/*!
The shape of a tri
2 / condition number of weighted jacobian matrix
*/
C_FUNC_DEF double v_tri_shape( int num_nodes, double coordinates[][3] )
{
double condition = v_tri_condition( num_nodes, coordinates );
double shape;
if( condition <= VERDICT_DBL_MIN )
shape = VERDICT_DBL_MAX;
else
shape = (1 / condition);
if( shape > 0 )
return (double) VERDICT_MIN( shape, VERDICT_DBL_MAX );
return (double) VERDICT_MAX( shape, -VERDICT_DBL_MAX );
}
double avtVMetricCondition::Metric (double coords[][3], int type)
{
#ifdef HAVE_VERDICT
switch (type)
{
case VTK_HEXAHEDRON:
case VTK_VOXEL:
return v_hex_condition(8, coords);
case VTK_TETRA:
return v_tet_condition(4,coords);
case VTK_QUAD:
return v_quad_condition(4, coords);
case VTK_TRIANGLE:
return v_tri_condition(3, coords);
}
#endif
return 0;
}
/*!
the condition of a quad
maximum condition number of the Jacobian matrix at 4 corners
*/
C_FUNC_DEF VERDICT_REAL v_quad_condition( int /*num_nodes*/, VERDICT_REAL coordinates[][3] )
{
if ( is_collapsed_quad( coordinates ) == VERDICT_TRUE )
return v_tri_condition(3,coordinates);
double areas[4];
signed_corner_areas( areas, coordinates );
double max_condition = 0.;
VerdictVector xxi, xet;
double condition;
for ( int i=0; i<4; i++ )
{
xxi.set( coordinates[i][0] - coordinates[(i+1)%4][0],
coordinates[i][1] - coordinates[(i+1)%4][1],
coordinates[i][2] - coordinates[(i+1)%4][2] );
xet.set( coordinates[i][0] - coordinates[(i+3)%4][0],
coordinates[i][1] - coordinates[(i+3)%4][1],
coordinates[i][2] - coordinates[(i+3)%4][2] );
if ( areas[i] < VERDICT_DBL_MIN )
condition = VERDICT_DBL_MAX;
else
condition = ( xxi % xxi + xet % xet ) / areas[i];
max_condition = VERDICT_MAX(max_condition, condition);
}
max_condition /= 2;
if( max_condition > 0 )
return (VERDICT_REAL) VERDICT_MIN( max_condition, VERDICT_DBL_MAX );
return (VERDICT_REAL) VERDICT_MAX( max_condition, -VERDICT_DBL_MAX );
}
