Exemplo n.º 1
0
/*!
   the radius ratio of a triangle

   NB (P. Pebay 01/13/07): 
     CR / (2.0*IR) where CR is the circumradius and IR is the inradius

     The radius ratio is also known to VERDICT, for tetrahedral elements only,
     as the "aspect beta".
   
*/
C_FUNC_DEF double v_tri_radius_ratio( int /*num_nodes*/, double coordinates[][3] )
{

  // three vectors for each side 
  VerdictVector a( coordinates[1][0] - coordinates[0][0],
                   coordinates[1][1] - coordinates[0][1],
                   coordinates[1][2] - coordinates[0][2] );
  
  VerdictVector b( coordinates[2][0] - coordinates[1][0],
                   coordinates[2][1] - coordinates[1][1],
                   coordinates[2][2] - coordinates[1][2] );
  
  VerdictVector c( coordinates[0][0] - coordinates[2][0],
                   coordinates[0][1] - coordinates[2][1],
                   coordinates[0][2] - coordinates[2][2] );

  double a1 = a.length();
  double b1 = b.length();
  double c1 = c.length();
 
  VerdictVector ab = a * b;
  double denominator = ab.length_squared();

  if( denominator < VERDICT_DBL_MIN ) 
    return (double)VERDICT_DBL_MAX;

  double radius_ratio;
  radius_ratio = .25 * a1 * b1 * c1 * ( a1 + b1 + c1 ) / denominator;
  
  if( radius_ratio > 0 )
    return (double) VERDICT_MIN( radius_ratio, VERDICT_DBL_MAX );
  return (double) VERDICT_MAX( radius_ratio, -VERDICT_DBL_MAX );
}
Exemplo n.º 2
0
inline double normalize_jacobian( double jacobi,
                                  VerdictVector& v1,
                                  VerdictVector& v2,
                                  VerdictVector& v3,
                                  int tet_flag = 0 )
{
    double return_value = 0.0;

    if ( jacobi != 0.0 )
    {

        double l1, l2, l3, length_product;
        // Note: there may be numerical problems if one is a lot shorter
        // than the others this way. But scaling each vector before the
        // triple product would involve 3 square roots instead of just
        // one.
        l1 = v1.length_squared();
        l2 = v2.length_squared();
        l3 = v3.length_squared();
        length_product = sqrt( l1 * l2 * l3 );

        // if some numerical scaling problem, or just plain roundoff,
        // then push back into range [-1,1].
        if ( length_product < fabs(jacobi) )
        {
            length_product = fabs(jacobi);
        }

        if( tet_flag == 1)
            return_value = v_sqrt_2 * jacobi / length_product;
        else
            return_value = jacobi / length_product;

    }
    return return_value;

}
Exemplo n.º 3
0
double VerdictVector::vector_angle(const VerdictVector &vector1,
                                   const VerdictVector &vector2) const
{
    // This routine does not assume that any of the input vectors are of unit
    // length. This routine does not normalize the input vectors.
    // Special cases:
    //     If the normal vector is zero length:
    //         If a new one can be computed from vectors 1 & 2:
    //             the normal is replaced with the vector cross product
    //         else the two vectors are colinear and zero or 2PI is returned.
    //     If the normal is colinear with either (or both) vectors
    //         a new one is computed with the cross products
    //         (and checked again).

    // Check for zero length normal vector
    VerdictVector normal = *this;
    double normal_lensq = normal.length_squared();
    double len_tol = 0.0000001;
    if( normal_lensq <= len_tol )
    {
        // null normal - make it the normal to the plane defined by vector1
        // and vector2. If still null, the vectors are colinear so check
        // for zero or 180 angle.
        normal = vector1 * vector2;
        normal_lensq = normal.length_squared();
        if( normal_lensq <= len_tol )
        {
            double cosine = vector1 % vector2;
            if( cosine > 0.0 ) return 0.0;
            else               return VERDICT_PI;
        }
    }

    //Trap for normal vector colinear to one of the other vectors. If so,
    //use a normal defined by the two vectors.
    double dot_tol = 0.985;
    double dot = vector1 % normal;
    if( dot * dot >= vector1.length_squared() * normal_lensq * dot_tol )
    {
        normal = vector1 * vector2;
        normal_lensq = normal.length_squared();

        //Still problems if all three vectors were colinear
        if( normal_lensq <= len_tol )
        {
            double cosine = vector1 % vector2;
            if( cosine >= 0.0 ) return 0.0;
            else                return VERDICT_PI;
        }
    }
    else
    {
        //The normal and vector1 are not colinear, now check for vector2
        dot = vector2 % normal;
        if( dot * dot >= vector2.length_squared() * normal_lensq * dot_tol )
        {
            normal = vector1 * vector2;
        }
    }

    // Assume a plane such that the normal vector is the plane's normal.
    // Create yAxis perpendicular to both the normal and vector1. yAxis is
    // now in the plane. Create xAxis as the perpendicular to both yAxis and
    // the normal. xAxis is in the plane and is the projection of vector1
    // into the plane.

    normal.normalize();
    VerdictVector yAxis = normal;
    yAxis *= vector1;
    double yv = vector2 % yAxis;
    //  yAxis memory slot will now be used for xAxis
    yAxis *= normal;
    double xv = vector2 % yAxis;


    //  assert(x != 0.0 || y != 0.0);
    if( xv == 0.0 && yv == 0.0 )
    {
        return 0.0;
    }
    double angle = atan2( yv, xv );

    if (angle < 0.0)
    {
        angle += TWO_VERDICT_PI;
    }
    return angle;
}
Exemplo n.º 4
0
/*! 
  tri_quality for calculating multiple tri functions at once

  using this method is generally faster than using the individual 
  method multiple times.

*/
C_FUNC_DEF void v_tri_quality( int num_nodes, double coordinates[][3], 
    unsigned int metrics_request_flag, TriMetricVals *metric_vals ) 
{

  memset( metric_vals, 0, sizeof(TriMetricVals) );

  // for starts, lets set up some basic and common information

  /*  node numbers and side numbers used below

             2
             ++
            /  \ 
         2 /    \ 1
          /      \
         /        \
       0 ---------+ 1
             0
  */
  
  // vectors for each side
  VerdictVector sides[3];
  sides[0].set(
      coordinates[1][0] - coordinates[0][0],
      coordinates[1][1] - coordinates[0][1],
      coordinates[1][2] - coordinates[0][2]
      );
  sides[1].set(
      coordinates[2][0] - coordinates[1][0],
      coordinates[2][1] - coordinates[1][1],
      coordinates[2][2] - coordinates[1][2]
      );
  sides[2].set(
      coordinates[2][0] - coordinates[0][0],
      coordinates[2][1] - coordinates[0][1],
      coordinates[2][2] - coordinates[0][2]
      );
  VerdictVector tri_normal = sides[0] * sides[2];
    //if we have access to normal information, check to see if the
    //element is inverted.  If we don't have the normal information
    //that we need for this, assume the element is not inverted.
    //This flag will be used for condition number, jacobian, shape,
    //and size and shape.
  bool is_inverted = false;
  if( compute_normal )
  {
      //center of tri
    double point[3], surf_normal[3];
    point[0] =  (coordinates[0][0] + coordinates[1][0] + coordinates[2][0]) / 3;
    point[1] =  (coordinates[0][1] + coordinates[1][1] + coordinates[2][1]) / 3;
    point[2] =  (coordinates[0][2] + coordinates[1][2] + coordinates[2][2]) / 3;
      //dot product
    compute_normal( point, surf_normal ); 
    if( (tri_normal.x()*surf_normal[0] + 
         tri_normal.y()*surf_normal[1] +
         tri_normal.z()*surf_normal[2] ) < 0 )
      is_inverted=true; 
  }
  
  // lengths squared of each side
  double sides_lengths_squared[3];
  sides_lengths_squared[0] = sides[0].length_squared();
  sides_lengths_squared[1] = sides[1].length_squared();
  sides_lengths_squared[2] = sides[2].length_squared();
 

  // if we are doing angle calcuations
  if( metrics_request_flag & (V_TRI_MINIMUM_ANGLE | V_TRI_MAXIMUM_ANGLE) )
  {
    // which is short and long side
    int short_side=0, long_side=0;

    if(sides_lengths_squared[1] < sides_lengths_squared[0])
      short_side = 1;
    if(sides_lengths_squared[2] < sides_lengths_squared[short_side])
      short_side = 2;
  
    if(sides_lengths_squared[1] > sides_lengths_squared[0])
      long_side = 1;
    if(sides_lengths_squared[2] > sides_lengths_squared[long_side])
      long_side = 2;


    // calculate the minimum angle of the tri
    if( metrics_request_flag & V_TRI_MINIMUM_ANGLE )
    {
      if(sides_lengths_squared[0] == 0.0 || 
        sides_lengths_squared[1] == 0.0 ||
        sides_lengths_squared[2] == 0.0)
      {
        metric_vals->minimum_angle = 0.0;
      }        
      else if(short_side == 0)
        metric_vals->minimum_angle = (double)sides[2].interior_angle(sides[1]);
      else if(short_side == 1)
        metric_vals->minimum_angle = (double)sides[0].interior_angle(sides[2]);
      else
        metric_vals->minimum_angle = (double)sides[0].interior_angle(-sides[1]);
    }
    
    // calculate the maximum angle of the tri
    if( metrics_request_flag & V_TRI_MAXIMUM_ANGLE )
    {
      if(sides_lengths_squared[0] == 0.0 || 
        sides_lengths_squared[1] == 0.0 ||
        sides_lengths_squared[2] == 0.0)
      {
        metric_vals->maximum_angle = 0.0;
      }        
      else if(long_side == 0)
        metric_vals->maximum_angle = (double)sides[2].interior_angle(sides[1]);
      else if(long_side == 1)
        metric_vals->maximum_angle = (double)sides[0].interior_angle(sides[2]);
      else
        metric_vals->maximum_angle = (double)sides[0].interior_angle(-sides[1]);
    }
  }


  // calculate the area of the tri
  // the following functions depend on area
  if( metrics_request_flag & (V_TRI_AREA | V_TRI_SCALED_JACOBIAN | 
    V_TRI_SHAPE | V_TRI_RELATIVE_SIZE_SQUARED | V_TRI_SHAPE_AND_SIZE ) )
  {
    metric_vals->area = (double)((sides[0] * sides[2]).length() * 0.5);
  }

  // calculate the aspect ratio
  if(metrics_request_flag & V_TRI_ASPECT_FROBENIUS)
  {
    // sum the lengths squared
    double srms = 
      sides_lengths_squared[0] +
      sides_lengths_squared[1] +
      sides_lengths_squared[2] ;

    // calculate once and reuse
    static const double twoTimesRootOf3 = 2*sqrt(3.0);

    double div = (twoTimesRootOf3 * 
      ( (sides[0] * sides[2]).length() ));

    if(div == 0.0)
      metric_vals->aspect_frobenius = (double)VERDICT_DBL_MAX;
    else
      metric_vals->aspect_frobenius = (double)(srms / div);
  }

  // calculate the radius ratio of the triangle
  if( metrics_request_flag & V_TRI_RADIUS_RATIO )
  {
  double a1 = sqrt( sides_lengths_squared[0] );
  double b1 = sqrt( sides_lengths_squared[1] );
  double c1 = sqrt( sides_lengths_squared[2] );

  VerdictVector ab = sides[0] * sides[1];

  metric_vals->radius_ratio = (double) .25 * a1 * b1 * c1 * ( a1 + b1 + c1 ) / ab.length_squared();
  }

  // calculate the scaled jacobian
  if(metrics_request_flag & V_TRI_SCALED_JACOBIAN)
  {
    // calculate once and reuse
    static const double twoOverRootOf3 = 2/sqrt(3.0);
    // use the area from above
    
    double tmp = tri_normal.length() * twoOverRootOf3;
      
    // now scale it by the lengths of the sides
    double min_scaled_jac = VERDICT_DBL_MAX;
    double temp_scaled_jac;
    for(int i=0; i<3; i++)
    {
      if(sides_lengths_squared[i%3] == 0.0 || sides_lengths_squared[(i+2)%3] == 0.0)
        temp_scaled_jac = 0.0;
      else
        temp_scaled_jac = tmp / sqrt(sides_lengths_squared[i%3]) / sqrt(sides_lengths_squared[(i+2)%3]);
      if( temp_scaled_jac < min_scaled_jac )
        min_scaled_jac = temp_scaled_jac;
    }
      //multiply by -1 if the normals are in opposite directions
    if( is_inverted )
    {
      min_scaled_jac *= -1; 
    }
    metric_vals->scaled_jacobian = (double)min_scaled_jac;

  }

  // calculate the condition number
  if(metrics_request_flag & V_TRI_CONDITION)
  {
    // calculate once and reuse
    static const double rootOf3 = sqrt(3.0);
      //if it is inverted, the condition number is considered to be infinity.
    if(is_inverted){
      metric_vals->condition = VERDICT_DBL_MAX;
    }
    else{
      double area2x = (sides[0] * sides[2]).length();
      if(area2x == 0.0 ) 
        metric_vals->condition = (double)(VERDICT_DBL_MAX);
      else
        metric_vals->condition = (double) ( (sides[0]%sides[0] +
                                                   sides[2]%sides[2] -
                                                   sides[0]%sides[2])  /
                                                  (area2x*rootOf3) );
    }
    
  }

  // calculate the shape
  if(metrics_request_flag & V_TRI_SHAPE || metrics_request_flag & V_TRI_SHAPE_AND_SIZE)
  {
      //if element is inverted, shape is zero.  We don't need to
      //calculate anything.
    if(is_inverted ){
      metric_vals->shape = 0.0;
    }
    else{//otherwise, we calculate the shape
        // calculate once and reuse
      static const double rootOf3 = sqrt(3.0);
        // reuse area from before
      double area2x = metric_vals->area * 2;
        // dot products
      double dots[3] = { 
        sides[0] % sides[0],
          sides[2] % sides[2],
          sides[0] % sides[2]
          };

        // add the dots
      double sum_dots = dots[0] + dots[1] - dots[2];

        // then the finale
      if( sum_dots == 0.0 ) 
        metric_vals->shape = 0.0;
      else
        metric_vals->shape = (double)(rootOf3 * area2x / sum_dots);
    }
    
  }

  // calculate relative size squared
  if(metrics_request_flag & V_TRI_RELATIVE_SIZE_SQUARED || metrics_request_flag & V_TRI_SHAPE_AND_SIZE)
  {
    // get weights
    double w11, w21, w12, w22;
    v_tri_get_weight(w11,w21,w12,w22);
    // get the determinant
    double detw = v_determinant(w11,w21,w12,w22);
    // use the area from above and divide with the determinant
    if( metric_vals->area == 0.0  || detw == 0.0 )
      metric_vals->relative_size_squared = 0.0;
    else
    {
      double size = metric_vals->area * 2.0 / detw;
      // square the size
      size *= size;
      // value ranges between 0 to 1
      metric_vals->relative_size_squared = (double)VERDICT_MIN(size, 1.0/size );
    }
  }

  // calculate shape and size
  if(metrics_request_flag & V_TRI_SHAPE_AND_SIZE)
  {
    metric_vals->shape_and_size = 
      metric_vals->relative_size_squared * metric_vals->shape;
  }

  // calculate distortion
  if(metrics_request_flag & V_TRI_DISTORTION)
    metric_vals->distortion = v_tri_distortion(num_nodes, coordinates);

  //take care of any over-flow problems
  if( metric_vals->aspect_frobenius > 0 )
    metric_vals->aspect_frobenius = (double) VERDICT_MIN( metric_vals->aspect_frobenius, VERDICT_DBL_MAX );\
  else
    metric_vals->aspect_frobenius = (double) VERDICT_MAX( metric_vals->aspect_frobenius, -VERDICT_DBL_MAX );

  if( metric_vals->area > 0 )
    metric_vals->area = (double) VERDICT_MIN( metric_vals->area, VERDICT_DBL_MAX );
  else
    metric_vals->area = (double) VERDICT_MAX( metric_vals->area, -VERDICT_DBL_MAX );

  if( metric_vals->minimum_angle > 0 )
    metric_vals->minimum_angle = (double) VERDICT_MIN( metric_vals->minimum_angle, VERDICT_DBL_MAX );
  else
    metric_vals->minimum_angle = (double) VERDICT_MAX( metric_vals->minimum_angle, -VERDICT_DBL_MAX );

  if( metric_vals->maximum_angle > 0 )
    metric_vals->maximum_angle = (double) VERDICT_MIN( metric_vals->maximum_angle, VERDICT_DBL_MAX );
  else
    metric_vals->maximum_angle = (double) VERDICT_MAX( metric_vals->maximum_angle , -VERDICT_DBL_MAX );

  if( metric_vals->condition > 0 )
    metric_vals->condition = (double) VERDICT_MIN( metric_vals->condition, VERDICT_DBL_MAX );
  else
    metric_vals->condition = (double) VERDICT_MAX( metric_vals->condition, -VERDICT_DBL_MAX );

  if( metric_vals->shape > 0 )
    metric_vals->shape = (double) VERDICT_MIN( metric_vals->shape, VERDICT_DBL_MAX );
  else
    metric_vals->shape = (double) VERDICT_MAX( metric_vals->shape, -VERDICT_DBL_MAX );

  if( metric_vals->radius_ratio > 0 )
    metric_vals->radius_ratio = (double) VERDICT_MIN( metric_vals->radius_ratio, VERDICT_DBL_MAX );\
  else
    metric_vals->radius_ratio = (double) VERDICT_MAX( metric_vals->radius_ratio, -VERDICT_DBL_MAX );

  if( metric_vals->scaled_jacobian > 0 )
    metric_vals->scaled_jacobian = (double) VERDICT_MIN( metric_vals->scaled_jacobian, VERDICT_DBL_MAX );
  else
    metric_vals->scaled_jacobian = (double) VERDICT_MAX( metric_vals->scaled_jacobian, -VERDICT_DBL_MAX );

  if( metric_vals->relative_size_squared > 0 )
    metric_vals->relative_size_squared = (double) VERDICT_MIN( metric_vals->relative_size_squared, VERDICT_DBL_MAX );
  else
    metric_vals->relative_size_squared = (double) VERDICT_MAX( metric_vals->relative_size_squared, -VERDICT_DBL_MAX );

  if( metric_vals->shape_and_size > 0 )
    metric_vals->shape_and_size = (double) VERDICT_MIN( metric_vals->shape_and_size, VERDICT_DBL_MAX );
  else
    metric_vals->shape_and_size = (double) VERDICT_MAX( metric_vals->shape_and_size, -VERDICT_DBL_MAX );

  if( metric_vals->distortion > 0 )
    metric_vals->distortion = (double) VERDICT_MIN( metric_vals->distortion, VERDICT_DBL_MAX );
  else
    metric_vals->distortion = (double) VERDICT_MAX( metric_vals->distortion, -VERDICT_DBL_MAX );
}
Exemplo n.º 5
0
/*!
  multiple quality measures of a quad
*/
C_FUNC_DEF void v_quad_quality( int num_nodes, VERDICT_REAL coordinates[][3], 
    unsigned int metrics_request_flag, QuadMetricVals *metric_vals )
{

  memset( metric_vals, 0, sizeof(QuadMetricVals) );

  // for starts, lets set up some basic and common information

  /*  node numbers and side numbers used below

                  2
            3 +--------- 2
             /         +
            /          |
         3 /           | 1
          /            |
         +             |
       0 -------------+ 1
             0
  */
  
  // vectors for each side
  VerdictVector edges[4];
  make_quad_edges( edges, coordinates );

  double areas[4]; 
  signed_corner_areas( areas, coordinates );

  double lengths[4];
  lengths[0] = edges[0].length();
  lengths[1] = edges[1].length();
  lengths[2] = edges[2].length();
  lengths[3] = edges[3].length();

  VerdictBoolean is_collapsed = is_collapsed_quad(coordinates);

  // handle collapsed quads metrics here
  if(is_collapsed == VERDICT_TRUE && metrics_request_flag & 
      ( V_QUAD_MINIMUM_ANGLE | V_QUAD_MAXIMUM_ANGLE | V_QUAD_JACOBIAN |
        V_QUAD_SCALED_JACOBIAN ))
  {
    if(metrics_request_flag & V_QUAD_MINIMUM_ANGLE)
      metric_vals->minimum_angle = v_tri_minimum_angle(3, coordinates);
    if(metrics_request_flag & V_QUAD_MAXIMUM_ANGLE)
      metric_vals->maximum_angle = v_tri_maximum_angle(3, coordinates);
    if(metrics_request_flag & V_QUAD_JACOBIAN)
      metric_vals->jacobian = (VERDICT_REAL)(v_tri_area(3, coordinates) * 2.0);
    if(metrics_request_flag & V_QUAD_SCALED_JACOBIAN)
      metric_vals->jacobian = (VERDICT_REAL)(v_tri_scaled_jacobian(3, coordinates) * 2.0);
  }
  
  // calculate both largest and smallest angles
  if(metrics_request_flag & (V_QUAD_MINIMUM_ANGLE | V_QUAD_MAXIMUM_ANGLE) 
      && is_collapsed == VERDICT_FALSE )
  {
    // gather the angles
    double angles[4];
    angles[0] = acos( -(edges[0] % edges[1])/(lengths[0]*lengths[1]) );
    angles[1] = acos( -(edges[1] % edges[2])/(lengths[1]*lengths[2]) );
    angles[2] = acos( -(edges[2] % edges[3])/(lengths[2]*lengths[3]) );
    angles[3] = acos( -(edges[3] % edges[0])/(lengths[3]*lengths[0]) );

    if( lengths[0] <= VERDICT_DBL_MIN ||
        lengths[1] <= VERDICT_DBL_MIN ||
        lengths[2] <= VERDICT_DBL_MIN ||
        lengths[3] <= VERDICT_DBL_MIN )
    {
      metric_vals->minimum_angle = 360.0;
      metric_vals->maximum_angle = 0.0;
    }
    else
    {
      // if smallest angle, find the smallest angle
      if(metrics_request_flag & V_QUAD_MINIMUM_ANGLE)
      {
        metric_vals->minimum_angle = VERDICT_DBL_MAX;
        for(int i = 0; i<4; i++)
          metric_vals->minimum_angle = VERDICT_MIN(angles[i], metric_vals->minimum_angle);
        metric_vals->minimum_angle *= 180.0 / VERDICT_PI;
      }
      // if largest angle, find the largest angle
      if(metrics_request_flag & V_QUAD_MAXIMUM_ANGLE)
      {
        metric_vals->maximum_angle = 0.0;
        for(int i = 0; i<4; i++)
          metric_vals->maximum_angle = VERDICT_MAX(angles[i], metric_vals->maximum_angle);
        metric_vals->maximum_angle *= 180.0 / VERDICT_PI;

        if( areas[0] < 0 || areas[1] < 0 || 
            areas[2] < 0 || areas[3] < 0 )
          metric_vals->maximum_angle = 360 - metric_vals->maximum_angle;
      }
    }
  }

  // handle aspect, skew, taper, and area together
  if( metrics_request_flag & ( V_QUAD_ASPECT | V_QUAD_SKEW | V_QUAD_TAPER ) )
  {
    //get principle axes
    VerdictVector principal_axes[2];
    principal_axes[0] = edges[0] - edges[2];
    principal_axes[1] = edges[1] - edges[3];

    if(metrics_request_flag & (V_QUAD_ASPECT | V_QUAD_SKEW | V_QUAD_TAPER))
    {
      double len1 = principal_axes[0].length();
      double len2 = principal_axes[1].length();

      // calculate the aspect ratio 
      if(metrics_request_flag & V_QUAD_ASPECT)
      {
        if( len1 < VERDICT_DBL_MIN || len2 < VERDICT_DBL_MIN )
          metric_vals->aspect = VERDICT_DBL_MAX;
        else
          metric_vals->aspect = VERDICT_MAX( len1 / len2, len2 / len1 );
      }
    
      // calculate the taper
      if(metrics_request_flag & V_QUAD_TAPER)
      {
        double min_length = VERDICT_MIN( len1, len2 );

        VerdictVector cross_derivative = edges[1] + edges[3]; 

        if( min_length < VERDICT_DBL_MIN )
          metric_vals->taper = VERDICT_DBL_MAX;
        else
          metric_vals->taper = cross_derivative.length()/ min_length;
      }
      
      // calculate the skew 
      if(metrics_request_flag & V_QUAD_SKEW)
      {
        if( principal_axes[0].normalize() < VERDICT_DBL_MIN ||
            principal_axes[1].normalize() < VERDICT_DBL_MIN )
          metric_vals->skew = 0.0; 
        else
          metric_vals->skew = fabs( principal_axes[0] % principal_axes[1] );
      }
    }
  }

  // calculate the area
  if(metrics_request_flag & (V_QUAD_AREA | V_QUAD_RELATIVE_SIZE_SQUARED) )
  {
    metric_vals->area = 0.25 * (areas[0] + areas[1] + areas[2] + areas[3]);
  }

  // calculate the relative size 
  if(metrics_request_flag & (V_QUAD_RELATIVE_SIZE_SQUARED | V_QUAD_SHAPE_AND_SIZE |
                             V_QUAD_SHEAR_AND_SIZE ) )
  {
    double quad_area = v_quad_area (4, coordinates); 
    v_set_quad_size( quad_area );
    double w11,w21,w12,w22;
    get_weight(w11,w21,w12,w22);
    double avg_area = determinant(w11,w21,w12,w22);

    if( avg_area < VERDICT_DBL_MIN )
      metric_vals->relative_size_squared = 0.0;
    else
      metric_vals->relative_size_squared =  pow( VERDICT_MIN( 
                                              metric_vals->area/avg_area,  
                                              avg_area/metric_vals->area ), 2 );
  }

  // calculate the jacobian
  if(metrics_request_flag & V_QUAD_JACOBIAN)
  {
    metric_vals->jacobian = VERDICT_MIN(
                              VERDICT_MIN( areas[0], areas[1] ),
                              VERDICT_MIN( areas[2], areas[3] ) );
  }

  if( metrics_request_flag & ( V_QUAD_SCALED_JACOBIAN | V_QUAD_SHEAR | V_QUAD_SHEAR_AND_SIZE ) )
  {
    double scaled_jac, min_scaled_jac = VERDICT_DBL_MAX;
    
    if( lengths[0] < VERDICT_DBL_MIN ||
        lengths[1] < VERDICT_DBL_MIN ||
        lengths[2] < VERDICT_DBL_MIN ||
        lengths[3] < VERDICT_DBL_MIN )
    {
      metric_vals->scaled_jacobian = 0.0;  
      metric_vals->shear = 0.0;  
    }
    else
    {
      scaled_jac = areas[0] / (lengths[0] * lengths[3]);
      min_scaled_jac = VERDICT_MIN( scaled_jac, min_scaled_jac );

      scaled_jac = areas[1] / (lengths[1] * lengths[0]);
      min_scaled_jac = VERDICT_MIN( scaled_jac, min_scaled_jac );

      scaled_jac = areas[2] / (lengths[2] * lengths[1]);
      min_scaled_jac = VERDICT_MIN( scaled_jac, min_scaled_jac );

      scaled_jac = areas[3] / (lengths[3] * lengths[2]);
      min_scaled_jac = VERDICT_MIN( scaled_jac, min_scaled_jac );

      metric_vals->scaled_jacobian = min_scaled_jac;
     
      //what the heck...set shear as well 
      if( min_scaled_jac <= VERDICT_DBL_MIN )
        metric_vals->shear = 0.0;
      else
        metric_vals->shear = min_scaled_jac;
    }
  }

  if( metrics_request_flag & (V_QUAD_WARPAGE | V_QUAD_ODDY) )
  {
    VerdictVector corner_normals[4];
    corner_normals[0] = edges[3] * edges[0];
    corner_normals[1] = edges[0] * edges[1];
    corner_normals[2] = edges[1] * edges[2];
    corner_normals[3] = edges[2] * edges[3];

    if( metrics_request_flag & V_QUAD_ODDY )
    {
      double oddy, max_oddy = 0.0;

      double diff, dot_prod;

      double length_squared[4];
      length_squared[0] = corner_normals[0].length_squared();
      length_squared[1] = corner_normals[1].length_squared();
      length_squared[2] = corner_normals[2].length_squared();
      length_squared[3] = corner_normals[3].length_squared();

      if( length_squared[0] < VERDICT_DBL_MIN ||
          length_squared[1] < VERDICT_DBL_MIN ||
          length_squared[2] < VERDICT_DBL_MIN ||
          length_squared[3] < VERDICT_DBL_MIN )
       metric_vals->oddy = VERDICT_DBL_MAX; 
      else
      {
        diff = (lengths[0]*lengths[0]) - (lengths[1]*lengths[1]);
        dot_prod = edges[0]%edges[1];
        oddy = ((diff*diff) + 4*dot_prod*dot_prod ) / (2*length_squared[1]);
        max_oddy = VERDICT_MAX( oddy, max_oddy );

        diff = (lengths[1]*lengths[1]) - (lengths[2]*lengths[2]);
        dot_prod = edges[1]%edges[2];
        oddy = ((diff*diff) + 4*dot_prod*dot_prod ) / (2*length_squared[2]);
        max_oddy = VERDICT_MAX( oddy, max_oddy );

        diff = (lengths[2]*lengths[2]) - (lengths[3]*lengths[3]);
        dot_prod = edges[2]%edges[3];
        oddy = ((diff*diff) + 4*dot_prod*dot_prod ) / (2*length_squared[3]);
        max_oddy = VERDICT_MAX( oddy, max_oddy );

        diff = (lengths[3]*lengths[3]) - (lengths[0]*lengths[0]);
        dot_prod = edges[3]%edges[0];
        oddy = ((diff*diff) + 4*dot_prod*dot_prod ) / (2*length_squared[0]);
        max_oddy = VERDICT_MAX( oddy, max_oddy );

        metric_vals->oddy = max_oddy;
      }
    }

    if( metrics_request_flag & V_QUAD_WARPAGE )
    {
      if( corner_normals[0].normalize() < VERDICT_DBL_MIN ||
          corner_normals[1].normalize() < VERDICT_DBL_MIN ||
          corner_normals[2].normalize() < VERDICT_DBL_MIN ||
          corner_normals[3].normalize() < VERDICT_DBL_MIN )
        metric_vals->warpage = VERDICT_DBL_MAX;
      else 
      {
        metric_vals->warpage = pow( 
                             VERDICT_MIN( corner_normals[0]%corner_normals[2],
                                          corner_normals[1]%corner_normals[3]), 3 ); 
      }
    }
  }

  if( metrics_request_flag & V_QUAD_STRETCH )
  {
    VerdictVector temp;

    temp.set( coordinates[2][0] - coordinates[0][0],
              coordinates[2][1] - coordinates[0][1],
              coordinates[2][2] - coordinates[0][2]);
    double diag02 = temp.length_squared();

    temp.set( coordinates[3][0] - coordinates[1][0],
              coordinates[3][1] - coordinates[1][1],
              coordinates[3][2] - coordinates[1][2]);
    double diag13 = temp.length_squared();
    
    static const double QUAD_STRETCH_FACTOR = sqrt(2.0);

    // 'diag02' is now the max diagonal of the quad
    diag02 = VERDICT_MAX( diag02, diag13 );

    if( diag02 < VERDICT_DBL_MIN )
      metric_vals->stretch = VERDICT_DBL_MAX; 
    else
      metric_vals->stretch =  QUAD_STRETCH_FACTOR *
                              VERDICT_MIN(
                                VERDICT_MIN( lengths[0], lengths[1] ),
                                VERDICT_MIN( lengths[2], lengths[3] ) ) /
                              sqrt(diag02);
  }

  if(metrics_request_flag & (V_QUAD_CONDITION | V_QUAD_SHAPE | V_QUAD_SHAPE_AND_SIZE ) )
  {
    double lengths_squared[4];
    lengths_squared[0] = edges[0].length_squared();
    lengths_squared[1] = edges[1].length_squared();
    lengths_squared[2] = edges[2].length_squared();
    lengths_squared[3] = edges[3].length_squared();

    if( areas[0] < VERDICT_DBL_MIN ||
        areas[1] < VERDICT_DBL_MIN ||
        areas[2] < VERDICT_DBL_MIN ||
        areas[3] < VERDICT_DBL_MIN )
    {
      metric_vals->condition = VERDICT_DBL_MAX;
      metric_vals->shape= VERDICT_DBL_MAX;
    }
    else
    {
      double max_condition = 0.0, condition;

      condition = (lengths_squared[0] + lengths_squared[3])/areas[0];
      max_condition = VERDICT_MAX( max_condition, condition ); 

      condition = (lengths_squared[1] + lengths_squared[0])/areas[1];
      max_condition = VERDICT_MAX( max_condition, condition ); 
     
      condition = (lengths_squared[2] + lengths_squared[1])/areas[2];
      max_condition = VERDICT_MAX( max_condition, condition ); 

      condition = (lengths_squared[3] + lengths_squared[2])/areas[3];
      max_condition = VERDICT_MAX( max_condition, condition ); 

      metric_vals->condition = 0.5*max_condition;
      metric_vals->shape =  2/max_condition;
    }
  } 

  if(metrics_request_flag & V_QUAD_AREA )
  {
    if( metric_vals->area > 0 ) 
      metric_vals->area = (VERDICT_REAL) VERDICT_MIN( metric_vals->area, VERDICT_DBL_MAX );
    metric_vals->area = (VERDICT_REAL) VERDICT_MAX( metric_vals->area, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_ASPECT )
  {
    if( metric_vals->aspect > 0 ) 
      metric_vals->aspect = (VERDICT_REAL) VERDICT_MIN( metric_vals->aspect, VERDICT_DBL_MAX );
    metric_vals->aspect = (VERDICT_REAL) VERDICT_MAX( metric_vals->aspect, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_CONDITION )
  {
    if( metric_vals->condition > 0 ) 
      metric_vals->condition = (VERDICT_REAL) VERDICT_MIN( metric_vals->condition, VERDICT_DBL_MAX );
    metric_vals->condition = (VERDICT_REAL) VERDICT_MAX( metric_vals->condition, -VERDICT_DBL_MAX );
  }

  // calculate distortion
  if(metrics_request_flag & V_QUAD_DISTORTION)
  {
    metric_vals->distortion = v_quad_distortion(num_nodes, coordinates);

    if( metric_vals->distortion > 0 ) 
      metric_vals->distortion = (VERDICT_REAL) VERDICT_MIN( metric_vals->distortion, VERDICT_DBL_MAX );
    metric_vals->distortion = (VERDICT_REAL) VERDICT_MAX( metric_vals->distortion, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_JACOBIAN )
  {
    if( metric_vals->jacobian > 0 ) 
      metric_vals->jacobian = (VERDICT_REAL) VERDICT_MIN( metric_vals->jacobian, VERDICT_DBL_MAX );
    metric_vals->jacobian = (VERDICT_REAL) VERDICT_MAX( metric_vals->jacobian, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_MAXIMUM_ANGLE )
  {
    if( metric_vals->maximum_angle > 0 ) 
      metric_vals->maximum_angle = (VERDICT_REAL) VERDICT_MIN( metric_vals->maximum_angle, VERDICT_DBL_MAX );
    metric_vals->maximum_angle = (VERDICT_REAL) VERDICT_MAX( metric_vals->maximum_angle, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_MINIMUM_ANGLE )
  {
    if( metric_vals->minimum_angle > 0 ) 
      metric_vals->minimum_angle = (VERDICT_REAL) VERDICT_MIN( metric_vals->minimum_angle, VERDICT_DBL_MAX );
    metric_vals->minimum_angle = (VERDICT_REAL) VERDICT_MAX( metric_vals->minimum_angle, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_ODDY )
  {
    if( metric_vals->oddy > 0 ) 
      metric_vals->oddy = (VERDICT_REAL) VERDICT_MIN( metric_vals->oddy, VERDICT_DBL_MAX );
    metric_vals->oddy = (VERDICT_REAL) VERDICT_MAX( metric_vals->oddy, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_RELATIVE_SIZE_SQUARED )
  {
    if( metric_vals->relative_size_squared> 0 ) 
      metric_vals->relative_size_squared = (VERDICT_REAL) VERDICT_MIN( metric_vals->relative_size_squared, VERDICT_DBL_MAX );
    metric_vals->relative_size_squared = (VERDICT_REAL) VERDICT_MAX( metric_vals->relative_size_squared, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_SCALED_JACOBIAN )
  {
    if( metric_vals->scaled_jacobian> 0 ) 
      metric_vals->scaled_jacobian = (VERDICT_REAL) VERDICT_MIN( metric_vals->scaled_jacobian, VERDICT_DBL_MAX );
    metric_vals->scaled_jacobian = (VERDICT_REAL) VERDICT_MAX( metric_vals->scaled_jacobian, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_SHEAR )
  {
    if( metric_vals->shear > 0 ) 
      metric_vals->shear = (VERDICT_REAL) VERDICT_MIN( metric_vals->shear, VERDICT_DBL_MAX );
    metric_vals->shear = (VERDICT_REAL) VERDICT_MAX( metric_vals->shear, -VERDICT_DBL_MAX );
  }

  // calculate shear and size
  // reuse values from above
  if(metrics_request_flag & V_QUAD_SHEAR_AND_SIZE)
  {
    metric_vals->shear_and_size = metric_vals->shear * metric_vals->relative_size_squared;

    if( metric_vals->shear_and_size > 0 ) 
      metric_vals->shear_and_size = (VERDICT_REAL) VERDICT_MIN( metric_vals->shear_and_size, VERDICT_DBL_MAX );
    metric_vals->shear_and_size = (VERDICT_REAL) VERDICT_MAX( metric_vals->shear_and_size, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_SHAPE )
  {
    if( metric_vals->shape > 0 ) 
      metric_vals->shape = (VERDICT_REAL) VERDICT_MIN( metric_vals->shape, VERDICT_DBL_MAX );
    metric_vals->shape = (VERDICT_REAL) VERDICT_MAX( metric_vals->shape, -VERDICT_DBL_MAX );
  }

  // calculate shape and size
  // reuse values from above
  if(metrics_request_flag & V_QUAD_SHAPE_AND_SIZE)
  {
    metric_vals->shape_and_size = metric_vals->shape * metric_vals->relative_size_squared;

    if( metric_vals->shape_and_size > 0 ) 
      metric_vals->shape_and_size = (VERDICT_REAL) VERDICT_MIN( metric_vals->shape_and_size, VERDICT_DBL_MAX );
    metric_vals->shape_and_size = (VERDICT_REAL) VERDICT_MAX( metric_vals->shape_and_size, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_SKEW )
  {
    if( metric_vals->skew > 0 ) 
      metric_vals->skew = (VERDICT_REAL) VERDICT_MIN( metric_vals->skew, VERDICT_DBL_MAX );
    metric_vals->skew = (VERDICT_REAL) VERDICT_MAX( metric_vals->skew, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_STRETCH )
  {
    if( metric_vals->stretch > 0 ) 
      metric_vals->stretch = (VERDICT_REAL) VERDICT_MIN( metric_vals->stretch, VERDICT_DBL_MAX );
    metric_vals->stretch = (VERDICT_REAL) VERDICT_MAX( metric_vals->stretch, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_TAPER )
  {
    if( metric_vals->taper > 0 ) 
      metric_vals->taper = (VERDICT_REAL) VERDICT_MIN( metric_vals->taper, VERDICT_DBL_MAX );
    metric_vals->taper = (VERDICT_REAL) VERDICT_MAX( metric_vals->taper, -VERDICT_DBL_MAX );
  }

  if(metrics_request_flag & V_QUAD_WARPAGE )
  {
    if( metric_vals->warpage > 0 ) 
      metric_vals->warpage = (VERDICT_REAL) VERDICT_MIN( metric_vals->warpage, VERDICT_DBL_MAX );
    metric_vals->warpage = (VERDICT_REAL) VERDICT_MAX( metric_vals->warpage, -VERDICT_DBL_MAX );
  }

}