// SPDX-FileComment: This file is part of TNL - Template Numerical Library (https://tnl-project.org/)
// SPDX-License-Identifier: MIT

#pragma once

#include <TNL/Backend/Macros.h>
#include <TNL/Meshes/GridEntity.h>
#include <TNL/Meshes/Mesh.h>
#include <TNL/Meshes/MeshEntity.h>
#include <TNL/Meshes/Geometry/getOutwardNormalVector.h>
#include <TNL/Meshes/Topologies/Vertex.h>
#include <TNL/Meshes/Topologies/Edge.h>
#include <TNL/Meshes/Topologies/Triangle.h>
#include <TNL/Meshes/Topologies/Quadrangle.h>
#include <TNL/Meshes/Topologies/Tetrahedron.h>
#include <TNL/Meshes/Topologies/Hexahedron.h>
#include <TNL/Meshes/Topologies/Polygon.h>
#include <TNL/Meshes/Topologies/Wedge.h>
#include <TNL/Meshes/Topologies/Pyramid.h>
#include <TNL/Meshes/Topologies/Polyhedron.h>

namespace TNL::Meshes {

template< typename Grid >
__cuda_callable__
typename Grid::RealType
getEntityMeasure( const Grid& grid, const GridEntity< Grid, 0 >& entity )
{
   // entity.getMeasure() returns 0.0 !!!
   return 1.0;
}

template< typename Grid, int EntityDimension, typename Config >
__cuda_callable__
typename Grid::RealType
getEntityMeasure( const Grid& grid, const GridEntity< Grid, EntityDimension >& entity )
{
   return entity.getMeasure();
}

// Vertex
template< typename MeshConfig, typename Device >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure( const Mesh< MeshConfig, Device >& mesh, const MeshEntity< MeshConfig, Device, Topologies::Vertex >& entity )
{
   return 1.0;
}

// Edge
template< typename MeshConfig, typename Device >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure( const Mesh< MeshConfig, Device >& mesh, const MeshEntity< MeshConfig, Device, Topologies::Edge >& entity )
{
   const auto& v0 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 0 ) );
   const auto& v1 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 1 ) );
   return l2Norm( v1 - v0 );
}

// Triangle
template< typename VectorExpression, std::enable_if_t< VectorExpression::getSize() == 2, bool > = true >
__cuda_callable__
typename VectorExpression::RealType
getTriangleArea( const VectorExpression& v1, const VectorExpression& v2 )
{
   using Real = typename VectorExpression::RealType;
   return Real( 0.5 ) * TNL::abs( v1.x() * v2.y() - v1.y() * v2.x() );
}

template< typename VectorExpression, std::enable_if_t< VectorExpression::getSize() == 3, bool > = true >
__cuda_callable__
typename VectorExpression::RealType
getTriangleArea( const VectorExpression& v1, const VectorExpression& v2 )
{
   using Real = typename VectorExpression::RealType;
   // formula from http://math.stackexchange.com/a/128999
   const Real c1 = v1.y() * v2.z() - v1.z() * v2.y();  // first component of the cross product
   const Real c2 = v1.z() * v2.x() - v1.x() * v2.z();  // second component of the cross product
   const Real c3 = v1.x() * v2.y() - v1.y() * v2.x();  // third component of the cross product
   return Real( 0.5 ) * TNL::sqrt( c1 * c1 + c2 * c2 + c3 * c3 );
}

template< typename MeshConfig, typename Device >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure( const Mesh< MeshConfig, Device >& mesh, const MeshEntity< MeshConfig, Device, Topologies::Triangle >& entity )
{
   const auto& v0 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 0 ) );
   const auto& v1 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 1 ) );
   const auto& v2 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 2 ) );
   return getTriangleArea( v2 - v0, v1 - v0 );
}

// Quadrangle
template< typename MeshConfig, typename Device >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure(
   const Mesh< MeshConfig, Device >& mesh,
   const MeshEntity< MeshConfig, Device, Topologies::Quadrangle >& entity )
{
   // measure = 0.5 * |AC x BD|, where AC and BD are the diagonals
   // Hence, we can use the same formula as for the triangle area.
   const auto& v0 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 0 ) );
   const auto& v1 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 1 ) );
   const auto& v2 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 2 ) );
   const auto& v3 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 3 ) );
   return getTriangleArea( v2 - v0, v3 - v1 );
}

template< typename VectorExpression >
__cuda_callable__
typename VectorExpression::RealType
getTetrahedronVolume( const VectorExpression& v1, const VectorExpression& v2, const VectorExpression& v3 )
{
   using Real = typename VectorExpression::RealType;
   // V = (1/6) * det(v1, v2, v3)
   const Real det = v1.x() * v2.y() * v3.z() + v1.y() * v2.z() * v3.x() + v1.z() * v2.x() * v3.y()
                  - ( v1.z() * v2.y() * v3.x() + v1.y() * v2.x() * v3.z() + v1.x() * v2.z() * v3.y() );
   return Real( 1.0 / 6.0 ) * TNL::abs( det );
}

template< typename MeshConfig, typename Device >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure(
   const Mesh< MeshConfig, Device >& mesh,
   const MeshEntity< MeshConfig, Device, Topologies::Tetrahedron >& entity )
{
   const auto& v0 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 0 ) );
   const auto& v1 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 1 ) );
   const auto& v2 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 2 ) );
   const auto& v3 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 3 ) );
   return getTetrahedronVolume( v3 - v0, v2 - v0, v1 - v0 );
}

template< typename MeshConfig, typename Device >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure(
   const Mesh< MeshConfig, Device >& mesh,
   const MeshEntity< MeshConfig, Device, Topologies::Hexahedron >& entity )
{
   const auto& v0 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 0 ) );
   const auto& v1 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 1 ) );
   const auto& v2 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 2 ) );
   const auto& v3 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 3 ) );
   const auto& v4 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 4 ) );
   const auto& v5 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 5 ) );
   const auto& v6 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 6 ) );
   const auto& v7 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 7 ) );
   // https://www.cfd-online.com/Forums/main/163122-volume-general-hexahedron.html#post574650
   return getTetrahedronVolume( v0 - v4, v3 - v4, v1 - v4 ) + getTetrahedronVolume( v2 - v4, v3 - v4, v1 - v4 )
        + getTetrahedronVolume( v1 - v4, v2 - v4, v5 - v4 ) + getTetrahedronVolume( v6 - v4, v2 - v4, v5 - v4 )
        + getTetrahedronVolume( v3 - v4, v2 - v4, v7 - v4 ) + getTetrahedronVolume( v6 - v4, v2 - v4, v7 - v4 );
}

// Polygon
template< int Coord1, int Coord2, typename MeshConfig, typename Device >
__cuda_callable__
typename MeshConfig::RealType
getPolygon2DArea( const Mesh< MeshConfig, Device >& mesh, const MeshEntity< MeshConfig, Device, Topologies::Polygon >& entity )
{
   // http://geomalgorithms.com/code.html (function area2D_Polygon)

   static_assert(
      Coord1 >= 0 && Coord1 <= 2 && Coord2 >= 0 && Coord2 <= 2 && Coord1 != Coord2,
      "Coord1 and Coord2 must be different integers with possible values {0, 1, 2}." );

   using Real = typename MeshConfig::RealType;
   using Index = typename MeshConfig::LocalIndexType;

   Real area = 0;
   const auto n = entity.template getSubentitiesCount< 0 >();
   auto v0 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 0 ) );
   auto v1 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 1 ) );
   for( Index j = 2; j < n; j++ ) {
      const auto& vj = mesh.getPoint( entity.template getSubentityIndex< 0 >( j ) );
      area += v1[ Coord1 ] * ( vj[ Coord2 ] - v0[ Coord2 ] );
      v0 = v1;
      v1 = vj;
   }

   // 1. wrap around term
   {
      const auto& vj = mesh.getPoint( entity.template getSubentityIndex< 0 >( 0 ) );
      area += v1[ Coord1 ] * ( vj[ Coord2 ] - v0[ Coord2 ] );
      v0 = v1;
      v1 = vj;
   }

   // 2. wrap around term
   {
      const auto& vj = mesh.getPoint( entity.template getSubentityIndex< 0 >( 1 ) );
      area += v1[ Coord1 ] * ( vj[ Coord2 ] - v0[ Coord2 ] );
   }

   return Real( 0.5 ) * area;
}

template< typename MeshConfig, typename Device, std::enable_if_t< MeshConfig::spaceDimension == 2, bool > = true >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure( const Mesh< MeshConfig, Device >& mesh, const MeshEntity< MeshConfig, Device, Topologies::Polygon >& entity )
{
   const auto area = getPolygon2DArea< 0, 1 >( mesh, entity );
   return TNL::abs( area );
}

template< typename MeshConfig, typename Device, std::enable_if_t< MeshConfig::spaceDimension == 3, bool > = true >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure( const Mesh< MeshConfig, Device >& mesh, const MeshEntity< MeshConfig, Device, Topologies::Polygon >& entity )

{
   // http://geomalgorithms.com/code.html (function area3D_Polygon)

   using Real = typename MeshConfig::RealType;

   // select largest abs coordinate of normal vector to ignore for projection
   auto normal = getNormalVector( mesh, entity );
   normal = TNL::abs( normal );
   int coord = 2;  // ignore z-coord
   if( normal.x() > normal.y() ) {
      if( normal.x() > normal.z() )
         coord = 0;  // ignore x-coord
   }
   else if( normal.y() > normal.z() ) {
      coord = 1;  // ignore y-coord
   }

   Real area;
   switch( coord ) {
      case 0:  // ignored x-coord
         area = getPolygon2DArea< 1, 2 >( mesh, entity );
         area *= l2Norm( normal ) / normal.x();
         break;
      case 1:  // ignored y-coord
         area = getPolygon2DArea< 0, 2 >( mesh, entity );
         area *= l2Norm( normal ) / normal.y();
         break;
      default:  // ignored z-coord
         area = getPolygon2DArea< 0, 1 >( mesh, entity );
         area *= l2Norm( normal ) / normal.z();
         break;
   }
   return TNL::abs( area );
}

// Wedge
template< typename MeshConfig, typename Device >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure( const Mesh< MeshConfig, Device >& mesh, const MeshEntity< MeshConfig, Device, Topologies::Wedge >& entity )
{
   const auto& v0 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 0 ) );
   const auto& v1 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 1 ) );
   const auto& v2 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 2 ) );
   const auto& v3 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 3 ) );
   const auto& v4 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 4 ) );
   const auto& v5 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 5 ) );
   // Partition wedge into three tetrahedrons.
   return getTetrahedronVolume( v2 - v3, v0 - v3, v1 - v3 ) + getTetrahedronVolume( v2 - v3, v1 - v3, v4 - v3 )
        + getTetrahedronVolume( v2 - v3, v4 - v3, v5 - v3 );
}

// Pyramid
template< typename MeshConfig, typename Device >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure( const Mesh< MeshConfig, Device >& mesh, const MeshEntity< MeshConfig, Device, Topologies::Pyramid >& entity )
{
   const auto& v0 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 0 ) );
   const auto& v1 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 1 ) );
   const auto& v2 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 2 ) );
   const auto& v3 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 3 ) );
   const auto& v4 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 4 ) );
   // Partition pyramid into two tetrahedrons.
   return getTetrahedronVolume( v4 - v0, v3 - v0, v1 - v0 ) + getTetrahedronVolume( v4 - v2, v1 - v2, v3 - v2 );
}

// Polyhedron
/*template< typename MeshConfig,
          typename Device >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure( const Mesh< MeshConfig, Device > & mesh,
                  const MeshEntity< MeshConfig, Device, Topologies::Polyhedron > & entity )
{
    using Real = typename MeshConfig::RealType;
    using Index = typename MeshConfig::LocalIndexType;
    Real volume{ 0.0 };
    const Index facesCount = entity.template getSubentitiesCount< 2 >();
    for( Index faceIdx = 0; faceIdx < facesCount; faceIdx++ ) {
        const auto face = mesh.template getEntity< 2 >( entity.template getSubentityIndex< 2 >( faceIdx ) );
        const Index verticesCount = face.template getSubentitiesCount< 0 >();
        const auto& v0 = mesh.getPoint( face.template getSubentityIndex< 0 >( 0 ) );
        for( Index i = 1, j = 2; j < verticesCount; i++, j++ ) {
            const auto& v1 = mesh.getPoint( face.template getSubentityIndex< 0 >( i ) );
            const auto& v2 = mesh.getPoint( face.template getSubentityIndex< 0 >( j ) );
            // Partition polyhedron into tetrahedrons by triangulating faces and connecting each triangle to the origin point
(0,0,0).
            // It is required that vertices of all faces are stored consistently in CW or CCW order as faces are viewed from the
outside.
            // Otherwise signs of some tetrahedron volumes may be incorrect, resulting in overall incorrect volume.
            // https://stackoverflow.com/a/1849746

            // volume += dot(v0 x v1, v2)
            volume += Real {
                  ( v0.y() * v1.z() - v0.z() * v1.y() ) * v2.x()
                + ( v0.z() * v1.x() - v0.x() * v1.z() ) * v2.y()
                + ( v0.x() * v1.y() - v0.y() * v1.x() ) * v2.z()
            };
        }
    }
    return Real{ 1.0 / 6.0 } * TNL::abs( volume );
}*/

template< typename MeshConfig, typename Device >
__cuda_callable__
typename MeshConfig::RealType
getEntityMeasure(
   const Mesh< MeshConfig, Device >& mesh,
   const MeshEntity< MeshConfig, Device, Topologies::Polyhedron >& entity )
{
   using Real = typename MeshConfig::RealType;
   using Index = typename MeshConfig::LocalIndexType;
   using Point = typename Mesh< MeshConfig, Device >::PointType;
   Real volume = 0;
   const Index facesCount = entity.template getSubentitiesCount< 2 >();
   const Point& v0 = mesh.getPoint( entity.template getSubentityIndex< 0 >( 0 ) );
   // start from faceIdx = 1, since faceIdx = 0 contains the v0 (the tetrahedron would be degenerate)
   for( Index faceIdx = 1; faceIdx < facesCount; faceIdx++ ) {
      const auto face = mesh.template getEntity< 2 >( entity.template getSubentityIndex< 2 >( faceIdx ) );
      const Index verticesCount = face.template getSubentitiesCount< 0 >();
      const Point& v1 = mesh.getPoint( face.template getSubentityIndex< 0 >( 0 ) ) - v0;
      Point v2 = mesh.getPoint( face.template getSubentityIndex< 0 >( 1 ) ) - v0;
      for( Index j = 2; j < verticesCount; j++ ) {
         const Point& v3 = mesh.getPoint( face.template getSubentityIndex< 0 >( j ) ) - v0;
         // Partition the polyhedron into tetrahedrons by triangulating faces and connecting
         // each triangle to one point of the polyhedron.
         volume += getTetrahedronVolume( v1, v2, v3 );
         v2 = v3;
      }
   }
   return volume;
}

}  // namespace TNL::Meshes
