Tri3.hpp

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#pragma once
// Auto-generated by tools/gen_shape_functions -- DO NOT EDIT
// Element: Tri3
// 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<Tri3>
    {
        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];
            v(0, 0) = -et - xi + 1;
            v(0, 1) = xi;
            v(0, 2) = et;
        }
 
        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];
            v(0, 0) = -1;
            v(0, 1) = 1;
            v(1, 0) = -1;
            v(1, 2) = 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];
            // 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];
            // all zero
        }
    };
    // <GEN_SHAPE_FUNCS_END>
 
 
    /**
     * @brief Element traits for 3-node linear triangle (Tri3)
     * 
     * Tri3 is the simplest 2D element, commonly used for:
     * - Unstructured triangular meshes
     * - Simplex mesh generation
     * - Boundary layer regions requiring high aspect ratio cells
     * 
     * Geometry:
     * - Reference triangle with vertices at (0,0), (1,0), (0,1)
     * - Parametric space is a right triangle with area = 0.5
     * 
     * Faces:
     * - 3 edges, each is a Line2 element
     */
    template <>
    struct ElementTraits<Tri3>
    {
        // ============================================================
        // Core Element Identification
        // ============================================================
        
        static constexpr ElemType elemType = Tri3;
        static constexpr int dim = 2;
        static constexpr int order = 1;
        static constexpr int numVertices = 3;
        static constexpr int numNodes = 3;
        static constexpr int numFaces = 3;
        static constexpr ParamSpace paramSpace = TriSpace;
        static constexpr t_real paramSpaceVol = 0.5;
 
        // ============================================================
        // Geometry Definition
        // ============================================================
        
        /**
         * @brief Standard coordinates of nodes in parametric space
         * 
         * Node 0: (0, 0) - origin
         * Node 1: (1, 0) - on xi axis
         * Node 2: (0, 1) - on eta axis
         * 
         * Forms a right triangle covering half of the unit square.
         */
        static constexpr std::array<t_real, 3 * 3> standardCoords = {
            0, 0, 0,   // Node 0: origin
            1, 0, 0,   // Node 1: xi = 1
            0, 1, 0};  // Node 2: eta = 1
 
        // ============================================================
        // Face/Edge Definitions
        // ============================================================
        
        /**
         * @brief Get the element type of a face (edge)
         * @return Line2 (all edges of triangle are linear lines)
         */
        static constexpr ElemType GetFaceType(t_index /*iFace*/) { return Line2; }
 
        /**
         * @brief Node indices for each face (edge)
         * 
         * Edge 0: nodes 0-1 (bottom edge along xi axis)
         * Edge 1: nodes 1-2 (hypotenuse from (1,0) to (0,1))
         * Edge 2: nodes 2-0 (left edge along eta axis)
         * 
         * Note: Face normal direction follows right-hand rule.
         */
        static constexpr std::array<std::array<t_index, 10>, 3> faceNodes = {{
            {0, 1},     // Edge 0: bottom
            {1, 2},     // Edge 1: hypotenuse
            {2, 0}}};   // Edge 2: left
 
        // ============================================================
        // Order Elevation (P-Refinement)
        // ============================================================
        
        /**
         * @brief Element type after order elevation (O1 -> O2)
         * Tri3 elevates to Tri6 (6-node quadratic triangle)
         */
        static constexpr ElemType elevatedType = Tri6;
        
        /// @brief Number of additional nodes created during elevation (3 edge midpoints)
        static constexpr int numElevNodes = 3;
        
        /**
         * @brief Elevation spans define edge midpoints
         * 
         * Each new node is at the midpoint of an edge:
         *   Span 0: nodes {0, 1} -> edge 0 midpoint
         *   Span 1: nodes {1, 2} -> edge 1 midpoint
         *   Span 2: nodes {2, 0} -> edge 2 midpoint
         */
        static constexpr std::array<tElevSpan, 3> elevSpans = {{
            {0, 1},     // Edge 0 midpoint
            {1, 2},     // Edge 1 midpoint
            {2, 0}}};   // Edge 2 midpoint
        
        /// @brief Element type of each elevation span (all are Line2 edges)
        static constexpr std::array<ElemType, 3> elevNodeSpanTypes = {Line2, Line2, Line2};
 
        // ============================================================
        // VTK/Visualization Support
        // ============================================================
        
        /// @brief VTK cell type identifier (5 = VTK_TRIANGLE)
        static constexpr int vtkCellType = 5;
        
        /**
         * @brief VTK node ordering map
         * 
         * VTK uses the same ordering as DNDS for Tri3:
         *   VTK node 0 = DNDS node 0
         *   VTK node 1 = DNDS node 1
         *   VTK node 2 = DNDS node 2
         */
        static constexpr std::array<int, 3> vtkNodeOrder = {0, 1, 2};
    };
 
} // namespace DNDS::Geom::Elem