double avtVMetricMaximumAngle::Metric (double coords[][3], int type)
{
#ifdef HAVE_VERDICT
switch (type)
{
case VTK_TRIANGLE:
return v_tri_maximum_angle(3, coords);
case VTK_QUAD:
return v_quad_maximum_angle(4, coords);
}
#endif
return -1;
}
/*!
the largest angle of a quad
largest included quad area (degrees)
*/
C_FUNC_DEF VERDICT_REAL v_quad_maximum_angle( int /*num_nodes*/, VERDICT_REAL coordinates[][3] )
{
// if this is a collapsed quad, just pass it on to
// the tri_largest_angle routine
if( is_collapsed_quad(coordinates) == VERDICT_TRUE )
return v_tri_maximum_angle(3, coordinates);
double angle;
double max_angle = 0.0;
VerdictVector edges[4];
edges[0].set(
coordinates[1][0] - coordinates[0][0],
coordinates[1][1] - coordinates[0][1],
coordinates[1][2] - coordinates[0][2]
);
edges[1].set(
coordinates[2][0] - coordinates[1][0],
coordinates[2][1] - coordinates[1][1],
coordinates[2][2] - coordinates[1][2]
);
edges[2].set(
coordinates[3][0] - coordinates[2][0],
coordinates[3][1] - coordinates[2][1],
coordinates[3][2] - coordinates[2][2]
);
edges[3].set(
coordinates[0][0] - coordinates[3][0],
coordinates[0][1] - coordinates[3][1],
coordinates[0][2] - coordinates[3][2]
);
// go around each node and calculate the angle
// at each node
double length[4];
length[0] = edges[0].length();
length[1] = edges[1].length();
length[2] = edges[2].length();
length[3] = edges[3].length();
if( length[0] <= VERDICT_DBL_MIN ||
length[1] <= VERDICT_DBL_MIN ||
length[2] <= VERDICT_DBL_MIN ||
length[3] <= VERDICT_DBL_MIN )
return 0.0;
angle = acos( -(edges[0] % edges[1])/(length[0]*length[1]) );
max_angle = VERDICT_MAX(angle, max_angle);
angle = acos( -(edges[1] % edges[2])/(length[1]*length[2]) );
max_angle = VERDICT_MAX(angle, max_angle);
angle = acos( -(edges[2] % edges[3])/(length[2]*length[3]) );
max_angle = VERDICT_MAX(angle, max_angle);
angle = acos( -(edges[3] % edges[0])/(length[3]*length[0]) );
max_angle = VERDICT_MAX(angle, max_angle);
max_angle = max_angle *180.0/VERDICT_PI;
//if any signed areas are < 0, then you are getting the wrong angle
double areas[4];
signed_corner_areas( areas, coordinates );
if( areas[0] < 0 || areas[1] < 0 ||
areas[2] < 0 || areas[3] < 0 )
{
max_angle = 360 - max_angle;
}
if( max_angle > 0 )
return (VERDICT_REAL) VERDICT_MIN( max_angle, VERDICT_DBL_MAX );
return (VERDICT_REAL) VERDICT_MAX( max_angle, -VERDICT_DBL_MAX );
}
/*!
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 );
}
}
