linear_hex_map.hpp

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#ifndef MOAB_LINEAR_HEX_HPP
#define MOAB_LINEAR_HEX_HPP

#include "moab/Matrix3.hpp"
#include "moab/CartVect.hpp"
#include <sstream>
#include <iomanip>
#include <iostream>

namespace moab
{

namespace element_utility
{

    class Linear_hex_map
    {
      public:
        // Constructor
        Linear_hex_map() {}
        // Copy constructor
        Linear_hex_map( const Linear_hex_map& ) {}

      public:
        // Natural coordinates
        template < typename Moab, typename Entity_handle, typename Points, typename Point >
        std::pair< bool, CartVect > evaluate_reverse( const double* verts,
                                                      const double* eval_point,
                                                      const double tol = 1.e-6 ) const
        {
            CartVect params( 3, 0.0 );
            solve_inverse( eval_point, params, verts );
            bool point_found = solve_inverse( eval_point, params, verts, tol ) && is_contained( params, tol );
            return std::make_pair( point_found, params );
        }

      private:
        // This is a hack to avoid a .cpp file and C++11
        // reference_points(i,j) will be a 1 or -1;
        // This should unroll..
        inline const CartVect& reference_points( const std::size_t& i ) const
        {
            const CartVect rpts[8] = { CartVect( -1, -1, -1 ), CartVect( 1, -1, -1 ), CartVect( 1, 1, -1 ),
                                       CartVect( -1, 1, -1 ),  CartVect( -1, -1, 1 ), CartVect( 1, -1, 1 ),
                                       CartVect( 1, 1, 1 ),    CartVect( -1, 1, 1 ) };
            return rpts[i];
        }

        bool is_contained( const CartVect& params, const double tol ) const
        {
            // just look at the box+tol here
            return ( params[0] >= -1. - tol ) && ( params[0] <= 1. + tol ) && ( params[1] >= -1. - tol ) &&
                   ( params[1] <= 1. + tol ) && ( params[2] >= -1. - tol ) && ( params[2] <= 1. + tol );
        }

        bool solve_inverse( const CartVect& point,
                            CartVect& params,
                            const CartVect* verts,
                            const double tol = 1.e-6 ) const
        {
            const double error_tol_sqr = tol * tol;
            CartVect delta( 0.0, 0.0, 0.0 );
            params = delta;
            evaluate_forward( params, verts, delta );
            delta -= point;
            std::size_t num_iterations = 0;
#ifdef LINEAR_HEX_DEBUG
            std::stringstream ss;
            ss << "CartVect: ";
            ss << point[0] << ", " << point[1] << ", " << point[2] << std::endl;
            ss << "Hex: ";
            for( int i = 0; i < 8; ++i )
                ss << points[i][0] << ", " << points[i][1] << ", " << points[i][2] << std::endl;
            ss << std::endl;
#endif
            while( delta.length_squared() > error_tol_sqr )
            {
#ifdef LINEAR_HEX_DEBUG
                ss << "Iter #: " << num_iterations << " Err: " << delta.length() << " Iterate: ";
                ss << params[0] << ", " << params[1] << ", " << params[2] << std::endl;
#endif
                if( ++num_iterations >= 5 )
                {
                    return false;
                }
                Matrix3 J;
                jacobian( params, verts, J );
                double det = moab::Matrix3::determinant3( J );
                if( fabs( det ) < 1.e-10 )
                {
#ifdef LINEAR_HEX_DEBUG
                    std::cerr << ss.str();
#endif
#ifndef LINEAR_HEX_DEBUG
                    std::cerr << x[0] << ", " << x[1] << ", " << x[2] << std::endl;
#endif
                    std::cerr << "inverse solve failure: det: " << det << std::endl;
                    exit( -1 );
                }
                params -= moab::Matrix3::inverse( J, 1.0 / det ) * delta;
                evaluate_forward( params, points, delta );
                delta -= x;
            }
            return true;
        }

        void evaluate_forward( const CartVect& p, const CartVect* verts, CartVect& f ) const
        {
            typedef typename Points::value_type Vector;
            f.set( 0.0, 0.0, 0.0 );
            for( unsigned i = 0; i < 8; ++i )
            {
                const double N_i = ( 1 + p[0] * reference_points( i )[0] ) * ( 1 + p[1] * reference_points( i )[1] ) *
                                   ( 1 + p[2] * reference_points( i )[2] );
                f += N_i * verts[i];
            }
            f *= 0.125;
            return f;
        }

        double integrate_scalar_field( const CartVect* points, const double* field_values ) const {}

        template < typename Point, typename Points >
        Matrix3& jacobian( const Point& p, const Points& points, Matrix3& J ) const
        {
        }

      private:
    };  // Class Linear_hex_map

}  // namespace element_utility

}  // namespace moab
#endif  // MOAB_LINEAR_HEX_nPP