brief Element traits for 4-node linear tetrahedron (Tet4)
     *
     * Tet4 is the simplest 3D element, commonly used for:
     * - Unstructured tetrahedral meshes
     * - Automatic mesh generation
     * - Complex geometry representation
     *
     * Geometry:
     * - Reference tetrahedron with vertices at (0,0,0), (1,0,0), (0,1,0), (0,0,1)
     * - Parametric space volume = 1/6
     *
     * Faces:
     * - 4 triangular faces, each is a Tri3 element
     */
    template <>
    struct ElementTraits<Tet4>
    {
        // ============================================================
        // Core Element Identification
        // ============================================================
 
        static constexpr ElemType elemType = Tet4;
        static constexpr int dim = 3;
        static constexpr int order = 1;
        static constexpr int numVertices = 4;
        static constexpr int numNodes = 4;
        static constexpr int numFaces = 4;
        static constexpr ParamSpace paramSpace = TetSpace;
        static constexpr t_real paramSpaceVol = 1.0 / 6.0;
 
        // ============================================================
        // Geometry Definition
        // ============================================================
 
        /**
         * @brief Standard coordinates of nodes in parametric space
         *
         * Reference tetrahedron with nodes at:
         * Node 0: (0, 0, 0) - origin
         * Node 1: (1, 0, 0) - on x-axis
         * Node 2: (0, 1, 0) - on y-axis
         * Node 3: (0, 0, 1) - on z-axis
         */
        static constexpr std::array<t_real, 3 * 4> standardCoords = {
            0, 0, 0,   // Node 0: origin
            1, 0, 0,   // Node 1: x-axis
            0, 1, 0,   // Node 2: y-axis
            0, 0, 1};  // Node 3: z-axis
 
        // ============================================================
        // Face/Edge Definitions
        // ============================================================
 
        /**
         * @brief Get the element type of a face
         * @return Tri3 (all faces of tet are triangles)
         */
        static constexpr ElemType GetFaceType(t_index /*iFace*/) { return Tri3; }
 
        /**
         * @brief Node indices for each face (triangular face)
         *
         * Face 0: nodes 0-2-1 (bottom face, z=0)
         * Face 1: nodes 0-1-3 (side face, y=0)
         * Face 2: nodes 1-2-3 (side face, x=0 is opposite)
         * Face 3: nodes 2-0-3 (side face, x=0)
         *
         * Note: Node ordering follows right-hand rule for outward normals.
         */
        static constexpr std::array<std::array<t_index, 10>, 4> faceNodes = {{
            {0, 2, 1},     // Face 0: bottom (z=0 plane)
            {0, 1, 3},     // Face 1: side (y=0 plane)
            {1, 2, 3},     // Face 2: side (diagonal)
            {2, 0, 3}}};   // Face 3: side (x=0 plane)
 
        // ============================================================
        // Order Elevation (P-Refinement)
        // ============================================================
 
        /**
         * @brief Element type after order elevation (O1 -> O2)
         * Tet4 elevates to Tet10 (10-node quadratic tetrahedron)
         */
        static constexpr ElemType elevatedType = Tet10;
 
        /// @brief Number of additional nodes created during elevation (6 edge midpoints)
        static constexpr int numElevNodes = 6;
 
        /**
         * @brief Elevation spans define edge midpoints
         *
         * Each new node is at the midpoint of an edge:
         *   Span 0-2: edges of base triangle
         *   Span 3-5: edges connecting apex to base vertices
         */
        static constexpr std::array<tElevSpan, 6> elevSpans = {{
            {0, 1},     // Edge 0-1 midpoint
            {1, 2},     // Edge 1-2 midpoint
            {2, 0},     // Edge 2-0 midpoint
            {0, 3},     // Edge 0-3 midpoint
            {1, 3},     // Edge 1-3 midpoint
            {2, 3}}};   // Edge 2-3 midpoint
 
        /// @brief Element type of each elevation span (all are Line2 edges)
        static constexpr std::array<ElemType, 6> elevNodeSpanTypes = {
            Line2, Line2, Line2, Line2, Line2, Line2};
 
        // ============================================================
        // VTK/Visualization Support
        // ============================================================
 
        /// @brief VTK cell type identifier (10 = VTK_TETRA)
        static constexpr int vtkCellType = 10;
 
        /**
         * @brief VTK node ordering map
         *
         * VTK uses the same ordering as DNDS for Tet4:
         *   VTK node 0 = DNDS node 0, VTK node 1 = DNDS node 1, etc.
         */
        static constexpr std::array<int, 4> vtkNodeOrder = {0, 1, 2, 3};
    };
 
} // namespace DNDS::Geom::Elem