MOAB: Mesh Oriented datABase  (version 5.2.1)
LinearTri.cpp
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00001 #include "moab/LocalDiscretization/LinearTri.hpp"
00002 #include "moab/Forward.hpp"
00003 #include <algorithm>
00004 #include <math.h>
00005 #include <limits>
00006 
00007 namespace moab
00008 {
00009 
00010 const double LinearTri::corner[3][2] = { { 0, 0 }, { 1, 0 }, { 0, 1 } };
00011 
00012 ErrorCode LinearTri::initFcn( const double* verts, const int nverts, double*& work )
00013 {
00014     // allocate work array as:
00015     // work[0..8] = T
00016     // work[9..17] = Tinv
00017     // work[18] = detT
00018     // work[19] = detTinv
00019     assert( nverts == 3 && verts );
00020     if( !work ) work = new double[20];
00021 
00022     Matrix3 J( verts[1 * 3 + 0] - verts[0 * 3 + 0], verts[2 * 3 + 0] - verts[0 * 3 + 0], 0.0,
00023                verts[1 * 3 + 1] - verts[0 * 3 + 1], verts[2 * 3 + 1] - verts[0 * 3 + 1], 0.0,
00024                verts[1 * 3 + 2] - verts[0 * 3 + 2], verts[2 * 3 + 2] - verts[0 * 3 + 2], 1.0 );
00025     J *= 0.5;
00026 
00027     J.copyto( work );
00028     J.inverse().copyto( work + Matrix3::size );
00029     work[18] = J.determinant();
00030     work[19] = ( work[18] < 1e-12 ? std::numeric_limits< double >::max() : 1.0 / work[18] );
00031 
00032     return MB_SUCCESS;
00033 }
00034 
00035 ErrorCode LinearTri::evalFcn( const double* params, const double* field, const int /*ndim*/, const int num_tuples,
00036                               double* /*work*/, double* result )
00037 {
00038     assert( params && field && num_tuples > 0 );
00039     // convert to [0,1]
00040     double p1 = 0.5 * ( 1.0 + params[0] ), p2 = 0.5 * ( 1.0 + params[1] ), p0 = 1.0 - p1 - p2;
00041 
00042     for( int j = 0; j < num_tuples; j++ )
00043         result[j] = p0 * field[0 * num_tuples + j] + p1 * field[1 * num_tuples + j] + p2 * field[2 * num_tuples + j];
00044 
00045     return MB_SUCCESS;
00046 }
00047 
00048 ErrorCode LinearTri::integrateFcn( const double* field, const double* /*verts*/, const int nverts, const int /*ndim*/,
00049                                    const int num_tuples, double* work, double* result )
00050 {
00051     assert( field && num_tuples > 0 );
00052     std::fill( result, result + num_tuples, 0.0 );
00053     for( int i = 0; i < nverts; ++i )
00054     {
00055         for( int j = 0; j < num_tuples; j++ )
00056             result[j] += field[i * num_tuples + j];
00057     }
00058     double tmp = work[18] / 6.0;
00059     for( int i = 0; i < num_tuples; i++ )
00060         result[i] *= tmp;
00061 
00062     return MB_SUCCESS;
00063 }
00064 
00065 ErrorCode LinearTri::jacobianFcn( const double*, const double*, const int, const int, double* work, double* result )
00066 {
00067     // jacobian is cached in work array
00068     assert( work );
00069     std::copy( work, work + 9, result );
00070     return MB_SUCCESS;
00071 }
00072 
00073 ErrorCode LinearTri::reverseEvalFcn( EvalFcn eval, JacobianFcn jacob, InsideFcn ins, const double* posn,
00074                                      const double* verts, const int nverts, const int ndim, const double iter_tol,
00075                                      const double inside_tol, double* work, double* params, int* is_inside )
00076 {
00077     assert( posn && verts );
00078     return evaluate_reverse( eval, jacob, ins, posn, verts, nverts, ndim, iter_tol, inside_tol, work, params,
00079                              is_inside );
00080 }
00081 
00082 int LinearTri::insideFcn( const double* params, const int, const double tol )
00083 {
00084     return ( params[0] >= -1.0 - tol && params[1] >= -1.0 - tol && params[0] + params[1] <= 1.0 + tol );
00085 }
00086 
00087 ErrorCode LinearTri::evaluate_reverse( EvalFcn eval, JacobianFcn jacob, InsideFcn inside_f, const double* posn,
00088                                        const double* verts, const int nverts, const int ndim, const double iter_tol,
00089                                        const double inside_tol, double* work, double* params, int* inside )
00090 {
00091     // TODO: should differentiate between epsilons used for
00092     // Newton Raphson iteration, and epsilons used for curved boundary geometry errors
00093     // right now, fix the tolerance used for NR
00094     const double error_tol_sqr = iter_tol * iter_tol;
00095     CartVect* cvparams         = reinterpret_cast< CartVect* >( params );
00096     const CartVect* cvposn     = reinterpret_cast< const CartVect* >( posn );
00097 
00098     // find best initial guess to improve convergence
00099     CartVect tmp_params[] = { CartVect( -1, -1, -1 ), CartVect( 1, -1, -1 ), CartVect( -1, 1, -1 ) };
00100     double resl           = std::numeric_limits< double >::max();
00101     CartVect new_pos, tmp_pos;
00102     ErrorCode rval;
00103     for( unsigned int i = 0; i < 3; i++ )
00104     {
00105         rval = ( *eval )( tmp_params[i].array(), verts, ndim, 3, work, tmp_pos.array() );
00106         if( MB_SUCCESS != rval ) return rval;
00107         double tmp_resl = ( tmp_pos - *cvposn ).length_squared();
00108         if( tmp_resl < resl )
00109         {
00110             *cvparams = tmp_params[i];
00111             new_pos   = tmp_pos;
00112             resl      = tmp_resl;
00113         }
00114     }
00115 
00116     // residual is diff between old and new pos; need to minimize that
00117     CartVect res = new_pos - *cvposn;
00118     Matrix3 J;
00119     rval = ( *jacob )( cvparams->array(), verts, nverts, ndim, work, J[0] );
00120 #ifndef NDEBUG
00121     double det = J.determinant();
00122     assert( det > std::numeric_limits< double >::epsilon() );
00123 #endif
00124     Matrix3 Ji = J.inverse();
00125 
00126     int iters = 0;
00127     // while |res| larger than tol
00128     while( res % res > error_tol_sqr )
00129     {
00130         if( ++iters > 25 ) return MB_FAILURE;
00131 
00132         // new params tries to eliminate residual
00133         *cvparams -= Ji * res;
00134 
00135         // get the new forward-evaluated position, and its difference from the target pt
00136         rval = ( *eval )( params, verts, ndim, 3, work, new_pos.array() );
00137         if( MB_SUCCESS != rval ) return rval;
00138         res = new_pos - *cvposn;
00139     }
00140 
00141     if( inside ) *inside = ( *inside_f )( params, ndim, inside_tol );
00142 
00143     return MB_SUCCESS;
00144 }  // Map::evaluate_reverse()
00145 
00146 /*  ErrorCode LinearTri::get_normal( int facet, double *work, double *normal)
00147   {
00148     ErrorCode error;
00149     //Get the local vertex ids of  local edge
00150     int id1 = ledges[facet][0];
00151     int id2 = ledges[facet][1];
00152 
00153     //Find the normal to the face
00154     double face_normal[3];
00155 
00156 
00157   }*/
00158 
00159 ErrorCode LinearTri::normalFcn( const int ientDim, const int facet, const int nverts, const double* verts,
00160                                 double normal[3] )
00161 {
00162     // assert(facet < 3 && ientDim == 1 && nverts==3);
00163     if( nverts != 3 ) MB_SET_ERR( MB_FAILURE, "Incorrect vertex count for passed triangle :: expected value = 3 " );
00164     if( ientDim != 1 ) MB_SET_ERR( MB_FAILURE, "Requesting normal for unsupported dimension :: expected value = 1 " );
00165     if( facet > 3 || facet < 0 ) MB_SET_ERR( MB_FAILURE, "Incorrect local edge id :: expected value = one of 0-2" );
00166 
00167     // Get the local vertex ids of  local edge
00168     int id0 = CN::mConnectivityMap[MBTRI][ientDim - 1].conn[facet][0];
00169     int id1 = CN::mConnectivityMap[MBTRI][ientDim - 1].conn[facet][1];
00170 
00171     // Find a vector along the edge
00172     double edge[3];
00173     for( int i = 0; i < 3; i++ )
00174     {
00175         edge[i] = verts[3 * id1 + i] - verts[3 * id0 + i];
00176     }
00177     // Find the normal of the face
00178     double x0[3], x1[3], fnrm[3];
00179     for( int i = 0; i < 3; i++ )
00180     {
00181         x0[i] = verts[3 * 1 + i] - verts[3 * 0 + i];
00182         x1[i] = verts[3 * 2 + i] - verts[3 * 0 + i];
00183     }
00184     fnrm[0] = x0[1] * x1[2] - x1[1] * x0[2];
00185     fnrm[1] = x1[0] * x0[2] - x0[0] * x1[2];
00186     fnrm[2] = x0[0] * x1[1] - x1[0] * x0[1];
00187 
00188     // Find the normal of the edge as the cross product of edge and face normal
00189 
00190     double a   = edge[1] * fnrm[2] - fnrm[1] * edge[2];
00191     double b   = edge[2] * fnrm[0] - fnrm[2] * edge[0];
00192     double c   = edge[0] * fnrm[1] - fnrm[0] * edge[1];
00193     double nrm = sqrt( a * a + b * b + c * c );
00194 
00195     if( nrm > std::numeric_limits< double >::epsilon() )
00196     {
00197         normal[0] = a / nrm;
00198         normal[1] = b / nrm;
00199         normal[2] = c / nrm;
00200     }
00201     return MB_SUCCESS;
00202 }
00203 
00204 }  // namespace moab
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