qwt_scale_engine.cpp

QWT5.01用于Qt开发的二维图形库程序

   \param x1 First interval limit 
   \param x2 Second interval limit 
   \param maxMajSteps Maximum for the number of major steps
   \param maxMinSteps Maximum number of minor steps
   \param stepSize Step size. If stepSize == 0, the scaleEngine
                   calculates one.

   \sa QwtScaleEngine::stepSize, QwtScaleEngine::subDivide
*/
QwtScaleDiv QwtLinearScaleEngine::divideScale(double x1, double x2,
    int maxMajSteps, int maxMinSteps, double stepSize) const
{
    QwtDoubleInterval interval = QwtDoubleInterval(x1, x2).normalized();
    if (interval.width() <= 0 )
        return QwtScaleDiv();

    stepSize = qwtAbs(stepSize);
    if ( stepSize == 0.0 )
    {
        if ( maxMajSteps < 1 )
            maxMajSteps = 1;

        stepSize = divideInterval(interval.width(), maxMajSteps);
    }

    QwtScaleDiv scaleDiv;

    if ( stepSize != 0.0 )
    {
        QwtValueList ticks[QwtScaleDiv::NTickTypes];
        buildTicks(interval, stepSize, maxMinSteps, ticks);

        scaleDiv = QwtScaleDiv(interval, ticks);
    }

    if ( x1 > x2 )
        scaleDiv.invert();

    return scaleDiv;
}

void QwtLinearScaleEngine::buildTicks(
    const QwtDoubleInterval& interval, double stepSize, int maxMinSteps,
    QwtValueList ticks[QwtScaleDiv::NTickTypes]) const
{
    const QwtDoubleInterval boundingInterval =
        align(interval, stepSize);
    
    ticks[QwtScaleDiv::MajorTick] = 
        buildMajorTicks(boundingInterval, stepSize);

    if ( maxMinSteps > 0 )
    {
        buildMinorTicks(ticks[QwtScaleDiv::MajorTick], maxMinSteps, stepSize,
            ticks[QwtScaleDiv::MinorTick], ticks[QwtScaleDiv::MediumTick]);
    }
    
    for ( int i = 0; i < QwtScaleDiv::NTickTypes; i++ )
    {
        ticks[i] = strip(ticks[i], interval);

        // ticks very close to 0.0 are 
        // explicitely set to 0.0

        for ( int j = 0; j < (int)ticks[i].count(); j++ )
        {
            if ( QwtScaleArithmetic::compareEps(ticks[i][j], 0.0, stepSize) == 0 )
                ticks[i][j] = 0.0;
        }
    }
}

QwtValueList QwtLinearScaleEngine::buildMajorTicks(
    const QwtDoubleInterval &interval, double stepSize) const
{
    int numTicks = qRound(interval.width() / stepSize) + 1;
#if 1
    if ( numTicks > 10000 )
        numTicks = 10000;
#endif

    QwtValueList ticks;

    ticks += interval.minValue();
    for (int i = 1; i < numTicks - 1; i++)
        ticks += interval.minValue() + i * stepSize;
    ticks += interval.maxValue();

    return ticks;
}

void QwtLinearScaleEngine::buildMinorTicks(
    const QwtValueList& majorTicks,
    int maxMinSteps, double stepSize,
    QwtValueList &minorTicks, 
    QwtValueList &mediumTicks) const
{   
    double minStep = divideInterval(stepSize, maxMinSteps);
    if (minStep == 0.0)  
        return; 
        
    // # minor steps per interval
    int nMin = qwtAbs(qRound(stepSize / minStep)) - 1;
    
    // Do the minor steps fit into the interval?
    if ( QwtScaleArithmetic::compareEps((nMin +  1) * qwtAbs(minStep), 
        qwtAbs(stepSize), stepSize) > 0)
    {   
        nMin = 1;
        minStep = stepSize * 0.5;
    }

    int medIndex = -1;
    if ( nMin % 2 )
        medIndex = nMin / 2;

    // calculate minor ticks

    for (int i = 0; i < (int)majorTicks.count(); i++)
    {
        double val = majorTicks[i];
        for (int k=0; k< nMin; k++)
        {
            val += minStep;

            double alignedValue = val;
            if (QwtScaleArithmetic::compareEps(val, 0.0, stepSize) == 0) 
                alignedValue = 0.0;

            if ( k == medIndex )
                mediumTicks += alignedValue;
            else
                minorTicks += alignedValue;
        }
    }
}

/*!
  \brief Align an interval to a step size

  The limits of an interval are aligned that both are integer
  multiples of the step size.

  \param interval Interval
  \param stepSize Step size

  \return Aligned interval
*/
QwtDoubleInterval QwtLinearScaleEngine::align(
    const QwtDoubleInterval &interval, double stepSize) const
{
    const double x1 = 
        QwtScaleArithmetic::floorEps(interval.minValue(), stepSize);
    const double x2 = 
        QwtScaleArithmetic::ceilEps(interval.maxValue(), stepSize);

    return QwtDoubleInterval(x1, x2);
}

/*!
  Return a transformation, for logarithmic (base 10) scales
*/
QwtScaleTransformation *QwtLog10ScaleEngine::transformation() const
{
    return new QwtScaleTransformation(QwtScaleTransformation::Log10);
}

/*!
    Align and divide an interval

   \param maxNumSteps Max. number of steps
   \param x1 First limit of the interval (In/Out)
   \param x2 Second limit of the interval (In/Out)
   \param stepSize Step size (Out)

   \sa QwtScaleEngine::setAttribute
*/
void QwtLog10ScaleEngine::autoScale(int maxNumSteps, 
    double &x1, double &x2, double &stepSize) const
{
    if ( x1 > x2 )
        qSwap(x1, x2);

    QwtDoubleInterval interval(x1 / pow(10.0, loMargin()), 
        x2 * pow(10.0, hiMargin()) );

    double logRef = 1.0;
    if (reference() > LOG_MIN / 2)
        logRef = qwtMin(reference(), LOG_MAX / 2);

    if (testAttribute(QwtScaleEngine::Symmetric))
    {
        const double delta = qwtMax(interval.maxValue() / logRef,  
            logRef / interval.minValue());
        interval.setInterval(logRef / delta, logRef * delta);
    }

    if (testAttribute(QwtScaleEngine::IncludeReference))
        interval = interval.extend(logRef);

    interval = interval.limited(LOG_MIN, LOG_MAX);

    if (interval.width() == 0.0)
        interval = buildInterval(interval.minValue());

    stepSize = divideInterval(log10(interval).width(), qwtMax(maxNumSteps, 1));
    if ( stepSize < 1.0 )
        stepSize = 1.0;

    if (!testAttribute(QwtScaleEngine::Floating))
        interval = align(interval, stepSize);

    x1 = interval.minValue();
    x2 = interval.maxValue();

    if (testAttribute(QwtScaleEngine::Inverted))
    {
        qSwap(x1, x2);
        stepSize = -stepSize;
    }
}

/*!
   \brief Calculate a scale division

   \param x1 First interval limit 
   \param x2 Second interval limit 
   \param maxMajSteps Maximum for the number of major steps
   \param maxMinSteps Maximum number of minor steps
   \param stepSize Step size. If stepSize == 0, the scaleEngine
                   calculates one.

   \sa QwtScaleEngine::stepSize, QwtLog10ScaleEngine::subDivide
*/
QwtScaleDiv QwtLog10ScaleEngine::divideScale(double x1, double x2,
    int maxMajSteps, int maxMinSteps, double stepSize) const
{
    QwtDoubleInterval interval = QwtDoubleInterval(x1, x2).normalized();
    interval = interval.limited(LOG_MIN, LOG_MAX);

    if (interval.width() <= 0 )
        return QwtScaleDiv();

    if (interval.maxValue() / interval.minValue() < 10.0)
    {
        // scale width is less than one decade -> build linear scale
    
        QwtLinearScaleEngine linearScaler;
        linearScaler.setAttributes(attributes());
        linearScaler.setReference(reference());
        linearScaler.setMargins(loMargin(), hiMargin());

        return linearScaler.divideScale(x1, x2, 
            maxMajSteps, maxMinSteps, stepSize);
    }

    stepSize = qwtAbs(stepSize);
    if ( stepSize == 0.0 )
    {
        if ( maxMajSteps < 1 )
            maxMajSteps = 1;

        stepSize = divideInterval(log10(interval).width(), maxMajSteps);
        if ( stepSize < 1.0 )
            stepSize = 1.0; // major step must be >= 1 decade
    }

    QwtScaleDiv scaleDiv;
    if ( stepSize != 0.0 )
    {
        QwtValueList ticks[QwtScaleDiv::NTickTypes];
        buildTicks(interval, stepSize, maxMinSteps, ticks);

        scaleDiv = QwtScaleDiv(interval, ticks);
    }

    if ( x1 > x2 )
        scaleDiv.invert();

    return scaleDiv;
}

void QwtLog10ScaleEngine::buildTicks(
    const QwtDoubleInterval& interval, double stepSize, int maxMinSteps,
    QwtValueList ticks[QwtScaleDiv::NTickTypes]) const
{
    const QwtDoubleInterval boundingInterval =
        align(interval, stepSize);
    
    ticks[QwtScaleDiv::MajorTick] = 
        buildMajorTicks(boundingInterval, stepSize);

    if ( maxMinSteps > 0 )
    {
        ticks[QwtScaleDiv::MinorTick] = buildMinorTicks(
            ticks[QwtScaleDiv::MajorTick], maxMinSteps, stepSize);
    }
    
    for ( int i = 0; i < QwtScaleDiv::NTickTypes; i++ )
        ticks[i] = strip(ticks[i], interval);
}

QwtValueList QwtLog10ScaleEngine::buildMajorTicks(
    const QwtDoubleInterval &interval, double stepSize) const
{
    double width = log10(interval).width();

    int numTicks = qRound(width / stepSize) + 1;
    if ( numTicks > 10000 )
        numTicks = 10000;

    const double lxmin = log(interval.minValue());
    const double lxmax = log(interval.maxValue());
    const double lstep = (lxmax - lxmin) / double(numTicks - 1);

    QwtValueList ticks;

    ticks += interval.minValue();

    for (int i = 1; i < numTicks; i++)
       ticks += exp(lxmin + double(i) * lstep);

    ticks += interval.maxValue();

    return ticks;
}

QwtValueList QwtLog10ScaleEngine::buildMinorTicks(
    const QwtValueList &majorTicks, 
    int maxMinSteps, double stepSize) const
{   
    if (stepSize < 1.1)            // major step width is one decade
    {
        if ( maxMinSteps < 1 )
            return QwtValueList();
            
        int k0, kstep, kmax;
        
        if (maxMinSteps >= 8)
        {
            k0 = 2;
            kmax = 9;
            kstep = 1;
        }   
        else if (maxMinSteps >= 4)
        {
            k0 = 2;
            kmax = 8;
            kstep = 2;
        }   
        else if (maxMinSteps >= 2)
        {
            k0 = 2;
            kmax = 5;
            kstep = 3;
        }
        else
        {
            k0 = 5;
            kmax = 5;
            kstep = 1;
        }

        QwtValueList minorTicks;

        for (int i = 0; i < (int)majorTicks.count(); i++)
        {
            const double v = majorTicks[i];
            for (int k = k0; k<= kmax; k+=kstep)
                minorTicks += v * double(k);
        }

        return minorTicks;
    }
    else  // major step > one decade
    {
        double minStep = divideInterval(stepSize, maxMinSteps);
        if ( minStep == 0.0 )
            return QwtValueList();

        if ( minStep < 1.0 )
            minStep = 1.0;

        // # subticks per interval
        int nMin = qRound(stepSize / minStep) - 1;

        // Do the minor steps fit into the interval?

        if ( QwtScaleArithmetic::compareEps((nMin +  1) * minStep, 
            qwtAbs(stepSize), stepSize) > 0)
        {
            nMin = 0;
        }

        if (nMin < 1)
            return QwtValueList();      // no subticks

        // substep factor = 10^substeps
        const double minFactor = qwtMax(pow(10.0, minStep), 10.0);

        QwtValueList minorTicks;
        for (int i = 0; i < (int)majorTicks.count(); i++)
        {
            double val = majorTicks[i];
            for (int k=0; k< nMin; k++)
            {
                val *= minFactor;
                minorTicks += val;
            }
        }
        return minorTicks;
    }
}

/*!
  \brief Align an interval to a step size

  The limits of an interval are aligned that both are integer
  multiples of the step size.

  \param interval Interval
  \param stepSize Step size

  \return Aligned interval
*/
QwtDoubleInterval QwtLog10ScaleEngine::align(
    const QwtDoubleInterval &interval, double stepSize) const
{
    const QwtDoubleInterval intv = log10(interval);

    const double x1 = QwtScaleArithmetic::floorEps(intv.minValue(), stepSize);
    const double x2 = QwtScaleArithmetic::ceilEps(intv.maxValue(), stepSize);

    return pow10(QwtDoubleInterval(x1, x2));
}

/*!
  Return the interval [log10(interval.minValue(), log10(interval.maxValue]
*/

QwtDoubleInterval QwtLog10ScaleEngine::log10(
    const QwtDoubleInterval &interval) const
{
    return QwtDoubleInterval(::log10(interval.minValue()),
            ::log10(interval.maxValue()));
}

/*!
  Return the interval [pow10(interval.minValue(), pow10(interval.maxValue]
*/
QwtDoubleInterval QwtLog10ScaleEngine::pow10(
    const QwtDoubleInterval &interval) const
{
    return QwtDoubleInterval(pow(10.0, interval.minValue()),
            pow(10.0, interval.maxValue()));
}