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;
        }
}
Esempio n. 3
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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 );
}