QskGraduation.cpp

/******************************************************************************
 * QSkinny - Copyright (C) The authors
 *           SPDX-License-Identifier: BSD-3-Clause
 *****************************************************************************/
 
#include "QskGraduation.h"
#include "QskFunctions.h"
#include "QskIntervalF.h"
#include "QskTickmarks.h"
 
#include <QDebug>
#include <QtMath>
 
#include <cmath>
 
namespace
{
    /*
        Code has been copied from the Qwt project ( with permission of the
        copyright holder ( = me ). Maybe the code could be adjusted using Qskinny
        fuzzy operators
     */
 
    class Engine
    {
      public:
        static QskTickmarks buildTicks( const QskIntervalF&, qreal, int );
        static QVector< qreal > buildMajorTicks( const QskIntervalF&, qreal );
        static void buildMinorTicks( const QVector< qreal >&, int, qreal,
            QVector< qreal >&, QVector< qreal >& );
 
      private:
        static bool fuzzyContains( const QskIntervalF&, double );
        static int fuzzyCompare( double, double, double );
        static double minorStepSize( double, int );
 
        static QVector< qreal > strip( const QVector< qreal >&, const QskIntervalF& );
    };
 
    inline int Engine::fuzzyCompare( double value1, double value2, double intervalSize )
    {
        const double eps = std::abs( 1.0e-6 * intervalSize );
 
        if ( value2 - value1 > eps )
            return -1;
 
        if ( value1 - value2 > eps )
            return 1;
 
        return 0;
    }
 
    inline bool Engine::fuzzyContains( const QskIntervalF& interval, double value )
    {
        if ( !interval.isValid() )
            return false;
 
        if ( fuzzyCompare( value, interval.lowerBound(), interval.length() ) < 0 )
            return false;
 
        if ( fuzzyCompare( value, interval.upperBound(), interval.length() ) > 0 )
            return false;
 
        return true;
    }
 
    double Engine::minorStepSize( double intervalSize, int maxSteps )
    {
        const double minStep = QskGraduation::stepSize( intervalSize, maxSteps );
 
        if ( minStep != 0.0 )
        {
            // # ticks per interval
            const int numTicks = qCeil( qAbs( intervalSize / minStep ) ) - 1;
 
            // Do the minor steps fit into the interval?
            if ( fuzzyCompare( ( numTicks + 1 ) * qAbs( minStep ),
                qAbs( intervalSize ), intervalSize ) > 0 )
            {
                // The minor steps doesn't fit into the interval
                return 0.5 * intervalSize;
            }
        }
 
        return minStep;
    }
 
    QVector< qreal > Engine::strip(
        const QVector< qreal >& ticks, const QskIntervalF& interval )
    {
        if ( !interval.isValid() || ticks.count() == 0 )
            return QVector< qreal >();
 
        if ( fuzzyContains( interval, ticks.first() )
            && fuzzyContains( interval, ticks.last() ) )
        {
            return ticks;
        }
 
        QVector< qreal > strippedTicks;
        strippedTicks.reserve( ticks.count() );
 
        for ( const auto tick : ticks )
        {
            if ( fuzzyContains( interval, tick ) )
                strippedTicks += tick;
        }
 
        return strippedTicks;
    }
 
    QVector< qreal > Engine::buildMajorTicks(
        const QskIntervalF& interval, qreal stepSize )
    {
        int numTicks = qRound( interval.length() / stepSize ) + 1;
        if ( numTicks > 10000 )
            numTicks = 10000;
 
        QVector< qreal > ticks;
        ticks.reserve( numTicks );
 
        ticks += interval.lowerBound();
        for ( int i = 1; i < numTicks - 1; i++ )
            ticks += interval.lowerBound() + i * stepSize;
        ticks += interval.upperBound();
 
        return ticks;
    }
 
    void Engine::buildMinorTicks(
        const QVector< qreal >& majorTicks, int maxMinorSteps, qreal stepSize,
        QVector< qreal >& minorTicks, QVector< qreal >& mediumTicks )
    {
        auto minStep = minorStepSize( stepSize, maxMinorSteps );
        if ( minStep == 0.0 )
            return;
 
        // # ticks per interval
        const int numTicks = qCeil( qAbs( stepSize / minStep ) ) - 1;
 
        int medIndex = -1;
        if ( numTicks % 2 )
            medIndex = numTicks / 2;
 
        // calculate minor ticks
 
        for ( int i = 0; i < majorTicks.count(); i++ )
        {
            auto val = majorTicks[i];
            for ( int k = 0; k < numTicks; k++ )
            {
                val += minStep;
 
                double alignedValue = val;
                if ( fuzzyCompare( val, 0.0, stepSize ) == 0 )
                    alignedValue = 0.0;
 
                if ( k == medIndex )
                    mediumTicks += alignedValue;
                else
                    minorTicks += alignedValue;
            }
        }
    }
 
    QskTickmarks Engine::buildTicks( const QskIntervalF& interval,
        qreal stepSize, int maxMinorSteps )
    {
        using T = QskTickmarks;
 
        const auto boundingInterval = interval.fuzzyAligned( stepSize );
 
        QVector< qreal > ticks[3];
        ticks[T::MajorTick] = buildMajorTicks( boundingInterval, stepSize );
 
        if ( maxMinorSteps > 0 )
        {
            buildMinorTicks( ticks[T::MajorTick], maxMinorSteps, stepSize,
                ticks[T::MinorTick], ticks[T::MediumTick] );
        }
 
        for ( auto& t : ticks )
        {
            t = strip( t, interval );
 
            // ticks very close to 0.0 are
            // explicitely set to 0.0
 
            for ( int i = 0; i < t.count(); i++ )
            {
                if ( fuzzyCompare( t[i], 0.0, stepSize ) == 0 )
                    t[i] = 0.0;
            }
        }
 
        return { ticks[T::MinorTick], ticks[T::MediumTick], ticks[T::MajorTick] };
    }
}
 
QskTickmarks QskGraduation::divideInterval(
    qreal x1, qreal x2, int maxMajorSteps, int maxMinorSteps, qreal stepSize )
{
    QskTickmarks tickmarks;
 
    const auto interval = QskIntervalF::normalized( x1, x2 );
 
    if ( interval.length() > std::numeric_limits< qreal >::max() )
    {
        qWarning() << "QskGraduation::divideInterval: overflow";
        return tickmarks;
    }
 
    if ( interval.length() <= 0.0 || stepSize < 0.0 )
        return tickmarks;
 
    if ( stepSize == 0.0 )
    {
        if ( maxMajorSteps < 1 )
            maxMajorSteps = 1;
 
        stepSize = QskGraduation::stepSize( interval.length(), maxMajorSteps );
    }
 
    if ( stepSize != 0.0 )
        tickmarks = Engine::buildTicks( interval, stepSize, maxMinorSteps );
 
    return tickmarks;
}
 
qreal QskGraduation::stepSize( double length, int numSteps )
{
    if ( numSteps <= 0 )
        return 0.0;
 
    const auto v = length / numSteps;
    if ( qFuzzyIsNull( v ) )
        return 0.0;
 
    constexpr double base = 10.0;
 
    // the same as std::log10( std::fabs( v ) );
    const double lx = std::log( std::fabs( v ) ) / std::log( base );
    const double p = std::floor( lx );
 
    const double fraction = std::pow( base, lx - p );
 
    double stepSize = std::pow( base, p );
    if ( v < 0 )
        stepSize = -stepSize;
 
    for ( const double f : { 2.0, 2.5, 5.0, 10.0 } )
    {
        if ( fraction <= f || qFuzzyCompare( fraction, f ) )
        {
            stepSize *= f;
            break;
        }
    }
 
    return stepSize;
}