GeoDataLatLonBox.cpp

// SPDX-License-Identifier: LGPL-2.1-or-later
//
// SPDX-FileCopyrightText: 2007 Andrew Manson <g.real.ate@gmail.com>
// SPDX-FileCopyrightText: 2008-2009 Torsten Rahn <rahn@kde.org>
//
 
 
#include "GeoDataLatLonBox.h"
 
#include "MarbleDebug.h"
#include "GeoDataLineString.h"
 
#include "GeoDataTypes.h"
 
#include <QDataStream>
 
namespace Marble
{
 
const GeoDataLatLonBox GeoDataLatLonBox::empty = GeoDataLatLonBox();
 
class GeoDataLatLonBoxPrivate
{
 public:
    GeoDataLatLonBoxPrivate()
        : m_north( 0.0 ),
          m_south( 0.0 ),
          m_east( 0.0 ),
          m_west( 0.0 ),
          m_rotation( 0.0 )
    {
    }
 
    qreal m_north;
    qreal m_south;
    qreal m_east;
    qreal m_west;
    qreal m_rotation; // NOT implemented yet!
};
 
bool operator==( GeoDataLatLonBox const& lhs, GeoDataLatLonBox const& rhs )
{
    return lhs.d->m_west == rhs.d->m_west &&
           lhs.d->m_east == rhs.d->m_east &&
           lhs.d->m_north == rhs.d->m_north &&
           lhs.d->m_south == rhs.d->m_south &&
           lhs.d->m_rotation == rhs.d->m_rotation;
}
 
bool operator!=( GeoDataLatLonBox const& lhs, GeoDataLatLonBox const& rhs )
{
    return !( lhs == rhs );
}
 
GeoDataLatLonBox::GeoDataLatLonBox()
    : GeoDataObject(),
      d( new GeoDataLatLonBoxPrivate )
{
}
 
GeoDataLatLonBox::GeoDataLatLonBox( qreal north, qreal south, qreal east, qreal west, GeoDataCoordinates::Unit unit )
    : GeoDataObject(),
      d( new GeoDataLatLonBoxPrivate )
{
    setBoundaries( north, south, east, west, unit );
}
 
GeoDataLatLonBox::GeoDataLatLonBox( const GeoDataLatLonBox & other )
    : GeoDataObject( other ),
      d( new GeoDataLatLonBoxPrivate( *other.d ) )
{
}
 
GeoDataLatLonBox::~GeoDataLatLonBox()
{
    delete d;
}
 
const char* GeoDataLatLonBox::nodeType() const
{
    return GeoDataTypes::GeoDataLatLonBoxType;
}
 
qreal GeoDataLatLonBox::north( GeoDataCoordinates::Unit unit ) const
{
    if ( unit == GeoDataCoordinates::Degree ) {
        return d->m_north * RAD2DEG;
    }
    return d->m_north;
}
 
void GeoDataLatLonBox::setNorth( const qreal north, GeoDataCoordinates::Unit unit )
{
    switch( unit ){
    default:
    case GeoDataCoordinates::Radian:
        d->m_north = GeoDataCoordinates::normalizeLat( north );
        break;
    case GeoDataCoordinates::Degree:
        d->m_north = GeoDataCoordinates::normalizeLat( north * DEG2RAD );
        break;
    }
}
 
qreal GeoDataLatLonBox::south( GeoDataCoordinates::Unit unit ) const
{
    if ( unit == GeoDataCoordinates::Degree ) {
        return d->m_south * RAD2DEG;
    }
    return d->m_south;
}
 
void GeoDataLatLonBox::setSouth( const qreal south, GeoDataCoordinates::Unit unit )
{
    switch( unit ){
    default:
    case GeoDataCoordinates::Radian:
        d->m_south = GeoDataCoordinates::normalizeLat( south );
        break;
    case GeoDataCoordinates::Degree:
        d->m_south = GeoDataCoordinates::normalizeLat( south * DEG2RAD );
        break;
    }
}
 
qreal GeoDataLatLonBox::east( GeoDataCoordinates::Unit unit ) const
{
    if ( unit == GeoDataCoordinates::Degree ) {
        return d->m_east * RAD2DEG;
    }
    return d->m_east;
}
 
void GeoDataLatLonBox::setEast( const qreal east, GeoDataCoordinates::Unit unit )
{
    switch( unit ){
    default:
    case GeoDataCoordinates::Radian:
        d->m_east = GeoDataCoordinates::normalizeLon( east );
        break;
    case GeoDataCoordinates::Degree:
        d->m_east = GeoDataCoordinates::normalizeLon( east * DEG2RAD );
        break;
    }
}
 
qreal GeoDataLatLonBox::west( GeoDataCoordinates::Unit unit ) const
{
    if ( unit == GeoDataCoordinates::Degree ) {
        return d->m_west * RAD2DEG;
    }
    return d->m_west;
}
 
void GeoDataLatLonBox::setWest( const qreal west, GeoDataCoordinates::Unit unit )
{
    switch( unit ){
    default:
    case GeoDataCoordinates::Radian:
        d->m_west = GeoDataCoordinates::normalizeLon( west );
        break;
    case GeoDataCoordinates::Degree:
        d->m_west = GeoDataCoordinates::normalizeLon( west * DEG2RAD );
        break;
    }
}
 
void GeoDataLatLonBox::setRotation( const qreal rotation, GeoDataCoordinates::Unit unit )
{
    switch( unit ){
    default:
    case GeoDataCoordinates::Radian:
        d->m_rotation = rotation;
        break;
    case GeoDataCoordinates::Degree:
        d->m_rotation = rotation * DEG2RAD;
        break;
    }
}
 
qreal GeoDataLatLonBox::rotation( GeoDataCoordinates::Unit unit ) const
{
    if ( unit == GeoDataCoordinates::Degree ) {
        return d->m_rotation * RAD2DEG;
    }
    return d->m_rotation;
}
 
void GeoDataLatLonBox::boundaries( qreal &north, qreal &south, qreal &east, qreal &west, GeoDataCoordinates::Unit unit ) const
{
    switch( unit ){
    default:
    case GeoDataCoordinates::Radian:
        north = d->m_north;
        south = d->m_south;
        east  = d->m_east;
        west  = d->m_west;
        break;
    case GeoDataCoordinates::Degree:
        north = d->m_north * RAD2DEG;
        south = d->m_south * RAD2DEG;
        east  = d->m_east  * RAD2DEG;
        west  = d->m_west  * RAD2DEG;
        break;
    }
}
 
void GeoDataLatLonBox::setBoundaries( qreal north, qreal south, qreal east, qreal west, GeoDataCoordinates::Unit unit )
{
    switch( unit ){
    default:
    case GeoDataCoordinates::Radian:
        d->m_north = GeoDataCoordinates::normalizeLat( north );
        d->m_south = GeoDataCoordinates::normalizeLat( south );
        d->m_east =  GeoDataCoordinates::normalizeLon( east );
        d->m_west =  GeoDataCoordinates::normalizeLon( west );
        break;
    case GeoDataCoordinates::Degree:
        d->m_north = GeoDataCoordinates::normalizeLat( north * DEG2RAD );
        d->m_south = GeoDataCoordinates::normalizeLat( south * DEG2RAD );
        d->m_east =  GeoDataCoordinates::normalizeLon( east * DEG2RAD );
        d->m_west =  GeoDataCoordinates::normalizeLon( west * DEG2RAD );
        break;
    }
}
 
void GeoDataLatLonBox::scale(qreal verticalFactor, qreal horizontalFactor) const
{
    GeoDataCoordinates const middle = center();
    qreal const deltaY = 0.5 * height() * verticalFactor;
    qreal const deltaX = 0.5 * width() * horizontalFactor;
    d->m_north = qMin((middle.latitude() + deltaY), static_cast<qreal>(M_PI/2));
    d->m_south = qMax((middle.latitude() - deltaY), static_cast<qreal>(-M_PI/2));
    if (deltaX > 180 * DEG2RAD) {
        d->m_east = M_PI;
        d->m_west = -M_PI;
    }
    else {
        d->m_east = GeoDataCoordinates::normalizeLon(middle.longitude() + deltaX);
        d->m_west = GeoDataCoordinates::normalizeLon(middle.longitude() - deltaX);
    }
}
 
GeoDataLatLonBox GeoDataLatLonBox::scaled(qreal verticalFactor, qreal horizontalFactor) const
{
    GeoDataLatLonBox result = *this;
    result.scale(verticalFactor, horizontalFactor);
    return result;
}
 
qreal GeoDataLatLonBox::width( GeoDataCoordinates::Unit unit ) const
{
    return GeoDataLatLonBox::width( d->m_east, d->m_west, unit );
}
 
qreal GeoDataLatLonBox::width( qreal east, qreal west, GeoDataCoordinates::Unit unit )
{
    qreal width = fabs( (qreal)( GeoDataLatLonBox::crossesDateLine(east, west)
                                     ? 2 * M_PI - west + east
                                     : east - west ) );
 
    // This also covers the case where this bounding box covers the whole
    // longitude range ( -180 <= lon <= + 180 ).
    if ( width > 2 * M_PI ) {
        width = 2 * M_PI;
    }
 
    if ( unit == GeoDataCoordinates::Degree ) {
        return width * RAD2DEG;
    }
 
    return width;
}
 
qreal GeoDataLatLonBox::height( GeoDataCoordinates::Unit unit ) const
{
    return GeoDataLatLonBox::height(d->m_north, d->m_south, unit);
}
 
qreal GeoDataLatLonBox::height(qreal north, qreal south, GeoDataCoordinates::Unit unit)
{
    qreal height = fabs( (qreal)( south - north ) );
 
    if ( unit == GeoDataCoordinates::Degree ) {
        return height * RAD2DEG;
    }
 
    return height;
}
 
bool GeoDataLatLonBox::crossesDateLine() const
{
    return GeoDataLatLonBox::crossesDateLine(d->m_east, d->m_west);
}
 
bool GeoDataLatLonBox::crossesDateLine(qreal east, qreal west)
{
    return east < west || ( east == M_PI && west == -M_PI );
}
 
GeoDataCoordinates GeoDataLatLonBox::center() const
{
    if( isEmpty() )
        return GeoDataCoordinates();
 
    if( crossesDateLine() )
        return GeoDataCoordinates( GeoDataCoordinates::normalizeLon( east() + 2 * M_PI - ( east() + 2 * M_PI - west() ) / 2 ) ,
                                north() - ( north() - south() ) / 2 );
    else
        return GeoDataCoordinates( east() - ( east() - west() ) / 2,
                                north() - ( north() - south() ) / 2 );
}
 
bool GeoDataLatLonBox::containsPole( Pole pole ) const
{
    switch ( pole ) {
      case NorthPole:
        return ( 2 * north() == +M_PI );
      case SouthPole:
        return ( 2 * south() == -M_PI );
      default:
      case AnyPole:
        return (    2 * north() == +M_PI
                 || 2 * south() == -M_PI );
    }
 
    mDebug() << "Invalid pole";
    return false;
}
 
bool GeoDataLatLonBox::contains(qreal lon, qreal lat) const
{
    if ( lat < d->m_south || lat > d->m_north ) {
        return false;
    }
 
    // We need to take care of the normal case ...
    if ( ( ( lon < d->m_west || lon > d->m_east ) && ( d->m_west < d->m_east ) ) ||
    // ... and the case where the bounding box crosses the date line:
         ( ( lon < d->m_west && lon > d->m_east ) && ( d->m_west > d->m_east ) ) )
        return false;
 
    return true;
}
 
bool GeoDataLatLonBox::contains( const GeoDataCoordinates &point ) const
{
    qreal lon, lat;
 
    point.geoCoordinates( lon, lat );
 
    return contains(lon, lat);
}
 
bool GeoDataLatLonBox::contains( const GeoDataLatLonBox &other ) const
{
    // check the contain criterion for the latitude first as this is trivial:
 
    if ( d->m_north >= other.north() && d->m_south <= other.south() ) {
 
        if ( !crossesDateLine() ) {
            if ( !other.crossesDateLine() ) {
                // "Normal" case: both bounding boxes don't cross the date line
                if ( d->m_west <= other.west() && d->m_east >= other.east() ) {
                    return true;
                }                
            }
            else {
                // The other bounding box crosses the date line, "this" one does not:
                // So the date line splits the other bounding box in two parts.
                // Hence "this" bounding box could be fully contained by one of them. 
                // So for both cases we are able to ignore the "overhanging" portion 
                // and thereby basically reduce the problem to the "normal" case: 
 
                if ( ( other.west() <= d->m_west && d->m_east <= +M_PI )
                  || ( other.east() >= d->m_east && d->m_west >= -M_PI ) ) {
                    return true;
                }
            }
        }
        else {
            if ( other.crossesDateLine() ) {
                // Other "Simple" case: both bounding boxes cross the date line
                if ( d->m_west <= other.west() && d->m_east >= other.east() ) {
                    return true;
                }                
            }
            else {
                // "This" bounding box crosses the date line, the other one does not.
                // So the date line splits "this" bounding box in two parts.
                // Hence the other bounding box could be fully contained by one of them. 
                // So for both cases we are able to ignore the "overhanging" portion 
                // and thereby basically reduce the problem to the "normal" case: 
 
                if ( ( d->m_west <= other.west() && other.east() <= +M_PI )
                  || ( d->m_east >= other.east() && other.west() >= -M_PI ) ) {
                    return true;
                }
 
                // if this bounding box covers the whole longitude range  ( -180 <= lon <= + 180 )
                // then of course the "inner" bounding box is "inside"
                if ( d->m_west == -M_PI && d->m_east == +M_PI ) {
                    return true;
                }
            }
 
        }
    }
 
    return false;
}
 
bool GeoDataLatLonBox::intersects( const GeoDataLatLonBox &other ) const
{
    if ( isEmpty() || other.isEmpty() ) {
        return false;
    }
 
    // check the intersection criterion for the latitude first:
 
    // Case 1: northern boundary of other box intersects:
    if (   (d->m_north >= other.d->m_north && d->m_south <= other.d->m_north)
           // Case 2: northern boundary of this box intersects:
           || (other.d->m_north >= d->m_north && other.d->m_south <= d->m_north)
           // Case 3: southern boundary of other box intersects:
           || (d->m_north >= other.d->m_south && d->m_south <= other.d->m_south)
           // Case 4: southern boundary of this box intersects:
           || (other.d->m_north >= d->m_south && other.d->m_south <= d->m_south)) {
 
        if ( !crossesDateLine() ) {
            if ( !other.crossesDateLine() ) {
                // "Normal" case: both bounding boxes don't cross the date line
                // Case 1: eastern boundary of other box intersects:
                if (    (d->m_east >= other.d->m_east && d->m_west <= other.d->m_east)
                        // Case 2: eastern boundary of this box intersects:
                        || (other.d->m_east >= d->m_east && other.d->m_west <= d->m_east)
                        // Case 3: western boundary of other box intersects:
                        || (d->m_east >= other.d->m_west && d->m_west <= other.d->m_west)
                        // Case 4: western boundary of this box intersects:
                        || (other.d->m_east >= d->m_west && other.d->m_west <= d->m_west)) {
                    return true;
                }
            }
            else {
                // The other bounding box crosses the date line, "this" one does not:
                // So the date line splits the other bounding box in two parts.
 
                if ( d->m_west <= other.d->m_east || d->m_east >= other.d->m_west) {
                    return true;
                }
            }
        }
        else {
            if ( other.crossesDateLine() ) {
                // The trivial case: both bounding boxes cross the date line and intersect
                return true;
            }
            else {
                // "This" bounding box crosses the date line, the other one does not.
                // So the date line splits "this" bounding box in two parts.
                //
                // This also covers the case where this bounding box covers the whole
                // longitude range ( -180 <= lon <= + 180 ).
                if ( other.d->m_west <= d->m_east || other.d->m_east >= d->m_west ) {
                    return true;
                }
            }
        }
    }
 
    return false;
}
 
GeoDataLatLonBox GeoDataLatLonBox::united( const GeoDataLatLonBox& other ) const
{
    if ( isEmpty() ) {
        return other;
    }
 
    if ( other.isEmpty() ) {
        return *this;
    }
 
    GeoDataLatLonBox result;
 
    // use the position of the centers of the boxes to determine the "smallest"
    // box (i.e. should the total box go through IDL or not). this
    // determination does not depend on one box or the other crossing IDL too
    GeoDataCoordinates c1 = center();
    GeoDataCoordinates c2 = other.center();
 
    // do latitude first, quite simple
    result.setNorth(qMax( d->m_north, other.north() ) );
    result.setSouth( qMin( d->m_south, other.south() ) );
 
    qreal w1 = d->m_west;
    qreal w2 = other.west();
    qreal e1 = d->m_east;
    qreal e2 = other.east();
 
    bool const idl1 = d->m_east < d->m_west;
    bool const idl2 = other.d->m_east < other.d->m_west;
 
    if ( idl1 ) {
        w1 += 2* M_PI;
        e1 += 2* M_PI;
    }
    if ( idl2 ) {
        w2 += 2* M_PI;
        e2 += 2* M_PI;
    }
 
    // in the usual case, we take the maximum of east bounds, and
    // the minimum of west bounds. The exceptions are:
    // - centers of boxes are more than 180 apart
    //    (so the smallest box should go around the IDL)
    //
    // - 1 but not 2 boxes are crossing IDL
    if ( fabs( c2.longitude()-c1.longitude() ) > M_PI
         || ( idl1 ^ idl2 ) ) {
        // exceptions, we go the unusual way:
        // min of east, max of west
        result.setEast( qMin( e1, e2 ) );
        result.setWest( qMax( w1, w2 ) );
    }
    else {
        // normal case, max of east, min of west
        result.setEast( qMax( e1, e2 ) );
        result.setWest( qMin( w1, w2 ) );
    }
    return result;
}
 
GeoDataLatLonBox GeoDataLatLonBox::toCircumscribedRectangle() const
{
    QVector<GeoDataCoordinates> coordinates;
    coordinates.reserve(4);
 
    coordinates.append( GeoDataCoordinates( west(), north() ) );
    coordinates.append( GeoDataCoordinates( west(), south() ) );
    coordinates.append( GeoDataCoordinates( east() + ( crossesDateLine() ? 2 * M_PI : 0 ), north() ) );
    coordinates.append( GeoDataCoordinates( east() + ( crossesDateLine() ? 2 * M_PI : 0 ), south() ) );
 
    const qreal cosRotation = cos( rotation() );
    const qreal sinRotation = sin( rotation() );
 
    qreal centerLat = center().latitude();
    qreal centerLon = center().longitude();
    if ( GeoDataLatLonBox( 0, 0, center().longitude(), west() ).crossesDateLine() ) {
        if ( !centerLon ) centerLon += M_PI;
        else centerLon += 2 * M_PI;
    }
 
    GeoDataLatLonBox box;
 
    bool northSet = false;
    bool southSet = false;
    bool eastSet = false;
    bool westSet = false;
 
    for ( const GeoDataCoordinates& coord: coordinates ) {
 
        const qreal lon = coord.longitude();
        const qreal lat = coord.latitude();
 
        const qreal rotatedLon = ( lon - centerLon ) * cosRotation - ( lat - centerLat ) * sinRotation + centerLon;
        const qreal rotatedLat = ( lon - centerLon ) * sinRotation + ( lat - centerLat ) * cosRotation + centerLat;
 
        if ( !northSet || rotatedLat > box.north() ) {
            northSet = true;
            box.setNorth( rotatedLat );
        }
 
        if ( !southSet || rotatedLat < box.south() ) {
            southSet = true;
            box.setSouth( rotatedLat );
        }
 
        if ( !westSet || rotatedLon < box.west() ) {
            westSet = true;
            box.setWest( rotatedLon );
        }
 
        if ( !eastSet || rotatedLon > box.east() ) {
            eastSet = true;
            box.setEast( rotatedLon );
        }
    }
 
    box.setBoundaries(box.north(), box.south(), box.east(), box.west());
 
    return box;
}
 
GeoDataLatLonBox& GeoDataLatLonBox::operator=( const GeoDataLatLonBox &other )
{
    GeoDataObject::operator=( other );
    
    *d = *other.d;
    return *this;
}
 
GeoDataLatLonBox GeoDataLatLonBox::operator|( const GeoDataLatLonBox& other ) const
{
    return united( other );
}
 
GeoDataLatLonBox& GeoDataLatLonBox::operator|=( const GeoDataLatLonBox& other )
{
    *this = united( other );
    return *this;
}
 
 
void GeoDataLatLonBox::pack( QDataStream& stream ) const
{
    GeoDataObject::pack( stream );
 
    stream << d->m_north << d->m_south << d->m_east << d->m_west << d->m_rotation;
}
 
void GeoDataLatLonBox::unpack( QDataStream& stream )
{
    GeoDataObject::unpack( stream );
 
    stream >> d->m_north >> d->m_south >> d->m_east >> d->m_west >> d->m_rotation;
}
 
GeoDataLatLonBox GeoDataLatLonBox::fromLineString(  const GeoDataLineString& lineString  )
{
    // If the line string is empty return an empty boundingbox
    if ( lineString.isEmpty() ) {
        return GeoDataLatLonBox();
    }
 
    qreal lon, lat;
    lineString.first().geoCoordinates( lon, lat );
    GeoDataCoordinates::normalizeLonLat( lon, lat );
 
    qreal north = lat;
    qreal south = lat;
    qreal west =  lon;
    qreal east =  lon;
 
    // If there's only a single node stored then the boundingbox only contains that point
    if ( lineString.size() == 1 )
        return GeoDataLatLonBox( north, south, east, west );
 
    // Specifies whether the polygon crosses the IDL
    bool idlCrossed = false;
 
    // "idlCrossState" specifies the state concerning IDL crossage.
    // This is needed in order to create optimal bounding boxes in case of covering the IDL 
    // Every time the IDL gets crossed from east to west the idlCrossState value gets 
    // increased by one.
    // Every time the IDL gets crossed from west to east the idlCrossState value gets 
    // decreased by one.
    
    int idlCrossState = 0;
    int idlMaxCrossState = 0;
    int idlMinCrossState = 0;
 
    // Holds values for east and west while idlCrossState != 0
    qreal otherWest =  lon;
    qreal otherEast =  lon;
    
    qreal previousLon = lon;
 
    int currentSign = ( lon < 0 ) ? -1 : +1;
    int previousSign = currentSign;
 
    QVector<GeoDataCoordinates>::ConstIterator it( lineString.constBegin() );
    QVector<GeoDataCoordinates>::ConstIterator itEnd( lineString.constEnd() );
 
    bool processingLastNode = false;
 
    while( it != itEnd ) {
        // Get coordinates and normalize them to the desired range.
        (it)->geoCoordinates( lon, lat );
        GeoDataCoordinates::normalizeLonLat( lon, lat );
 
        // Determining the maximum and minimum latitude
        if ( lat > north ) {
            north = lat;
        } else if ( lat < south ) {
            south = lat;
        }
 
        currentSign = ( lon < 0 ) ? -1 : +1;
 
        // Once the polyline crosses the dateline the covered bounding box
        // would cover the whole [-M_PI; M_PI] range.
        // When looking separately at the longitude range that gets covered
        // east and west from the IDL we get two bounding boxes (we prefix
        // the resulting longitude range on the "other side" with "other").
        // By picking the "inner" range values we get a more appropriate 
        // optimized single bounding box.
 
        // IDL check
        if ( previousSign != currentSign
             && fabs( previousLon ) + fabs( lon ) > M_PI ) {
 
            // Initialize values for otherWest and otherEast
            if ( idlCrossed == false ) {
                otherWest =  lon;
                otherEast =  lon;
                idlCrossed = true;
            }
 
            // Determine the new IDL Cross State
            if ( previousLon < 0 ) {
                idlCrossState++;
                if ( idlCrossState > idlMaxCrossState ) {
                    idlMaxCrossState = idlCrossState;
                }
            }
            else {
                idlCrossState--;
                if ( idlCrossState < idlMinCrossState ) {
                    idlMinCrossState = idlCrossState;
                }
            }
        }
 
        if ( idlCrossState == 0 ) {
            if ( lon > east ) east = lon;
            if ( lon < west ) west = lon;
        }
        else {
            if ( lon > otherEast ) otherEast = lon;
            if ( lon < otherWest ) otherWest = lon;
        }
 
        previousLon = lon;
        previousSign = currentSign;
 
        if ( processingLastNode ) {
            break;
        }
        ++it;
 
        if( lineString.isClosed() && it == itEnd ) {
                it = lineString.constBegin();
                processingLastNode = true;
        }
    }
 
    if ( idlCrossed ) {
        if ( idlMinCrossState < 0 ) {
            east = otherEast;
        }
        if ( idlMaxCrossState > 0 ) {
            west = otherWest;
        }
        if ( ( idlMinCrossState < 0 && idlMaxCrossState > 0 ) 
            || idlMinCrossState < -1  || idlMaxCrossState > 1 
            || west <= east ) {
            east = +M_PI;
            west = -M_PI;
            // if polygon fully in south hemisphere, contain south pole
            if( north < 0 ) {
                south = -M_PI/2;
            } else {
                north = M_PI/2;
            }
        }
    }
 
    return GeoDataLatLonBox( north, south, east, west );
}
 
bool GeoDataLatLonBox::isNull() const
{
    return d->m_north == d->m_south && d->m_east == d->m_west;
}
 
bool GeoDataLatLonBox::isEmpty() const
{
    return *this == empty;
}
 
bool GeoDataLatLonBox::fuzzyCompare(const GeoDataLatLonBox& lhs,
                                           const GeoDataLatLonBox& rhs,
                                           const qreal factor)
{
    bool equal = true;
 
    // Check the latitude for approximate equality
 
    double latDelta = lhs.height() * factor;
 
    if (fabs(lhs.north() - rhs.north()) > latDelta) equal = false;
    if (fabs(lhs.south() - rhs.south()) > latDelta) equal = false;
 
 
    // Check the longitude for approximate equality
 
    double lonDelta = lhs.width() * factor;
 
    double lhsEast = lhs.east();
    double rhsEast = rhs.east();
 
    if (!GeoDataLatLonBox::crossesDateLine(lhsEast, rhsEast)) {
        if (fabs(lhsEast - rhsEast) > lonDelta) equal = false;
    }
    else {
        if (lhsEast < 0 && rhsEast > 0) {
            lhsEast += 2 * M_PI;
            if (fabs(lhsEast - rhsEast) > lonDelta) equal = false;
        }
        if (lhsEast > 0 && rhsEast < 0) {
            rhsEast += 2 * M_PI;
            if (fabs(lhsEast - rhsEast) > lonDelta) equal = false;
        }
    }
 
    double lhsWest = lhs.west();
    double rhsWest = rhs.west();
 
    if (!GeoDataLatLonBox::crossesDateLine(lhsWest, rhsWest)) {
       if (fabs(lhsWest - rhsWest) > lonDelta) equal = false;
    }
    else {
        if (lhsWest < 0 && rhsWest > 0) {
            lhsWest += 2 * M_PI;
            if (fabs(lhsWest - rhsWest) > lonDelta) equal = false;
        }
        if (lhsWest > 0 && rhsWest < 0) {
            rhsWest += 2 * M_PI;
            if (fabs(lhsWest - rhsWest) > lonDelta) equal = false;
        }
    }
 
    return equal;
}
 
 
void GeoDataLatLonBox::clear()
{
    *this = empty;
}
}