/*!
moves and rotates the quad such that it enables us to
use components of ef's
*/
void localize_quad_for_ef( VerdictVector node_pos[4])
{
VerdictVector centroid(node_pos[0]);
centroid += node_pos[1];
centroid += node_pos[2];
centroid += node_pos[3];
centroid /= 4.0;
node_pos[0] -= centroid;
node_pos[1] -= centroid;
node_pos[2] -= centroid;
node_pos[3] -= centroid;
VerdictVector rotate = node_pos[1] + node_pos[2] - node_pos[3] - node_pos[0];
rotate.normalize();
double cosine = rotate.x();
double sine = rotate.y();
double xnew;
for (int i=0; i < 4; i++)
{
xnew = cosine * node_pos[i].x() + sine * node_pos[i].y();
node_pos[i].y( -sine * node_pos[i].x() + cosine * node_pos[i].y() );
node_pos[i].x(xnew);
}
}
double VerdictVector::distance_between(const VerdictVector& test_vector)
{
double xv = xVal - test_vector.x();
double yv = yVal - test_vector.y();
double zv = zVal - test_vector.z();
return( sqrt( xv * xv + yv * yv + zv * zv ) );
}
/*!
The scaled jacobian of a tri
minimum of the jacobian divided by the lengths of 2 edge vectors
*/
C_FUNC_DEF double v_tri_scaled_jacobian( int /*num_nodes*/, double coordinates[][3])
{
static const double detw = 2./sqrt(3.0);
VerdictVector first, second;
double jacobian;
VerdictVector edge[3];
edge[0].set(coordinates[1][0] - coordinates[0][0],
coordinates[1][1] - coordinates[0][1],
coordinates[1][2] - coordinates[0][2]);
edge[1].set(coordinates[2][0] - coordinates[0][0],
coordinates[2][1] - coordinates[0][1],
coordinates[2][2] - coordinates[0][2]);
edge[2].set(coordinates[2][0] - coordinates[1][0],
coordinates[2][1] - coordinates[1][1],
coordinates[2][2] - coordinates[1][2]);
first = edge[1]-edge[0];
second = edge[2]-edge[0];
VerdictVector cross = first * second;
jacobian = cross.length();
double max_edge_length_product;
max_edge_length_product = VERDICT_MAX( edge[0].length()*edge[1].length(),
VERDICT_MAX( edge[1].length()*edge[2].length(),
edge[0].length()*edge[2].length() ) );
if( max_edge_length_product < VERDICT_DBL_MIN )
return (double)0.0;
jacobian *= detw;
jacobian /= max_edge_length_product;
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( (cross.x()*surf_normal[0] +
cross.y()*surf_normal[1] +
cross.z()*surf_normal[2] ) < 0 )
jacobian *= -1;
}
if( jacobian > 0 )
return (double) VERDICT_MIN( jacobian, VERDICT_DBL_MAX );
return (double) VERDICT_MAX( jacobian, -VERDICT_DBL_MAX );
}
inline void product( VerdictVector& a1,
VerdictVector& a2,
VerdictVector& a3,
VerdictVector& b1,
VerdictVector& b2,
VerdictVector& b3,
VerdictVector& c1,
VerdictVector& c2,
VerdictVector& c3 )
{
VerdictVector x1, x2, x3;
x1.set( a1.x(), a2.x(), a3.x() );
x2.set( a1.y(), a2.y(), a3.y() );
x3.set( a1.z(), a2.z(), a3.z() );
c1.set( x1 % b1, x2 % b1, x3 % b1 );
c2.set( x1 % b2, x2 % b2, x3 % b2 );
c3.set( x1 % b3, x2 % b3, x3 % b3 );
}
//- Find next point from this point using a direction and distance
void VerdictVector::next_point( const VerdictVector &direction,
double distance, VerdictVector& out_point )
{
VerdictVector my_direction = direction;
my_direction.normalize();
// Determine next point in space
out_point.x( xVal + (distance * my_direction.x()) );
out_point.y( yVal + (distance * my_direction.y()) );
out_point.z( zVal + (distance * my_direction.z()) );
return;
}
bool VerdictVector::within_tolerance( const VerdictVector &vectorPtr2,
double tolerance) const
{
if (( fabs (this->x() - vectorPtr2.x()) < tolerance) &&
( fabs (this->y() - vectorPtr2.y()) < tolerance) &&
( fabs (this->z() - vectorPtr2.z()) < tolerance)
)
{
return true;
}
return false;
}
inline void inverse(VerdictVector x1,
VerdictVector x2,
VerdictVector x3,
VerdictVector& u1,
VerdictVector& u2,
VerdictVector& u3 )
{
double detx = v_determinant(x1, x2, x3);
VerdictVector rx1, rx2, rx3;
rx1.set(x1.x(), x2.x(), x3.x());
rx2.set(x1.y(), x2.y(), x3.y());
rx3.set(x1.z(), x2.z(), x3.z());
u1 = rx2 * rx3;
u2 = rx3 * rx1;
u3 = rx1 * rx2;
u1 /= detx;
u2 /= detx;
u3 /= detx;
}