labelposition.cpp

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/*
 *   libpal - Automated Placement of Labels Library
 *
 *   Copyright (C) 2008 Maxence Laurent, MIS-TIC, HEIG-VD
 *                      University of Applied Sciences, Western Switzerland
 *                      http://www.hes-so.ch
 *
 *   Contact:
 *      maxence.laurent <at> heig-vd <dot> ch
 *    or
 *      eric.taillard <at> heig-vd <dot> ch
 *
 * This file is part of libpal.
 *
 * libpal is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * libpal is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with libpal.  If not, see <http://www.gnu.org/licenses/>.
 *
 */
 
#include "labelposition.h"
 
#include <cmath>
 
#include "costcalculator.h"
#include "feature.h"
#include "layer.h"
#include "qgsgeometryutils_base.h"
#include "qgsgeos.h"
#include "qgslabelingenginerule.h"
#include "qgsmessagelog.h"
 
#include <QString>
 
using namespace Qt::StringLiterals;
 
using namespace pal;
 
LabelPosition::LabelPosition( int id, double x1, double y1, double w, double h, double alpha, double cost, FeaturePart *feature, LabelDirectionToLine directionToLine, Qgis::LabelQuadrantPosition quadrant )
  : id( id )
  , feature( feature )
  , alpha( alpha )
  , w( w )
  , h( h )
  , mQuadrant( quadrant )
  , mDirectionToLine( directionToLine )
  , mCost( cost )
{
  type = GEOS_POLYGON;
  nbPoints = 4;
  x.resize( nbPoints );
  y.resize( nbPoints );
 
  // alpha take his value bw 0 and 2*pi rad
  while ( this->alpha > 2 * M_PI )
    this->alpha -= 2 * M_PI;
 
  while ( this->alpha < 0 )
    this->alpha += 2 * M_PI;
 
  const double beta = this->alpha + M_PI_2;
 
  double dx1, dx2, dy1, dy2;
 
  dx1 = std::cos( this->alpha ) * w;
  dy1 = std::sin( this->alpha ) * w;
 
  dx2 = std::cos( beta ) * h;
  dy2 = std::sin( beta ) * h;
 
  x[0] = x1;
  y[0] = y1;
 
  x[1] = x1 + dx1;
  y[1] = y1 + dy1;
 
  x[2] = x1 + dx1 + dx2;
  y[2] = y1 + dy1 + dy2;
 
  x[3] = x1 + dx2;
  y[3] = y1 + dy2;
 
  // upside down ? (curved labels are always correct)
  if ( !feature->layer()->isCurved() && this->alpha > M_PI_2 && this->alpha <= 3 * M_PI_2 )
  {
    if ( feature->onlyShowUprightLabels() )
    {
      // Turn label upsidedown by inverting boundary points
      double tx, ty;
 
      tx = x[0];
      ty = y[0];
 
      x[0] = x[2];
      y[0] = y[2];
 
      x[2] = tx;
      y[2] = ty;
 
      tx = x[1];
      ty = y[1];
 
      x[1] = x[3];
      y[1] = y[3];
 
      x[3] = tx;
      y[3] = ty;
 
      if ( this->alpha < M_PI )
        this->alpha += M_PI;
      else
        this->alpha -= M_PI;
 
      // labels with text shown upside down are not classified as upsideDown,
      // only those whose boundary points have been inverted
      upsideDown = true;
    }
  }
 
  for ( int i = 0; i < nbPoints; ++i )
  {
    xmin = std::min( xmin, x[i] );
    xmax = std::max( xmax, x[i] );
    ymin = std::min( ymin, y[i] );
    ymax = std::max( ymax, y[i] );
  }
 
  createOuterBoundsGeom();
}
 
LabelPosition::LabelPosition( const LabelPosition &other )
  : PointSet( other )
{
  id = other.id;
  mCost = other.mCost;
  feature = other.feature;
  probFeat = other.probFeat;
  nbOverlap = other.nbOverlap;
 
  alpha = other.alpha;
  w = other.w;
  h = other.h;
 
  if ( other.mNextPart )
    mNextPart = std::make_unique< LabelPosition >( *other.mNextPart );
 
  partId = other.partId;
  upsideDown = other.upsideDown;
  mDirectionToLine = other.mDirectionToLine;
  mQuadrant = other.mQuadrant;
  mHasObstacleConflict = other.mHasObstacleConflict;
  mUpsideDownCharCount = other.mUpsideDownCharCount;
 
  createOuterBoundsGeom();
}
 
LabelPosition::~LabelPosition()
{
  if ( mPreparedOuterBoundsGeos )
  {
    GEOSPreparedGeom_destroy_r( QgsGeosContext::get(), mPreparedOuterBoundsGeos );
    mPreparedOuterBoundsGeos = nullptr;
  }
}
 
bool LabelPosition::intersects( const GEOSPreparedGeometry *geometry )
{
  // this method considers the label's outer bounds
  if ( !mOuterBoundsGeos && !mGeos )
    createGeosGeom();
 
  try
  {
    if ( GEOSPreparedIntersects_r( QgsGeosContext::get(), geometry, mOuterBoundsGeos ? mOuterBoundsGeos.get() : mGeos ) == 1 )
    {
      return true;
    }
    else if ( mNextPart )
    {
      return mNextPart->intersects( geometry );
    }
  }
  catch ( QgsGeosException &e )
  {
    qWarning( "GEOS exception: %s", e.what() );
    QgsMessageLog::logMessage( QObject::tr( "Exception: %1" ).arg( e.what() ), QObject::tr( "GEOS" ) );
    return false;
  }
 
  return false;
}
 
bool LabelPosition::within( const GEOSPreparedGeometry *geometry )
{
  // this method considers the label's outer bounds
  if ( !mOuterBoundsGeos && !mGeos )
    createGeosGeom();
 
  try
  {
    if ( GEOSPreparedContains_r( QgsGeosContext::get(), geometry, mOuterBoundsGeos ? mOuterBoundsGeos.get() : mGeos ) != 1 )
    {
      return false;
    }
    else if ( mNextPart )
    {
      return mNextPart->within( geometry );
    }
  }
  catch ( QgsGeosException &e )
  {
    qWarning( "GEOS exception: %s", e.what() );
    QgsMessageLog::logMessage( QObject::tr( "Exception: %1" ).arg( e.what() ), QObject::tr( "GEOS" ) );
    return false;
  }
 
  return true;
}
 
bool LabelPosition::isInConflict( const LabelPosition *lp ) const
{
  // this method considers the label's outer bounds
 
  if ( this->probFeat == lp->probFeat ) // bugfix #1
    return false;                       // always overlapping itself !
 
  const double minDuplicateSeparation = std::max( getFeaturePart()->feature()->thinningSettings().noRepeatDistance(), lp->getFeaturePart()->feature()->thinningSettings().noRepeatDistance() );
  const bool noDuplicateDistanceApplies = minDuplicateSeparation > 0 && getFeaturePart()->feature()->labelText() == lp->getFeaturePart()->feature()->labelText();
 
  // if either this label doesn't cause collisions, or the other one doesn't, then we don't conflict!
  const bool allowOverlapAtNoCost = this->feature->feature()->overlapHandling() == Qgis::LabelOverlapHandling::AllowOverlapAtNoCost
                                    || lp->feature->feature()->overlapHandling() == Qgis::LabelOverlapHandling::AllowOverlapAtNoCost;
 
  // early exit shortcut
  if ( !noDuplicateDistanceApplies && allowOverlapAtNoCost )
    return false;
 
  GEOSContextHandle_t geosctxt = QgsGeosContext::get();
 
  const bool bothLabelsAreSinglePart = !nextPart() && !lp->nextPart();
  if ( bothLabelsAreSinglePart )
  {
    if ( qgsDoubleNear( alpha, 0 ) && qgsDoubleNear( lp->alpha, 0 ) )
    {
      // simple case -- both candidates are oriented to axis, so shortcut with easy calculation
      if ( mOuterBoundsGeos )
      {
        if ( outerBoundingBoxIntersects( lp ) )
          return true;
      }
      else if ( boundingBoxIntersects( lp ) )
      {
        return true;
      }
 
      if ( noDuplicateDistanceApplies )
      {
        const double minSeparationSquared = minDuplicateSeparation * minDuplicateSeparation;
        for ( std::size_t i = 0; i < static_cast< std::size_t >( nbPoints ); ++i )
        {
          const double lx1 = x[i];
          const double ly1 = y[i];
          for ( std::size_t j = 0; j < static_cast< std::size_t>( lp->nbPoints ); ++j )
          {
            const double lx2 = lp->x[j];
            const double ly2 = lp->y[j];
            if ( ( lx2 - lx1 ) * ( lx2 - lx1 ) + ( ly2 - ly1 ) * ( ly2 - ly1 ) < minSeparationSquared )
              return true;
          }
        }
      }
 
      return false;
    }
    else
    {
      // this method considers the label's outer bounds
 
      if ( noDuplicateDistanceApplies )
      {
        try
        {
#if GEOS_VERSION_MAJOR > 3 || ( GEOS_VERSION_MAJOR == 3 && GEOS_VERSION_MINOR >= 10 )
          if ( GEOSPreparedDistanceWithin_r( geosctxt, lp->preparedOuterBoundsGeom() ? lp->preparedOuterBoundsGeom() : lp->preparedGeom(), mOuterBoundsGeos ? mOuterBoundsGeos.get() : mGeos, minDuplicateSeparation ) )
          {
            return true;
          }
#else
          QgsMessageLog::logMessage( u"label margin distance requires GEOS 3.10+"_s );
#endif
        }
        catch ( QgsGeosException &e )
        {
          QgsDebugError( u"GEOS exception: %1"_s.arg( e.what() ) );
        }
      }
      else
      {
        if ( !mOuterBoundsGeos && !mGeos )
          createGeosGeom();
 
        try
        {
          const bool result
            = ( GEOSPreparedIntersects_r( geosctxt, lp->preparedOuterBoundsGeom() ? lp->preparedOuterBoundsGeom() : lp->preparedGeom(), mOuterBoundsGeos ? mOuterBoundsGeos.get() : mGeos ) == 1 );
          return result;
        }
        catch ( QgsGeosException &e )
        {
          qWarning( "GEOS exception: %s", e.what() );
          QgsMessageLog::logMessage( QObject::tr( "Exception: %1" ).arg( e.what() ), QObject::tr( "GEOS" ) );
          return false;
        }
      }
      return false;
    }
  }
 
  return isInConflictMultiPart( lp );
}
 
bool LabelPosition::isInConflictMultiPart( const LabelPosition *lp ) const
{
  if ( !mMultipartGeos )
    createMultiPartGeosGeom();
 
  if ( !lp->mMultipartGeos )
    lp->createMultiPartGeosGeom();
 
  GEOSContextHandle_t geosctxt = QgsGeosContext::get();
 
  const bool noRepeatDistanceApplies = ( getFeaturePart()->feature()->thinningSettings().noRepeatDistance() > 0 || lp->getFeaturePart()->feature()->thinningSettings().noRepeatDistance() > 0 )
                                       && getFeaturePart()->feature()->labelText() == lp->getFeaturePart()->feature()->labelText();
 
  // test for duplicate labels too close together
  if ( noRepeatDistanceApplies )
  {
    const double minSeparation = std::max( getFeaturePart()->feature()->thinningSettings().noRepeatDistance(), lp->getFeaturePart()->feature()->thinningSettings().noRepeatDistance() );
 
    try
    {
#if GEOS_VERSION_MAJOR > 3 || ( GEOS_VERSION_MAJOR == 3 && GEOS_VERSION_MINOR >= 10 )
      if ( GEOSPreparedDistanceWithin_r( geosctxt, preparedMultiPartGeom(), lp->multiPartGeom(), minSeparation ) )
      {
        return true;
      }
#else
      QgsMessageLog::logMessage( u"label margin distance requires GEOS 3.10+"_s );
#endif
    }
    catch ( QgsGeosException &e )
    {
      QgsDebugError( u"GEOS exception: %1"_s.arg( e.what() ) );
    }
  }
  else
  {
    try
    {
      const bool result = ( GEOSPreparedIntersects_r( geosctxt, preparedMultiPartGeom(), lp->mMultipartGeos ) == 1 );
      return result;
    }
    catch ( QgsGeosException &e )
    {
      qWarning( "GEOS exception: %s", e.what() );
      QgsMessageLog::logMessage( QObject::tr( "Exception: %1" ).arg( e.what() ), QObject::tr( "GEOS" ) );
      return false;
    }
  }
 
  return false;
}
 
void LabelPosition::createOuterBoundsGeom()
{
  const QRectF outerBounds = getFeaturePart()->feature()->outerBounds();
  if ( outerBounds.isNull() )
    return;
 
  GEOSContextHandle_t geosctxt = QgsGeosContext::get();
 
  const double beta = this->alpha + M_PI_2;
 
  const double dx1 = std::cos( this->alpha ) * outerBounds.width();
  const double dy1 = std::sin( this->alpha ) * outerBounds.width();
 
  const double dx2 = std::cos( beta ) * outerBounds.height();
  const double dy2 = std::sin( beta ) * outerBounds.height();
 
  mOuterBoundsX.resize( 5 );
  mOuterBoundsY.resize( 5 );
 
  const double x1 = x[0] + outerBounds.left();
  const double y1 = y[0] + outerBounds.top();
 
  mOuterBoundsX[0] = x1;
  mOuterBoundsY[0] = y1;
 
  mOuterBoundsX[1] = x1 + dx1;
  mOuterBoundsY[1] = y1 + dy1;
 
  mOuterBoundsX[2] = x1 + dx1 + dx2;
  mOuterBoundsY[2] = y1 + dy1 + dy2;
 
  mOuterBoundsX[3] = x1 + dx2;
  mOuterBoundsY[3] = y1 + dy2;
 
  mOuterBoundsX[4] = mOuterBoundsX[0];
  mOuterBoundsY[4] = mOuterBoundsY[0];
 
  GEOSCoordSequence *coord = nullptr;
#if GEOS_VERSION_MAJOR > 3 || ( GEOS_VERSION_MAJOR == 3 && GEOS_VERSION_MINOR >= 10 )
  // use optimised method if we don't have to force close an open ring
  coord = GEOSCoordSeq_copyFromArrays_r( geosctxt, mOuterBoundsX.data(), mOuterBoundsY.data(), nullptr, nullptr, 5 );
#else
  coord = GEOSCoordSeq_create_r( geosctxt, 5, 2 );
  for ( int i = 0; i < nbPoints; ++i )
  {
    GEOSCoordSeq_setXY_r( geosctxt, coord, i, mOuterBoundsX[i], mOuterBoundsY[i] );
  }
#endif
 
  mOuterBoundsGeos.reset( GEOSGeom_createPolygon_r( geosctxt, GEOSGeom_createLinearRing_r( geosctxt, coord ), nullptr, 0 ) );
 
  mPreparedOuterBoundsGeos = GEOSPrepare_r( QgsGeosContext::get(), mOuterBoundsGeos.get() );
 
  auto xminmax = std::minmax_element( mOuterBoundsX.begin(), mOuterBoundsX.end() );
  mOuterBoundsXMin = *xminmax.first;
  mOuterBoundsXMax = *xminmax.second;
  auto yminmax = std::minmax_element( mOuterBoundsY.begin(), mOuterBoundsY.end() );
  mOuterBoundsYMin = *yminmax.first;
  mOuterBoundsYMax = *yminmax.second;
}
 
int LabelPosition::partCount() const
{
  if ( mNextPart )
    return mNextPart->partCount() + 1;
  else
    return 1;
}
 
int LabelPosition::getId() const
{
  return id;
}
 
double LabelPosition::getX( int i ) const
{
  return ( i >= 0 && i < 4 ? x[i] : -1 );
}
 
double LabelPosition::getY( int i ) const
{
  return ( i >= 0 && i < 4 ? y[i] : -1 );
}
 
double LabelPosition::getAlpha() const
{
  return alpha;
}
 
void LabelPosition::validateCost()
{
  if ( mCost >= 1 )
  {
    mCost -= int( mCost ); // label cost up to 1
  }
}
 
FeaturePart *LabelPosition::getFeaturePart() const
{
  return feature;
}
 
void LabelPosition::getBoundingBox( double amin[2], double amax[2] ) const
{
  // this method considers the label's outer bounds
  if ( mNextPart )
  {
    mNextPart->getBoundingBox( amin, amax );
  }
  else
  {
    amin[0] = std::numeric_limits<double>::max();
    amax[0] = std::numeric_limits<double>::lowest();
    amin[1] = std::numeric_limits<double>::max();
    amax[1] = std::numeric_limits<double>::lowest();
  }
  for ( int c = 0; c < 4; c++ )
  {
    if ( mOuterBoundsGeos )
    {
      if ( mOuterBoundsX[c] < amin[0] )
        amin[0] = mOuterBoundsX[c];
      if ( mOuterBoundsX[c] > amax[0] )
        amax[0] = mOuterBoundsX[c];
      if ( mOuterBoundsY[c] < amin[1] )
        amin[1] = mOuterBoundsY[c];
      if ( mOuterBoundsY[c] > amax[1] )
        amax[1] = mOuterBoundsY[c];
    }
    else
    {
      if ( x[c] < amin[0] )
        amin[0] = x[c];
      if ( x[c] > amax[0] )
        amax[0] = x[c];
      if ( y[c] < amin[1] )
        amin[1] = y[c];
      if ( y[c] > amax[1] )
        amax[1] = y[c];
    }
  }
}
 
QgsRectangle LabelPosition::outerBoundingBox() const
{
  double amin[2];
  double amax[2];
  getBoundingBox( amin, amax );
  return QgsRectangle( amin[0], amin[1], amax[0], amax[1] );
}
 
QgsRectangle LabelPosition::boundingBoxForCandidateConflicts( Pal *pal ) const
{
  if ( !mBoundsForConflictIndex.isNull() )
    return mBoundsForConflictIndex;
 
  QgsRectangle bounds = outerBoundingBox();
  mBoundsForConflictIndex = bounds;
 
  const double labelMarginDistance = feature->feature()->thinningSettings().labelMarginDistance();
  if ( labelMarginDistance > 0 )
  {
    mBoundsForConflictIndex.grow( labelMarginDistance );
  }
 
  const double noRepeatDistance = feature->feature()->thinningSettings().noRepeatDistance();
  if ( noRepeatDistance > 0 )
  {
    const QgsRectangle modifiedBounds = bounds.buffered( noRepeatDistance );
    mBoundsForConflictIndex.combineExtentWith( modifiedBounds );
  }
 
  const QList< QgsAbstractLabelingEngineRule * > rules = pal->rules();
  for ( QgsAbstractLabelingEngineRule *rule : rules )
  {
    const QgsRectangle modifiedBounds = rule->modifyCandidateConflictSearchBoundingBox( bounds );
    mBoundsForConflictIndex.combineExtentWith( modifiedBounds );
  }
  return mBoundsForConflictIndex;
}
 
bool LabelPosition::outerBoundingBoxIntersects( const LabelPosition *other ) const
{
  if ( other->mOuterBoundsGeos )
  {
    const double x1 = ( mOuterBoundsXMin > other->mOuterBoundsXMin ? mOuterBoundsXMin : other->mOuterBoundsXMin );
    const double x2 = ( mOuterBoundsXMax < other->mOuterBoundsXMax ? mOuterBoundsXMax : other->mOuterBoundsXMax );
    if ( x1 > x2 )
      return false;
    const double y1 = ( mOuterBoundsYMin > other->mOuterBoundsYMin ? mOuterBoundsYMin : other->mOuterBoundsYMin );
    const double y2 = ( mOuterBoundsYMax < other->mOuterBoundsYMax ? mOuterBoundsYMax : other->mOuterBoundsYMax );
    return y1 <= y2;
  }
  else
  {
    const double x1 = ( mOuterBoundsXMin > other->xmin ? mOuterBoundsXMin : other->xmin );
    const double x2 = ( mOuterBoundsXMax < other->xmax ? mOuterBoundsXMax : other->xmax );
    if ( x1 > x2 )
      return false;
    const double y1 = ( mOuterBoundsYMin > other->ymin ? mOuterBoundsYMin : other->ymin );
    const double y2 = ( mOuterBoundsYMax < other->ymax ? mOuterBoundsYMax : other->ymax );
    return y1 <= y2;
  }
}
 
void LabelPosition::setConflictsWithObstacle( bool conflicts )
{
  mHasObstacleConflict = conflicts;
  if ( mNextPart )
    mNextPart->setConflictsWithObstacle( conflicts );
}
 
void LabelPosition::setHasHardObstacleConflict( bool conflicts )
{
  mHasHardConflict = conflicts;
  if ( mNextPart )
    mNextPart->setHasHardObstacleConflict( conflicts );
}
 
void LabelPosition::removeFromIndex( PalRtree<LabelPosition> &index, Pal *pal )
{
  index.remove( this, boundingBoxForCandidateConflicts( pal ) );
}
 
void LabelPosition::insertIntoIndex( PalRtree<LabelPosition> &index, Pal *pal )
{
  index.insert( this, boundingBoxForCandidateConflicts( pal ) );
}
 
const GEOSGeometry *LabelPosition::multiPartGeom() const
{
  if ( !mMultipartGeos )
    createMultiPartGeosGeom();
 
  return mMultipartGeos;
}
 
void LabelPosition::createMultiPartGeosGeom() const
{
  GEOSContextHandle_t geosctxt = QgsGeosContext::get();
 
  std::vector< const GEOSGeometry * > geometries;
  const LabelPosition *tmp1 = this;
  while ( tmp1 )
  {
    const GEOSGeometry *partGeos = tmp1->geos();
    if ( !GEOSisEmpty_r( geosctxt, partGeos ) )
      geometries.emplace_back( partGeos );
    tmp1 = tmp1->nextPart();
  }
 
  const std::size_t partCount = geometries.size();
  GEOSGeometry **geomarr = new GEOSGeometry *[partCount];
  for ( std::size_t i = 0; i < partCount; ++i )
  {
    geomarr[i] = GEOSGeom_clone_r( geosctxt, geometries[i] );
  }
 
  mMultipartGeos = GEOSGeom_createCollection_r( geosctxt, GEOS_MULTIPOLYGON, geomarr, partCount );
  delete[] geomarr;
}
 
const GEOSPreparedGeometry *LabelPosition::preparedMultiPartGeom() const
{
  if ( !mMultipartGeos )
    createMultiPartGeosGeom();
 
  if ( !mMultipartPreparedGeos )
  {
    mMultipartPreparedGeos = GEOSPrepare_r( QgsGeosContext::get(), mMultipartGeos );
  }
  return mMultipartPreparedGeos;
}
 
const GEOSPreparedGeometry *LabelPosition::preparedOuterBoundsGeom() const
{
  return mPreparedOuterBoundsGeos;
}
 
double LabelPosition::getDistanceToPoint( double xp, double yp, bool useOuterBounds ) const
{
  // this method may consider the label's outer bounds!
 
  GEOSContextHandle_t geosctxt = QgsGeosContext::get();
 
  //first check if inside, if so then distance is -1
  bool contains = false;
  if ( alpha == 0 )
  {
    // easy case -- horizontal label
    if ( useOuterBounds && mOuterBoundsGeos )
    {
      contains = mOuterBoundsX[0] <= xp && mOuterBoundsX[1] >= xp && mOuterBoundsY[0] <= yp && mOuterBoundsY[2] >= yp;
    }
    else
    {
      contains = x[0] <= xp && x[1] >= xp && y[0] <= yp && y[2] >= yp;
    }
  }
  else
  {
    if ( useOuterBounds && mPreparedOuterBoundsGeos )
    {
      try
      {
        geos::unique_ptr point( GEOSGeom_createPointFromXY_r( geosctxt, xp, yp ) );
        contains = ( GEOSPreparedContainsProperly_r( geosctxt, mPreparedOuterBoundsGeos, point.get() ) == 1 );
      }
      catch ( QgsGeosException & )
      {
        contains = false;
      }
    }
    else
    {
      contains = containsPoint( xp, yp );
    }
  }
 
  double distance = -1;
  if ( !contains )
  {
    if ( alpha == 0 )
    {
      if ( useOuterBounds && mOuterBoundsGeos )
      {
        const double dx = std::max( std::max( mOuterBoundsX[0] - xp, 0.0 ), xp - mOuterBoundsX[1] );
        const double dy = std::max( std::max( mOuterBoundsY[0] - yp, 0.0 ), yp - mOuterBoundsY[2] );
        distance = std::sqrt( dx * dx + dy * dy );
      }
      else
      {
        const double dx = std::max( std::max( x[0] - xp, 0.0 ), xp - x[1] );
        const double dy = std::max( std::max( y[0] - yp, 0.0 ), yp - y[2] );
        distance = std::sqrt( dx * dx + dy * dy );
      }
    }
    else
    {
      if ( useOuterBounds && mPreparedOuterBoundsGeos )
      {
        try
        {
          geos::unique_ptr geosPt( GEOSGeom_createPointFromXY_r( geosctxt, xp, yp ) );
 
          const geos::coord_sequence_unique_ptr nearestCoord( GEOSPreparedNearestPoints_r( geosctxt, mPreparedOuterBoundsGeos, geosPt.get() ) );
          double nx;
          double ny;
          unsigned int nPoints = 0;
          GEOSCoordSeq_getSize_r( geosctxt, nearestCoord.get(), &nPoints );
          if ( nPoints == 0 )
          {
            distance = -1;
          }
          else
          {
            ( void ) GEOSCoordSeq_getXY_r( geosctxt, nearestCoord.get(), 0, &nx, &ny );
            distance = QgsGeometryUtilsBase::sqrDistance2D( xp, yp, nx, ny );
          }
        }
        catch ( QgsGeosException &e )
        {
          qWarning( "GEOS exception: %s", e.what() );
          QgsMessageLog::logMessage( QObject::tr( "Exception: %1" ).arg( e.what() ), QObject::tr( "GEOS" ) );
          distance = -1;
        }
      }
      else
      {
        distance = std::sqrt( minDistanceToPoint( xp, yp ) );
      }
    }
  }
 
  if ( mNextPart && distance > 0 )
    return std::min( distance, mNextPart->getDistanceToPoint( xp, yp, useOuterBounds ) );
 
  return distance;
}
 
bool LabelPosition::crossesLine( PointSet *line ) const
{
  // this method considers the label's outer bounds
  if ( !mOuterBoundsGeos && !mGeos )
    createGeosGeom();
 
  if ( !line->mGeos )
    line->createGeosGeom();
 
  GEOSContextHandle_t geosctxt = QgsGeosContext::get();
  try
  {
    if ( GEOSPreparedIntersects_r( geosctxt, line->preparedGeom(), mOuterBoundsGeos ? mOuterBoundsGeos.get() : mGeos ) == 1 )
    {
      return true;
    }
    else if ( mNextPart )
    {
      return mNextPart->crossesLine( line );
    }
  }
  catch ( QgsGeosException &e )
  {
    qWarning( "GEOS exception: %s", e.what() );
    QgsMessageLog::logMessage( QObject::tr( "Exception: %1" ).arg( e.what() ), QObject::tr( "GEOS" ) );
    return false;
  }
 
  return false;
}
 
bool LabelPosition::crossesBoundary( PointSet *polygon ) const
{
  // this method considers the label's outer bounds
  if ( !mOuterBoundsGeos && !mGeos )
    createGeosGeom();
 
  if ( !polygon->mGeos )
    polygon->createGeosGeom();
 
  GEOSContextHandle_t geosctxt = QgsGeosContext::get();
  try
  {
    if ( GEOSPreparedIntersects_r( geosctxt, polygon->preparedGeom(), mOuterBoundsGeos ? mOuterBoundsGeos.get() : mGeos ) == 1
         && GEOSPreparedContains_r( geosctxt, polygon->preparedGeom(), mOuterBoundsGeos ? mOuterBoundsGeos.get() : mGeos ) != 1 )
    {
      return true;
    }
    else if ( mNextPart )
    {
      return mNextPart->crossesBoundary( polygon );
    }
  }
  catch ( QgsGeosException &e )
  {
    qWarning( "GEOS exception: %s", e.what() );
    QgsMessageLog::logMessage( QObject::tr( "Exception: %1" ).arg( e.what() ), QObject::tr( "GEOS" ) );
    return false;
  }
 
  return false;
}
 
int LabelPosition::polygonIntersectionCost( PointSet *polygon ) const
{
  //effectively take the average polygon intersection cost for all label parts
  const double totalCost = polygonIntersectionCostForParts( polygon );
  const int n = partCount();
  return std::ceil( totalCost / n );
}
 
bool LabelPosition::intersectsWithPolygon( PointSet *polygon ) const
{
  // this method considers the label's outer bounds
  if ( !mOuterBoundsGeos && !mGeos )
    createGeosGeom();
 
  if ( !polygon->mGeos )
    polygon->createGeosGeom();
 
  GEOSContextHandle_t geosctxt = QgsGeosContext::get();
  try
  {
    if ( GEOSPreparedIntersects_r( geosctxt, polygon->preparedGeom(), mOuterBoundsGeos ? mOuterBoundsGeos.get() : mGeos ) == 1 )
    {
      return true;
    }
  }
  catch ( QgsGeosException &e )
  {
    qWarning( "GEOS exception: %s", e.what() );
    QgsMessageLog::logMessage( QObject::tr( "Exception: %1" ).arg( e.what() ), QObject::tr( "GEOS" ) );
  }
 
  if ( mNextPart )
  {
    return mNextPart->intersectsWithPolygon( polygon );
  }
  else
  {
    return false;
  }
}
 
double LabelPosition::polygonIntersectionCostForParts( PointSet *polygon ) const
{
  // this method considers the label's outer bounds
  if ( !mOuterBoundsGeos && !mGeos )
    createGeosGeom();
 
  if ( !polygon->mGeos )
    polygon->createGeosGeom();
 
  GEOSContextHandle_t geosctxt = QgsGeosContext::get();
  double cost = 0;
  try
  {
    if ( GEOSPreparedIntersects_r( geosctxt, polygon->preparedGeom(), mOuterBoundsGeos ? mOuterBoundsGeos.get() : mGeos ) == 1 )
    {
      //at least a partial intersection
      cost += 1;
 
      double px, py;
 
      // check each corner
      for ( int i = 0; i < 4; ++i )
      {
        px = x[i];
        py = y[i];
 
        for ( int a = 0; a < 2; ++a ) // and each middle of segment
        {
          if ( polygon->containsPoint( px, py ) )
            cost++;
          px = ( x[i] + x[( i + 1 ) % 4] ) / 2.0;
          py = ( y[i] + y[( i + 1 ) % 4] ) / 2.0;
        }
      }
 
      px = ( x[0] + x[2] ) / 2.0;
      py = ( y[0] + y[2] ) / 2.0;
 
      //check the label center. if covered by polygon, cost of 4
      if ( polygon->containsPoint( px, py ) )
        cost += 4;
    }
  }
  catch ( QgsGeosException &e )
  {
    qWarning( "GEOS exception: %s", e.what() );
    QgsMessageLog::logMessage( QObject::tr( "Exception: %1" ).arg( e.what() ), QObject::tr( "GEOS" ) );
  }
 
  //maintain scaling from 0 -> 12
  cost = 12.0 * cost / 13.0;
 
  if ( mNextPart )
  {
    cost += mNextPart->polygonIntersectionCostForParts( polygon );
  }
 
  return cost;
}
 
double LabelPosition::angleDifferential()
{
  double angleDiff = 0.0;
  double angleLast = 0.0;
  LabelPosition *tmp = this;
  while ( tmp )
  {
    if ( tmp != this ) // not first?
    {
      double diff = std::fabs( tmp->getAlpha() - angleLast );
      if ( diff > 2 * M_PI )
        diff -= 2 * M_PI;
      diff = std::min( diff, 2 * M_PI - diff ); // difference 350 deg is actually just 10 deg...
      angleDiff += diff;
    }
 
    angleLast = tmp->getAlpha();
    tmp = tmp->nextPart();
  }
  return angleDiff;
}