ConditionNumberFunctions.hpp

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/* *****************************************************************
    MESQUITE -- The Mesh Quality Improvement Toolkit

    Copyright 2004 Sandia Corporation and Argonne National
    Laboratory.  Under the terms of Contract DE-AC04-94AL85000
    with Sandia Corporation, the U.S. Government retains certain
    rights in this software.

    This library is free software; you can redistribute it and/or
    modify it under the terms of the GNU Lesser General Public
    License as published by the Free Software Foundation; either
    version 2.1 of the License, or (at your option) any later version.

    This library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public License
    (lgpl.txt) along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    [email protected], [email protected], [email protected],
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  ***************************************************************** */
// -*- Mode : c++; tab-width: 3; c-tab-always-indent: t; indent-tabs-mode: nil; c-basic-offset: 3
// -*-

/*! \file ConditionNumberFunctions.hpp

Header file for the MBMesquite::ShapeQualityMetric class

  \author Thomas Leurent
  \date   2002-09-01
 */

#ifndef ConditionNumberFunctions_hpp
#define ConditionNumberFunctions_hpp

#include "Mesquite.hpp"
#include "MsqError.hpp"
#include "QualityMetric.hpp"
#include "PatchData.hpp"

namespace MBMesquite
{
static inline bool condition_number_2d( const Vector3D temp_vec[],
                                        size_t e_ind,
                                        PatchData& pd,
                                        double& fval,
                                        MsqError& err )
{
    // norm squared of J
    double term1 = temp_vec[0] % temp_vec[0] + temp_vec[1] % temp_vec[1];

    Vector3D unit_surf_norm;
    pd.get_domain_normal_at_element( e_ind, unit_surf_norm, err );
    MSQ_ERRZERO( err );
    unit_surf_norm.normalize();

    // det J
    double temp_var = unit_surf_norm % ( temp_vec[0] * temp_vec[1] );

    // revert to old, non-barrier form
    if( temp_var <= 0.0 ) return false;
    fval = term1 / ( 2.0 * temp_var );
    return true;

    /*
    double h;
    double delta=pd.get_barrier_delta(err); MSQ_ERRZERO(err);

    // Note: technically, we want delta=eta*tau-max
    //       whereas the function above gives delta=eta*alpha-max
    //
    //       Because the only requirement on eta is eta << 1,
    //       and because tau-max = alpha-max/0.707 we can
    //       ignore the discrepancy

    if (delta==0) {
       if (temp_var < MSQ_DBL_MIN ) {
          return false;
       }
       else {
          h=temp_var;
       }

    // Note: when delta=0, the vertex_barrier_function
    //       formally gives h=temp_var as well.
    //       We just do it this way to avoid any
    //       roundoff issues.
    // Also: when delta=0, this metric is identical
    //       to the original condition number with
    //       the barrier at temp_var=0
    }
    else {
       h = QualityMetric::vertex_barrier_function(temp_var,delta);

       if (h<MSQ_DBL_MIN && fabs(temp_var) > MSQ_DBL_MIN ) {
         h = delta*delta/fabs(temp_var); }
       // Note: Analytically, h is strictly positive, but
       //       it can be zero numerically if temp_var
       //       is a large negative number
       //       In the case h=0, we use a different analytic
       //       approximation to compute h.
    }

    if (h<MSQ_DBL_MIN) {
      MSQ_SETERR(err)( "Barrier function is zero due to excessively large "
                       "negative area compared to delta. /n Try to untangle "
                       "mesh another way. ", MsqError::INVALID_MESH);
      return false;
    }

    fval=term1/(2*h);

    if (fval>MSQ_MAX_CAP) {
       fval=MSQ_MAX_CAP;
    }
    return true;
    */
}

//} //namespace

static inline bool condition_number_3d( const Vector3D temp_vec[], PatchData& /*pd*/, double& fval, MsqError& /*err*/ )
{
    // norm squared of J
    double term1 = temp_vec[0] % temp_vec[0] + temp_vec[1] % temp_vec[1] + temp_vec[2] % temp_vec[2];
    // norm squared of adjoint of J
    double term2 = ( temp_vec[0] * temp_vec[1] ) % ( temp_vec[0] * temp_vec[1] ) +
                   ( temp_vec[1] * temp_vec[2] ) % ( temp_vec[1] * temp_vec[2] ) +
                   ( temp_vec[2] * temp_vec[0] ) % ( temp_vec[2] * temp_vec[0] );
    // det of J
    double temp_var = temp_vec[0] % ( temp_vec[1] * temp_vec[2] );

    // revert to old, non-barrier formulation
    if( temp_var <= 0.0 ) return false;
    fval = sqrt( term1 * term2 ) / ( 3.0 * temp_var );
    return true;

    /*
    double h;
    double delta=pd.get_barrier_delta(err); MSQ_ERRZERO(err);

    // Note: technically, we want delta=eta*tau-max
    //       whereas the function above gives delta=eta*alpha-max
    //
    //       Because the only requirement on eta is eta << 1,
    //       and because tau-max = alpha-max/0.707 we can
    //       ignore the discrepancy

    if (delta==0) {
       if (temp_var < MSQ_DBL_MIN ) {
          return false;
       }
       else {
          h=temp_var;
       }

    // Note: when delta=0, the vertex_barrier_function
    //       formally gives h=temp_var as well.
    //       We just do it this way to avoid any
    //       roundoff issues.
    // Also: when delta=0, this metric is identical
    //       to the original condition number with
    //       the barrier at temp_var=0

    }
    else {
       h = QualityMetric::vertex_barrier_function(temp_var,delta);

       if (h<MSQ_DBL_MIN && fabs(temp_var) > MSQ_DBL_MIN ) {
         h = delta*delta/fabs(temp_var); }

       // Note: Analytically, h is strictly positive, but
       //       it can be zero numerically if temp_var
       //       is a large negative number
       //       In the h=0, we use a different analytic
       //       approximation to compute h.
    }
    if (h<MSQ_DBL_MIN) {
      MSQ_SETERR(err)("Barrier function is zero due to excessively large "
                      "negative area compared to delta. /n Try to untangle "
                      "mesh another way. ", MsqError::INVALID_MESH);
      return false;
    }

    fval=sqrt(term1*term2)/(3*h);

    if (fval>MSQ_MAX_CAP) {
       fval=MSQ_MAX_CAP;
    }
    return true;
    */
}

}  // namespace MBMesquite

#endif  // ConditionNumberFunctions_hpp