qgspropertytransformer.cpp

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/***************************************************************************
     qgspropertytransformer.cpp
     --------------------------
    Date                 : January 2017
    Copyright            : (C) 2017 by Nyall Dawson
    Email                : nyall dot dawson at gmail dot com
 ***************************************************************************
 *                                                                         *
 *   This program 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 2 of the License, or     *
 *   (at your option) any later version.                                   *
 *                                                                         *
 ***************************************************************************/

#include "qgspropertytransformer.h"

#include "qgslogger.h"
#include "qgsexpression.h"
#include "qgsexpressionnodeimpl.h"
#include "qgssymbollayerutils.h"
#include "qgscolorramp.h"
#include "qgspointxy.h"


//
// QgsPropertyTransformer
//

QgsPropertyTransformer *QgsPropertyTransformer::create( QgsPropertyTransformer::Type type )
{
  QgsPropertyTransformer *transformer = nullptr;
  switch ( type )
  {
    case GenericNumericTransformer:
      transformer = new QgsGenericNumericTransformer();
      break;
    case SizeScaleTransformer:
      transformer = new QgsSizeScaleTransformer();
      break;
    case ColorRampTransformer:
      transformer = new QgsColorRampTransformer();
      break;
  }
  return transformer;
}

QgsPropertyTransformer::QgsPropertyTransformer( double minValue, double maxValue )
  : mMinValue( minValue )
  , mMaxValue( maxValue )
{}

QgsPropertyTransformer::QgsPropertyTransformer( const QgsPropertyTransformer &other )
  : mMinValue( other.mMinValue )
  , mMaxValue( other.mMaxValue )
  , mCurveTransform( other.mCurveTransform ? new QgsCurveTransform( *other.mCurveTransform ) : nullptr )
{}

QgsPropertyTransformer &QgsPropertyTransformer::operator=( const QgsPropertyTransformer &other )
{
  mMinValue = other.mMinValue;
  mMaxValue = other.mMaxValue;
  mCurveTransform.reset( other.mCurveTransform ? new QgsCurveTransform( *other.mCurveTransform ) : nullptr );
  return *this;
}

bool QgsPropertyTransformer::loadVariant( const QVariant &transformer )
{
  QVariantMap transformerMap = transformer.toMap();

  mMinValue = transformerMap.value( QStringLiteral( "minValue" ), 0.0 ).toDouble();
  mMaxValue = transformerMap.value( QStringLiteral( "maxValue" ), 1.0 ).toDouble();
  mCurveTransform.reset( nullptr );

  QVariantMap curve = transformerMap.value( QStringLiteral( "curve" ) ).toMap();

  if ( !curve.isEmpty() )
  {
    mCurveTransform.reset( new QgsCurveTransform() );
    mCurveTransform->loadVariant( curve );
  }

  return true;
}

QVariant QgsPropertyTransformer::toVariant() const
{
  QVariantMap transformerMap;

  transformerMap.insert( QStringLiteral( "minValue" ), mMinValue );
  transformerMap.insert( QStringLiteral( "maxValue" ), mMaxValue );

  if ( mCurveTransform )
  {
    transformerMap.insert( QStringLiteral( "curve" ), mCurveTransform->toVariant() );
  }
  return transformerMap;
}

QgsPropertyTransformer *QgsPropertyTransformer::fromExpression( const QString &expression, QString &baseExpression, QString &fieldName )
{
  baseExpression.clear();
  fieldName.clear();

  if ( QgsPropertyTransformer *sizeScale = QgsSizeScaleTransformer::fromExpression( expression, baseExpression, fieldName ) )
    return sizeScale;
  else
    return nullptr;
}

double QgsPropertyTransformer::transformNumeric( double input ) const
{
  if ( !mCurveTransform )
    return input;

  if ( qgsDoubleNear( mMaxValue, mMinValue ) )
    return input;

  // convert input into target range
  double scaledInput = ( input - mMinValue ) / ( mMaxValue - mMinValue );

  return mMinValue + ( mMaxValue - mMinValue ) * mCurveTransform->y( scaledInput );
}


//
// QgsGenericNumericTransformer
//

QgsGenericNumericTransformer::QgsGenericNumericTransformer( double minValue, double maxValue, double minOutput, double maxOutput, double nullOutput, double exponent )
  : QgsPropertyTransformer( minValue, maxValue )
  , mMinOutput( minOutput )
  , mMaxOutput( maxOutput )
  , mNullOutput( nullOutput )
  , mExponent( exponent )
{}

QgsGenericNumericTransformer *QgsGenericNumericTransformer::clone() const
{
  std::unique_ptr< QgsGenericNumericTransformer > t( new QgsGenericNumericTransformer( mMinValue,
      mMaxValue,
      mMinOutput,
      mMaxOutput,
      mNullOutput,
      mExponent ) );
  if ( mCurveTransform )
    t->setCurveTransform( new QgsCurveTransform( *mCurveTransform ) );
  return t.release();
}

QVariant QgsGenericNumericTransformer::toVariant() const
{
  QVariantMap transformerMap = QgsPropertyTransformer::toVariant().toMap();

  transformerMap.insert( QStringLiteral( "minOutput" ), mMinOutput );
  transformerMap.insert( QStringLiteral( "maxOutput" ), mMaxOutput );
  transformerMap.insert( QStringLiteral( "nullOutput" ), mNullOutput );
  transformerMap.insert( QStringLiteral( "exponent" ), mExponent );

  return transformerMap;
}

bool QgsGenericNumericTransformer::loadVariant( const QVariant &transformer )
{
  QgsPropertyTransformer::loadVariant( transformer );

  QVariantMap transformerMap = transformer.toMap();

  mMinOutput = transformerMap.value( QStringLiteral( "minOutput" ), 0.0 ).toDouble();
  mMaxOutput = transformerMap.value( QStringLiteral( "maxOutput" ), 1.0 ).toDouble();
  mNullOutput = transformerMap.value( QStringLiteral( "nullOutput" ), 0.0 ).toDouble();
  mExponent = transformerMap.value( QStringLiteral( "exponent" ), 1.0 ).toDouble();
  return true;
}

double QgsGenericNumericTransformer::value( double input ) const
{
  if ( qgsDoubleNear( mMaxValue, mMinValue ) )
    return qBound( mMinOutput, input, mMaxOutput );

  input = transformNumeric( input );
  if ( qgsDoubleNear( mExponent, 1.0 ) )
    return mMinOutput + ( qBound( mMinValue, input, mMaxValue ) - mMinValue ) * ( mMaxOutput - mMinOutput ) / ( mMaxValue - mMinValue );
  else
    return mMinOutput + std::pow( qBound( mMinValue, input, mMaxValue ) - mMinValue, mExponent ) * ( mMaxOutput - mMinOutput ) / std::pow( mMaxValue - mMinValue, mExponent );
}

QVariant QgsGenericNumericTransformer::transform( const QgsExpressionContext &context, const QVariant &v ) const
{
  Q_UNUSED( context )

  if ( v.isNull() )
    return mNullOutput;

  bool ok;
  double dblValue = v.toDouble( &ok );

  if ( ok )
  {
    //apply scaling to value
    return value( dblValue );
  }
  else
  {
    return v;
  }
}

QString QgsGenericNumericTransformer::toExpression( const QString &baseExpression ) const
{
  QString minValueString = QString::number( mMinValue );
  QString maxValueString = QString::number( mMaxValue );
  QString minOutputString = QString::number( mMinOutput );
  QString maxOutputString = QString::number( mMaxOutput );
  QString nullOutputString = QString::number( mNullOutput );
  QString exponentString = QString::number( mExponent );

  if ( qgsDoubleNear( mExponent, 1.0 ) )
    return QStringLiteral( "coalesce(scale_linear(%1, %2, %3, %4, %5), %6)" ).arg( baseExpression, minValueString, maxValueString, minOutputString, maxOutputString, nullOutputString );
  else
    return QStringLiteral( "coalesce(scale_exp(%1, %2, %3, %4, %5, %6), %7)" ).arg( baseExpression, minValueString, maxValueString, minOutputString, maxOutputString, exponentString, nullOutputString );
}

QgsGenericNumericTransformer *QgsGenericNumericTransformer::fromExpression( const QString &expression, QString &baseExpression, QString &fieldName )
{
  bool ok = false;

  double nullValue = 0.0;
  double exponent = 1.0;

  baseExpression.clear();
  fieldName.clear();

  QgsExpression e( expression );

  if ( !e.rootNode() )
    return nullptr;

  const QgsExpressionNodeFunction *f = dynamic_cast<const QgsExpressionNodeFunction *>( e.rootNode() );
  if ( !f )
    return nullptr;

  QList<QgsExpressionNode *> args = f->args()->list();

  // the scale function may be enclosed in a coalesce(expr, 0) to avoid NULL value
  // to be drawn with the default size
  if ( "coalesce" == QgsExpression::Functions()[f->fnIndex()]->name() )
  {
    f = dynamic_cast<const QgsExpressionNodeFunction *>( args[0] );
    if ( !f )
      return nullptr;
    nullValue = QgsExpression( args[1]->dump() ).evaluate().toDouble( &ok );
    if ( ! ok )
      return nullptr;
    args = f->args()->list();
  }

  if ( "scale_linear" == QgsExpression::Functions()[f->fnIndex()]->name() )
  {
    exponent = 1.0;
  }
  else if ( "scale_exp" == QgsExpression::Functions()[f->fnIndex()]->name() )
  {
    exponent = QgsExpression( args[5]->dump() ).evaluate().toDouble( &ok );
  }
  else
  {
    return nullptr;
  }

  bool expOk = true;
  double minValue = QgsExpression( args[1]->dump() ).evaluate().toDouble( &ok );
  expOk &= ok;
  double maxValue = QgsExpression( args[2]->dump() ).evaluate().toDouble( &ok );
  expOk &= ok;
  double minOutput = QgsExpression( args[3]->dump() ).evaluate().toDouble( &ok );
  expOk &= ok;
  double maxOutput = QgsExpression( args[4]->dump() ).evaluate().toDouble( &ok );
  expOk &= ok;

  if ( !expOk )
  {
    return nullptr;
  }

  if ( args[0]->nodeType() == QgsExpressionNode::ntColumnRef )
  {
    fieldName = static_cast< QgsExpressionNodeColumnRef * >( args[0] )->name();
  }
  else
  {
    baseExpression = args[0]->dump();
  }
  return new QgsGenericNumericTransformer( minValue, maxValue, minOutput, maxOutput, nullValue, exponent );
}



//
// QgsSizeScaleProperty
//
QgsSizeScaleTransformer::QgsSizeScaleTransformer( ScaleType type, double minValue, double maxValue, double minSize, double maxSize, double nullSize, double exponent )
  : QgsPropertyTransformer( minValue, maxValue )
  , mMinSize( minSize )
  , mMaxSize( maxSize )
  , mNullSize( nullSize )
  , mExponent( exponent )
{
  setType( type );
}

QgsSizeScaleTransformer *QgsSizeScaleTransformer::clone() const
{
  std::unique_ptr< QgsSizeScaleTransformer > t( new QgsSizeScaleTransformer( mType,
      mMinValue,
      mMaxValue,
      mMinSize,
      mMaxSize,
      mNullSize,
      mExponent ) );
  if ( mCurveTransform )
    t->setCurveTransform( new QgsCurveTransform( *mCurveTransform ) );
  return t.release();
}

QVariant QgsSizeScaleTransformer::toVariant() const
{
  QVariantMap transformerMap = QgsPropertyTransformer::toVariant().toMap();

  transformerMap.insert( QStringLiteral( "scaleType" ), static_cast< int >( mType ) );
  transformerMap.insert( QStringLiteral( "minSize" ), mMinSize );
  transformerMap.insert( QStringLiteral( "maxSize" ), mMaxSize );
  transformerMap.insert( QStringLiteral( "nullSize" ), mNullSize );
  transformerMap.insert( QStringLiteral( "exponent" ), mExponent );

  return transformerMap;
}

bool QgsSizeScaleTransformer::loadVariant( const QVariant &transformer )
{
  QgsPropertyTransformer::loadVariant( transformer );

  QVariantMap transformerMap = transformer.toMap();

  mType = static_cast< ScaleType >( transformerMap.value( QStringLiteral( "scaleType" ), Linear ).toInt() );
  mMinSize = transformerMap.value( QStringLiteral( "minSize" ), 0.0 ).toDouble();
  mMaxSize = transformerMap.value( QStringLiteral( "maxSize" ), 1.0 ).toDouble();
  mNullSize = transformerMap.value( QStringLiteral( "nullSize" ), 0.0 ).toDouble();
  mExponent = transformerMap.value( QStringLiteral( "exponent" ), 1.0 ).toDouble();

  return true;
}

double QgsSizeScaleTransformer::size( double value ) const
{
  value = transformNumeric( value );

  switch ( mType )
  {
    case Linear:
      return mMinSize + ( qBound( mMinValue, value, mMaxValue ) - mMinValue ) * ( mMaxSize - mMinSize ) / ( mMaxValue - mMinValue );

    case Area:
    case Flannery:
    case Exponential:
      return mMinSize + std::pow( qBound( mMinValue, value, mMaxValue ) - mMinValue, mExponent ) * ( mMaxSize - mMinSize ) / std::pow( mMaxValue - mMinValue, mExponent );

  }
  return 0;
}

void QgsSizeScaleTransformer::setType( QgsSizeScaleTransformer::ScaleType type )
{
  mType = type;
  switch ( mType )
  {
    case Linear:
      mExponent = 1.0;
      break;
    case Area:
      mExponent = 0.5;
      break;
    case Flannery:
      mExponent = 0.57;
      break;
    case Exponential:
      //no change
      break;
  }
}

QVariant QgsSizeScaleTransformer::transform( const QgsExpressionContext &context, const QVariant &value ) const
{
  Q_UNUSED( context )

  if ( value.isNull() )
    return mNullSize;

  bool ok;
  double dblValue = value.toDouble( &ok );

  if ( ok )
  {
    //apply scaling to value
    return size( dblValue );
  }
  else
  {
    return value;
  }
}

QString QgsSizeScaleTransformer::toExpression( const QString &baseExpression ) const
{
  QString minValueString = QString::number( mMinValue );
  QString maxValueString = QString::number( mMaxValue );
  QString minSizeString = QString::number( mMinSize );
  QString maxSizeString = QString::number( mMaxSize );
  QString nullSizeString = QString::number( mNullSize );
  QString exponentString = QString::number( mExponent );

  switch ( mType )
  {
    case Linear:
      return QStringLiteral( "coalesce(scale_linear(%1, %2, %3, %4, %5), %6)" ).arg( baseExpression, minValueString, maxValueString, minSizeString, maxSizeString, nullSizeString );

    case Area:
    case Flannery:
    case Exponential:
      return QStringLiteral( "coalesce(scale_exp(%1, %2, %3, %4, %5, %6), %7)" ).arg( baseExpression, minValueString, maxValueString, minSizeString, maxSizeString, exponentString, nullSizeString );

  }
  return QString();
}

QgsSizeScaleTransformer *QgsSizeScaleTransformer::fromExpression( const QString &expression, QString &baseExpression, QString &fieldName )
{
  bool ok = false;

  ScaleType type = Linear;
  double nullSize = 0.0;
  double exponent = 1.0;

  baseExpression.clear();
  fieldName.clear();

  QgsExpression e( expression );

  if ( !e.rootNode() )
    return nullptr;

  const QgsExpressionNodeFunction *f = dynamic_cast<const QgsExpressionNodeFunction *>( e.rootNode() );
  if ( !f )
    return nullptr;

  QList<QgsExpressionNode *> args = f->args()->list();

  // the scale function may be enclosed in a coalesce(expr, 0) to avoid NULL value
  // to be drawn with the default size
  if ( "coalesce" == QgsExpression::Functions()[f->fnIndex()]->name() )
  {
    f = dynamic_cast<const QgsExpressionNodeFunction *>( args[0] );
    if ( !f )
      return nullptr;
    nullSize = QgsExpression( args[1]->dump() ).evaluate().toDouble( &ok );
    if ( ! ok )
      return nullptr;
    args = f->args()->list();
  }

  if ( "scale_linear" == QgsExpression::Functions()[f->fnIndex()]->name() )
  {
    type = Linear;
  }
  else if ( "scale_exp" == QgsExpression::Functions()[f->fnIndex()]->name() )
  {
    exponent = QgsExpression( args[5]->dump() ).evaluate().toDouble( &ok );
    if ( ! ok )
      return nullptr;
    if ( qgsDoubleNear( exponent, 0.57, 0.001 ) )
      type = Flannery;
    else if ( qgsDoubleNear( exponent, 0.5, 0.001 ) )
      type = Area;
    else
      type = Exponential;
  }
  else
  {
    return nullptr;
  }

  bool expOk = true;
  double minValue = QgsExpression( args[1]->dump() ).evaluate().toDouble( &ok );
  expOk &= ok;
  double maxValue = QgsExpression( args[2]->dump() ).evaluate().toDouble( &ok );
  expOk &= ok;
  double minSize = QgsExpression( args[3]->dump() ).evaluate().toDouble( &ok );
  expOk &= ok;
  double maxSize = QgsExpression( args[4]->dump() ).evaluate().toDouble( &ok );
  expOk &= ok;

  if ( !expOk )
  {
    return nullptr;
  }

  if ( args[0]->nodeType() == QgsExpressionNode::ntColumnRef )
  {
    fieldName = static_cast< QgsExpressionNodeColumnRef * >( args[0] )->name();
  }
  else
  {
    baseExpression = args[0]->dump();
  }
  return new QgsSizeScaleTransformer( type, minValue, maxValue, minSize, maxSize, nullSize, exponent );
}


//
// QgsColorRampTransformer
//

QgsColorRampTransformer::QgsColorRampTransformer( double minValue, double maxValue,
    QgsColorRamp *ramp,
    const QColor &nullColor )
  : QgsPropertyTransformer( minValue, maxValue )
  , mGradientRamp( ramp )
  , mNullColor( nullColor )
{

}

QgsColorRampTransformer::QgsColorRampTransformer( const QgsColorRampTransformer &other )
  : QgsPropertyTransformer( other )
  , mGradientRamp( other.mGradientRamp ? other.mGradientRamp->clone() : nullptr )
  , mNullColor( other.mNullColor )
  , mRampName( other.mRampName )
{

}

QgsColorRampTransformer &QgsColorRampTransformer::operator=( const QgsColorRampTransformer &other )
{
  QgsPropertyTransformer::operator=( other );
  mMinValue = other.mMinValue;
  mMaxValue = other.mMaxValue;
  mGradientRamp.reset( other.mGradientRamp ? other.mGradientRamp->clone() : nullptr );
  mNullColor = other.mNullColor;
  mRampName = other.mRampName;
  return *this;
}

QgsColorRampTransformer *QgsColorRampTransformer::clone() const
{
  std::unique_ptr< QgsColorRampTransformer > c( new QgsColorRampTransformer( mMinValue, mMaxValue,
      mGradientRamp ? mGradientRamp->clone() : nullptr,
      mNullColor ) );
  c->setRampName( mRampName );
  if ( mCurveTransform )
    c->setCurveTransform( new QgsCurveTransform( *mCurveTransform ) );
  return c.release();
}

QVariant QgsColorRampTransformer::toVariant() const
{
  QVariantMap transformerMap = QgsPropertyTransformer::toVariant().toMap();

  if ( mGradientRamp )
  {
    transformerMap.insert( QStringLiteral( "colorramp" ), QgsSymbolLayerUtils::colorRampToVariant( QStringLiteral( "[source]" ), mGradientRamp.get() ) );
  }
  transformerMap.insert( QStringLiteral( "nullColor" ), QgsSymbolLayerUtils::encodeColor( mNullColor ) );
  transformerMap.insert( QStringLiteral( "rampName" ), mRampName );

  return transformerMap;
}

bool QgsColorRampTransformer::loadVariant( const QVariant &definition )
{
  QVariantMap transformerMap = definition.toMap();

  QgsPropertyTransformer::loadVariant( definition );

  mGradientRamp.reset( nullptr );
  if ( transformerMap.contains( QStringLiteral( "colorramp" ) ) )
  {
    setColorRamp( QgsSymbolLayerUtils::loadColorRamp( transformerMap.value( QStringLiteral( "colorramp" ) ).toMap() ) );
  }

  mNullColor = QgsSymbolLayerUtils::decodeColor( transformerMap.value( QStringLiteral( "nullColor" ), QStringLiteral( "0,0,0,0" ) ).toString() );
  mRampName = transformerMap.value( QStringLiteral( "rampName" ) ).toString();
  return true;
}

QVariant QgsColorRampTransformer::transform( const QgsExpressionContext &context, const QVariant &value ) const
{
  Q_UNUSED( context )

  if ( value.isNull() )
    return mNullColor;

  bool ok;
  double dblValue = value.toDouble( &ok );

  if ( ok )
  {
    //apply scaling to value
    return color( dblValue );
  }
  else
  {
    return value;
  }
}

QString QgsColorRampTransformer::toExpression( const QString &baseExpression ) const
{
  if ( !mGradientRamp )
    return QgsExpression::quotedValue( mNullColor.name() );

  QString minValueString = QString::number( mMinValue );
  QString maxValueString = QString::number( mMaxValue );
  QString nullColorString = mNullColor.name();

  return QStringLiteral( "coalesce(ramp_color('%1',scale_linear(%2, %3, %4, 0, 1)), '%5')" ).arg( !mRampName.isEmpty() ? mRampName : QStringLiteral( "custom ramp" ),
         baseExpression, minValueString, maxValueString, nullColorString );
}

QColor QgsColorRampTransformer::color( double value ) const
{
  value = transformNumeric( value );
  double scaledVal = qBound( 0.0, ( value - mMinValue ) / ( mMaxValue - mMinValue ), 1.0 );

  if ( !mGradientRamp )
    return mNullColor;

  return mGradientRamp->color( scaledVal );
}

QgsColorRamp *QgsColorRampTransformer::colorRamp() const
{
  return mGradientRamp.get();
}

void QgsColorRampTransformer::setColorRamp( QgsColorRamp *ramp )
{
  mGradientRamp.reset( ramp );
}


//
// QgsCurveTransform
//

bool sortByX( const QgsPointXY &a, const QgsPointXY &b )
{
  return a.x() < b.x();
}

QgsCurveTransform::QgsCurveTransform()
{
  mControlPoints << QgsPointXY( 0, 0 ) << QgsPointXY( 1, 1 );
  calcSecondDerivativeArray();
}

QgsCurveTransform::QgsCurveTransform( const QList<QgsPointXY> &controlPoints )
  : mControlPoints( controlPoints )
{
  std::sort( mControlPoints.begin(), mControlPoints.end(), sortByX );
  calcSecondDerivativeArray();
}

QgsCurveTransform::~QgsCurveTransform()
{
  delete [] mSecondDerivativeArray;
}

QgsCurveTransform::QgsCurveTransform( const QgsCurveTransform &other )
  : mControlPoints( other.mControlPoints )
{
  if ( other.mSecondDerivativeArray )
  {
    mSecondDerivativeArray = new double[ mControlPoints.count()];
    memcpy( mSecondDerivativeArray, other.mSecondDerivativeArray, sizeof( double ) * mControlPoints.count() );
  }
}

QgsCurveTransform &QgsCurveTransform::operator=( const QgsCurveTransform &other )
{
  mControlPoints = other.mControlPoints;
  if ( other.mSecondDerivativeArray )
  {
    delete [] mSecondDerivativeArray;
    mSecondDerivativeArray = new double[ mControlPoints.count()];
    memcpy( mSecondDerivativeArray, other.mSecondDerivativeArray, sizeof( double ) * mControlPoints.count() );
  }
  return *this;
}

void QgsCurveTransform::setControlPoints( const QList<QgsPointXY> &points )
{
  mControlPoints = points;
  std::sort( mControlPoints.begin(), mControlPoints.end(), sortByX );
  for ( int i = 0; i < mControlPoints.count(); ++i )
  {
    mControlPoints[ i ] = QgsPointXY( qBound( 0.0, mControlPoints.at( i ).x(), 1.0 ),
                                      qBound( 0.0, mControlPoints.at( i ).y(), 1.0 ) );
  }
  calcSecondDerivativeArray();
}

void QgsCurveTransform::addControlPoint( double x, double y )
{
  QgsPointXY point( x, y );
  if ( mControlPoints.contains( point ) )
    return;

  mControlPoints << point;
  std::sort( mControlPoints.begin(), mControlPoints.end(), sortByX );
  calcSecondDerivativeArray();
}

void QgsCurveTransform::removeControlPoint( double x, double y )
{
  for ( int i = 0; i < mControlPoints.count(); ++i )
  {
    if ( qgsDoubleNear( mControlPoints.at( i ).x(), x )
         && qgsDoubleNear( mControlPoints.at( i ).y(), y ) )
    {
      mControlPoints.removeAt( i );
      break;
    }
  }
  calcSecondDerivativeArray();
}

// this code is adapted from https://github.com/OpenFibers/Photoshop-Curves
// which in turn was adapted from
// http://www.developpez.net/forums/d331608-3/autres-langages/algorithmes/contribuez/image-interpolation-spline-cubique/#post3513925  //#spellok

double QgsCurveTransform::y( double x ) const
{
  int n = mControlPoints.count();
  if ( n < 2 )
    return qBound( 0.0, x, 1.0 ); // invalid
  else if ( n < 3 )
  {
    // linear
    if ( x <= mControlPoints.at( 0 ).x() )
      return qBound( 0.0, mControlPoints.at( 0 ).y(), 1.0 );
    else if ( x >= mControlPoints.at( n - 1 ).x() )
      return qBound( 0.0, mControlPoints.at( 1 ).y(), 1.0 );
    else
    {
      double dx = mControlPoints.at( 1 ).x() - mControlPoints.at( 0 ).x();
      double dy = mControlPoints.at( 1 ).y() - mControlPoints.at( 0 ).y();
      return qBound( 0.0, ( x - mControlPoints.at( 0 ).x() ) * ( dy / dx ) + mControlPoints.at( 0 ).y(), 1.0 );
    }
  }

  // safety check
  if ( x <= mControlPoints.at( 0 ).x() )
    return qBound( 0.0, mControlPoints.at( 0 ).y(), 1.0 );
  if ( x >= mControlPoints.at( n - 1 ).x() )
    return qBound( 0.0, mControlPoints.at( n - 1 ).y(), 1.0 );

  // find corresponding segment
  QList<QgsPointXY>::const_iterator pointIt = mControlPoints.constBegin();
  QgsPointXY currentControlPoint = *pointIt;
  ++pointIt;
  QgsPointXY nextControlPoint = *pointIt;

  for ( int i = 0; i < n - 1; ++i )
  {
    if ( x < nextControlPoint.x() )
    {
      // found segment
      double h = nextControlPoint.x() - currentControlPoint.x();
      double t = ( x - currentControlPoint.x() ) / h;

      double a = 1 - t;

      return qBound( 0.0, a * currentControlPoint.y() + t * nextControlPoint.y() + ( h * h / 6 ) * ( ( a * a * a - a ) * mSecondDerivativeArray[i] + ( t * t * t - t ) * mSecondDerivativeArray[i + 1] ),
                     1.0 );
    }

    ++pointIt;
    if ( pointIt == mControlPoints.constEnd() )
      break;

    currentControlPoint = nextControlPoint;
    nextControlPoint = *pointIt;
  }

  //should not happen
  return qBound( 0.0, x, 1.0 );
}

// this code is adapted from https://github.com/OpenFibers/Photoshop-Curves
// which in turn was adapted from
// http://www.developpez.net/forums/d331608-3/autres-langages/algorithmes/contribuez/image-interpolation-spline-cubique/#post3513925  //#spellok

QVector<double> QgsCurveTransform::y( const QVector<double> &x ) const
{
  QVector<double> result;

  int n = mControlPoints.count();
  if ( n < 3 )
  {
    // invalid control points - use simple transform
    const auto constX = x;
    for ( double i : constX )
      result << y( i );

    return result;
  }

  // find corresponding segment
  QList<QgsPointXY>::const_iterator pointIt = mControlPoints.constBegin();
  QgsPointXY currentControlPoint = *pointIt;
  ++pointIt;
  QgsPointXY nextControlPoint = *pointIt;

  int xIndex = 0;
  double currentX = x.at( xIndex );
  // safety check
  while ( currentX <= currentControlPoint.x() )
  {
    result << qBound( 0.0, currentControlPoint.y(), 1.0 );
    xIndex++;
    currentX = x.at( xIndex );
  }

  for ( int i = 0; i < n - 1; ++i )
  {
    while ( currentX < nextControlPoint.x() )
    {
      // found segment
      double h = nextControlPoint.x() - currentControlPoint.x();

      double t = ( currentX - currentControlPoint.x() ) / h;

      double a = 1 - t;

      result << qBound( 0.0, a * currentControlPoint.y() + t * nextControlPoint.y() + ( h * h / 6 ) * ( ( a * a * a - a )*mSecondDerivativeArray[i] + ( t * t * t - t )*mSecondDerivativeArray[i + 1] ), 1.0 );
      xIndex++;
      if ( xIndex == x.count() )
        return result;

      currentX = x.at( xIndex );
    }

    ++pointIt;
    if ( pointIt == mControlPoints.constEnd() )
      break;

    currentControlPoint = nextControlPoint;
    nextControlPoint = *pointIt;
  }

  // safety check
  while ( xIndex < x.count() )
  {
    result << qBound( 0.0, nextControlPoint.y(), 1.0 );
    xIndex++;
  }

  return result;
}

bool QgsCurveTransform::readXml( const QDomElement &elem, const QDomDocument & )
{
  QString xString = elem.attribute( QStringLiteral( "x" ) );
  QString yString = elem.attribute( QStringLiteral( "y" ) );

  QStringList xVals = xString.split( ',' );
  QStringList yVals = yString.split( ',' );
  if ( xVals.count() != yVals.count() )
    return false;

  QList< QgsPointXY > newPoints;
  bool ok = false;
  for ( int i = 0; i < xVals.count(); ++i )
  {
    double x = xVals.at( i ).toDouble( &ok );
    if ( !ok )
      return false;
    double y = yVals.at( i ).toDouble( &ok );
    if ( !ok )
      return false;
    newPoints << QgsPointXY( x, y );
  }
  setControlPoints( newPoints );
  return true;
}

bool QgsCurveTransform::writeXml( QDomElement &transformElem, QDomDocument & ) const
{
  QStringList x;
  QStringList y;
  const auto constMControlPoints = mControlPoints;
  for ( const QgsPointXY &p : constMControlPoints )
  {
    x << qgsDoubleToString( p.x() );
    y << qgsDoubleToString( p.y() );
  }

  transformElem.setAttribute( QStringLiteral( "x" ), x.join( ',' ) );
  transformElem.setAttribute( QStringLiteral( "y" ), y.join( ',' ) );

  return true;
}

QVariant QgsCurveTransform::toVariant() const
{
  QVariantMap transformMap;

  QStringList x;
  QStringList y;
  const auto constMControlPoints = mControlPoints;
  for ( const QgsPointXY &p : constMControlPoints )
  {
    x << qgsDoubleToString( p.x() );
    y << qgsDoubleToString( p.y() );
  }

  transformMap.insert( QStringLiteral( "x" ), x.join( ',' ) );
  transformMap.insert( QStringLiteral( "y" ), y.join( ',' ) );

  return transformMap;
}

bool QgsCurveTransform::loadVariant( const QVariant &transformer )
{
  QVariantMap transformMap = transformer.toMap();

  QString xString = transformMap.value( QStringLiteral( "x" ) ).toString();
  QString yString = transformMap.value( QStringLiteral( "y" ) ).toString();

  QStringList xVals = xString.split( ',' );
  QStringList yVals = yString.split( ',' );
  if ( xVals.count() != yVals.count() )
    return false;

  QList< QgsPointXY > newPoints;
  bool ok = false;
  for ( int i = 0; i < xVals.count(); ++i )
  {
    double x = xVals.at( i ).toDouble( &ok );
    if ( !ok )
      return false;
    double y = yVals.at( i ).toDouble( &ok );
    if ( !ok )
      return false;
    newPoints << QgsPointXY( x, y );
  }
  setControlPoints( newPoints );
  return true;
}

// this code is adapted from https://github.com/OpenFibers/Photoshop-Curves
// which in turn was adapted from
// http://www.developpez.net/forums/d331608-3/autres-langages/algorithmes/contribuez/image-interpolation-spline-cubique/#post3513925  //#spellok

void QgsCurveTransform::calcSecondDerivativeArray()
{
  int n = mControlPoints.count();
  if ( n < 3 )
    return; // cannot proceed

  delete[] mSecondDerivativeArray;

  double *matrix = new double[ n * 3 ];
  double *result = new double[ n ];
  matrix[0] = 0;
  matrix[1] = 1;
  matrix[2] = 0;
  result[0] = 0;
  QList<QgsPointXY>::const_iterator pointIt = mControlPoints.constBegin();
  QgsPointXY pointIm1 = *pointIt;
  ++pointIt;
  QgsPointXY pointI = *pointIt;
  ++pointIt;
  QgsPointXY pointIp1 = *pointIt;

  for ( int i = 1; i < n - 1; ++i )
  {
    matrix[i * 3 + 0 ] = ( pointI.x() - pointIm1.x() ) / 6.0;
    matrix[i * 3 + 1 ] = ( pointIp1.x() - pointIm1.x() ) / 3.0;
    matrix[i * 3 + 2 ] = ( pointIp1.x() - pointI.x() ) / 6.0;
    result[i] = ( pointIp1.y() - pointI.y() ) / ( pointIp1.x() - pointI.x() ) - ( pointI.y() - pointIm1.y() ) / ( pointI.x() - pointIm1.x() );

    // shuffle points
    pointIm1 = pointI;
    pointI = pointIp1;
    ++pointIt;
    if ( pointIt == mControlPoints.constEnd() )
      break;

    pointIp1 = *pointIt;
  }
  matrix[( n - 1 ) * 3 + 0] = 0;
  matrix[( n - 1 ) * 3 + 1] = 1;
  matrix[( n - 1 ) * 3 + 2] = 0;
  result[n - 1] = 0;

  // solving pass1 (up->down)
  for ( int i = 1; i < n; ++i )
  {
    double k = matrix[i * 3 + 0] / matrix[( i - 1 ) * 3 + 1];
    matrix[i * 3 + 1] -= k * matrix[( i - 1 ) * 3 + 2];
    matrix[i * 3 + 0] = 0;
    result[i] -= k * result[i - 1];
  }
  // solving pass2 (down->up)
  for ( int i = n - 2; i >= 0; --i )
  {
    double k = matrix[i * 3 + 2] / matrix[( i + 1 ) * 3 + 1];
    matrix[i * 3 + 1] -= k * matrix[( i + 1 ) * 3 + 0];
    matrix[i * 3 + 2] = 0;
    result[i] -= k * result[i + 1];
  }

  // return second derivative value for each point
  mSecondDerivativeArray = new double[n];
  for ( int i = 0; i < n; ++i )
  {
    mSecondDerivativeArray[i] = result[i] / matrix[( i * 3 ) + 1];
  }

  delete[] result;
  delete[] matrix;
}