T FacePerimeter:: getFacePerimeter ( const HalfEdge <T> *e_start )
{
//Get perimeter of the Face given by start half edge
T perimeter = 0;
HalfEdge <T> *e = const_cast <HalfEdge <T> *> ( e_start );
//There is a valid edge
if ( e_start != NULL )
{
//Get point
Node3DCartesian <T> *pi = e->getPoint();
//Proces all edges of the Face
do
{
//Get point
Node3DCartesian <T> *pii = e->getNextEdge()->getPoint();
//Compute area
perimeter += EuclDistance::getEuclDistance2D ( pi->getX(), pi->getY(), pii->getX(), pii->getY() );
//Assign point
pi = pii;
//Assign edge
e = e->getNextEdge();
}
while ( e != e_start );
}
//Get area
return perimeter;
}
void TangentFunction::computeTangentFunctionFace ( const Face <T> *face, typename TTangentFunction <T>::Type & tf, T & rotation, const TTangentFunctionRotationMethod & rotation_method,
const TTangentFunctionScaleMethod & scale_method )
{
//Compute normalized tangent function for the Face given by HalfEdge
T turning_angle_sum = 0, normalize_length_sum = 0;
const HalfEdge <T> *e_start = face->getHalfEdge();
HalfEdge <T> *e = const_cast <HalfEdge <T> *> ( e_start ) ;
//Get triplet of points
Node3DCartesian <T> *pi, *piii = NULL;
Node3DCartesian <T> *pii = e_start->getPoint();
//Jump short segments
for ( pi = e->getPreviousEdge()->getPoint(); EuclDistance::getEuclDistance2D ( pi, pii ) < MIN_POSITION_DIFF ; e = e->getPreviousEdge(), pi = e->getPreviousEdge()->getPoint() ) {}
//Get third point for initial edge
for ( piii = e->getNextEdge()->getPoint(); EuclDistance::getEuclDistance2D ( pii, piii ) < MIN_POSITION_DIFF ; e = e->getNextEdge(), piii = e->getNextEdge()->getPoint() ) {}
//Compute perimeter of the Face
const T face_perimeter = FacePerimeter::getFacePerimeter ( e_start );
//Throw exception
if ( face_perimeter == 0 )
{
throw ErrorMathZeroDevision <T> ( "ErrorMathZeroDevision: tangent function, can not normalize function (1 / perimeter), ", "perimeter = 0." );
}
//Compute initial angle: rotation invariant
if ( rotation_method == RotationInvariant )
{
turning_angle_sum += 180 - Angle3Points::getAngle3Points ( pi, pii, piii );
}
//Compute initial angle: rotation dependent (do not compute the sum)
else
{
turning_angle_sum = 360 - Angle3Points::getAngle3Points ( &Node3DCartesian <T> ( pii->getX() - 1, pii->getY() ), pii, piii );
}
//Add turning angle computed for normalized length of initial edge to map
tf[normalize_length_sum] = turning_angle_sum;
//Assign points from initial edge
pi = pii;
pii = piii;
//Increment initial edge
e = e_start->getNextEdge();
//Process all edges of the Face (2, n-1)
do
{
//Get third point
piii = e->getNextEdge()->getPoint();
//Segment is too short
if ( EuclDistance::getEuclDistance2D ( pii, piii ) > MIN_POSITION_DIFF )
{
//Compute angle: rotation invariant
if ( rotation_method == RotationInvariant )
{
turning_angle_sum += 180 - Angle3Points::getAngle3Points ( pi, pii, piii );
}
//Compute initial angle: rotation dependent (do not compute the sum)
else
{
turning_angle_sum = 360 - Angle3Points::getAngle3Points ( &Node3DCartesian <T> ( pii->getX() - 1, pii->getY() ), pii, piii );
}
//Compute normalized length sum
normalize_length_sum += ( scale_method == ScaleDependent ? EuclDistance::getEuclDistance2D ( pi, pii ) / face_perimeter : EuclDistance::getEuclDistance2D ( pi, pii ) );
//Add turning angle computed for normalized length to map
tf[normalize_length_sum] = turning_angle_sum;
//Assign points
pi = pii;
pii = piii;
}
//Increment edge
e = e->getNextEdge();
} while ( e != e_start );
//Add last value: we visit first point again
const T last = ( scale_method == ScaleDependent ? 1.0 : face_perimeter );
if ( rotation_method == RotationInvariant )
{
tf[ last] = turning_angle_sum + tf.begin()->second;
}
else
{
tf[last] = tf.begin()->second;
}
}
void TurningFunction::computeTurningFunctionFace ( const Face <T> *face, typename TTurningFunction <T>::Type & tf, T & rotation, const TTurningFunctionRotationMethod & rotation_method,
const TTurningFunctionScaleMethod & scale_method )
{
//Compute normalized turning function for the Face given by HalfEdge
T turning_angle_sum = 0, normalize_length_sum = 0;
const HalfEdge <T> *e_start = face->getHalfEdge();
HalfEdge <T> *e = const_cast <HalfEdge <T> *> ( e_start ) ;
//Get triplet of points
Node3DCartesian <T> *pi, *piii = NULL;
Node3DCartesian <T> *pii = e_start->getPoint();
//Jump short segments
for ( pi = e->getPreviousEdge()->getPoint(); EuclDistance::getEuclDistance2D ( pi->getX(), pi->getY(), pii->getX(), pii->getY() ) < MIN_POSITION_DIFF ; e = e->getPreviousEdge(), pi = e->getPreviousEdge()->getPoint() );
//Get third point for initial edge
for ( piii = e->getNextEdge()->getPoint(); EuclDistance::getEuclDistance2D ( pii->getX(), pii->getY(), piii->getX(), piii->getY() ) < MIN_POSITION_DIFF ; e = e->getNextEdge(), piii = e->getNextEdge()->getPoint() );
//Compute perimeter of the Face
const T face_perimeter = FacePerimeter::getFacePerimeter ( e_start );
//Throw exception
if ( fabs ( face_perimeter ) < MIN_FLOAT )
{
throw MathZeroDevisionException <T> ( "MathZeroDevisionException: turning function, can not normalize function (1 / perimeter), ", "perimeter = 0.", face_perimeter );
}
//Compute initial angle: rotation invariant
if ( rotation_method == RotationInvariant )
{
turning_angle_sum += 180 - Angle3Points::getAngle3Points ( pi, pii, piii );
}
//Compute initial angle: rotation dependent (do not compute the sum)
else
{
//Create temporary point P (x_temp, y_temp) on x axis
const T dx = std::max ( fabs ( piii->getX() - pii->getX() ), fabs ( piii->getY() - pii->getY() ) );
Node3DCartesian <T> n_temp ( pii->getX() - 2 * dx , pii->getY() );
turning_angle_sum += Bearing::getBearing ( pii, &n_temp );
}
//Add turning angle computed for normalized length of initial edge to map
tf[normalize_length_sum] = turning_angle_sum;
//Assign points from initial edge
pi = pii;
pii = piii;
//Increment initial edge
e = e_start->getNextEdge();
//Process all edges of the Face (2, n-1)
do
{
//Get third point
piii = e->getNextEdge()->getPoint();
//Segment is too short
if ( EuclDistance::getEuclDistance2D ( pii->getX(), pii->getY(), piii->getX(), piii->getY() ) > MIN_POSITION_DIFF )
{
//Compute angle: rotation invariant
turning_angle_sum += 180.0 - Angle3Points::getAngle3Points ( pi, pii, piii );
//Compute normalized length sum
normalize_length_sum += ( scale_method == ScaleInvariant ? EuclDistance::getEuclDistance2D ( pi->getX(), pi->getY(), pii->getX(), pii->getY() ) / face_perimeter :
EuclDistance::getEuclDistance2D ( pi->getX(), pi->getY(), pii->getX(), pii->getY() ) );
//Add turning angle computed for normalized length to map
tf[normalize_length_sum] = turning_angle_sum;
//Assign points
pi = pii;
pii = piii;
}
//Increment edge
e = e->getNextEdge();
}
while ( e != e_start );
//Add last value: we visit first point again
const T last_key = ( scale_method == ScaleInvariant ? 1.0 : face_perimeter );
tf[last_key] = ( rotation_method == RotationInvariant ? turning_angle_sum + tf.begin()->second : tf.begin()->second );
}
