unsigned short PointFacePosition:: getPointFacePosition ( const Point3DCartesian <T> * q, const Face <T> *face )
{
/*Returns position of the point to the Face
0: q is strictly interior
1: q is strictly exterior
2: q is on the edge but not an endpoint
3: q is a vertex
*/
//There is a valid Face
if ( face != NULL )
{
unsigned short l_inters = 0, r_inters = 0;
HalfEdge <T> *e = face->getHalfEdge();
const HalfEdge <T> *e_start = e;
//Get point P[i-1]
const Node3DCartesian <T> *pi1 = e->getPreviousEdge()->getPoint();
//Process all edges
do
{
//Get point P[i]
const Node3DCartesian <T> *pi = e->getPoint();
//Test point is identical with end points: d(q, pi) < POSITION_ROUND_ERROR
if ( ( q->getX() - pi->getX() ) * ( q->getX() - pi->getX() ) + ( q->getY() - pi->getY() ) * ( q->getY() - pi->getY() ) < POSITION_ROUND_ERROR * POSITION_ROUND_ERROR )
{
return 3;
}
//Perform tests: different position of segment end points to ray
bool t1 = ( pi->getY() > q->getY() + POSITION_ROUND_ERROR ) != ( pi1->getY() > q->getY() + POSITION_ROUND_ERROR );
bool t2 = ( pi->getY() < q->getY() - POSITION_ROUND_ERROR ) != ( pi1->getY() < q->getY() - POSITION_ROUND_ERROR );
//Segment intersects left or ray
if ( t1 || t2 )
{
//Compute intersection
T x = ( ( pi->getX() - q->getX() ) * ( pi1->getY() - q->getY() ) - ( pi1->getX() - q->getX() ) * ( pi->getY() - q->getY() ) )
/ double ( ( pi1->getY() - pi->getY() ) );
//Aditional test to avoid roundness error: point too close to edge
if ( PointLineDistance::getPointLineSegmentDistance2D ( q, pi, pi1 ) < POSITION_ROUND_ERROR )
{
return 2;
}
//Increment number of right intersections
if ( t1 && x > 0 )
{
r_inters ++;
}
//Increment number of left intersections
if ( t2 && x < 0 )
{
l_inters ++;
}
}
//Assign point
pi1 = pi;
//Increment edge
e = e->getNextEdge();
}
while ( e != e_start );
//Point lies on the edge, but not at endpoints
if ( ( l_inters % 2 ) != ( r_inters % 2 ) )
{
return 2;
}
//Points is strictly interior
if ( l_inters % 2 == 1 )
{
return 0;
}
//Point is strictly exterior
return 1;
}
//Throw exception
else
{
throw ErrorBadData ( "ErrorBadData: no face incident to edge, ", "can not test point vs. face position" );
}
}
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 );
}