PowerScaleEngine.cpp

/***************************************************************************
    File                 : PowerScaleEngine.cpp
    Project              : QtiPlot
    --------------------------------------------------------------------
    Copyright            : (C) 2009 by Ion Vasilief
    Email (use @ for *)  : ion_vasilief*yahoo.fr
    Description          : Return a transformation for power (X^n) scales

 ***************************************************************************/

/***************************************************************************
 *                                                                         *
 *  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.                                    *
 *                                                                         *
 *  This program 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 this program; if not, write to the Free Software           *
 *   Foundation, Inc., 51 Franklin Street, Fifth Floor,                    *
 *   Boston, MA  02110-1301  USA                                           *
 *                                                                         *
 ***************************************************************************/

#include "PowerScaleEngine.h"

/*!
  Return a dummy transformation
*/
QwtScaleTransformation *PowerScaleEngine::transformation() const
{
    return new QwtScaleTransformation(QwtScaleTransformation::Other);
}

PowerScaleEngine::~PowerScaleEngine() {}

/*!
    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)
*/
void PowerScaleEngine::autoScale(int maxNumSteps,
    double &x1, double &x2, double &stepSize) const
{
    QwtDoubleInterval interval(x1, x2);
    interval = interval.normalized();

    interval.setMinValue(interval.minValue() - lowerMargin());
    interval.setMaxValue(interval.maxValue() + upperMargin());

    if (testAttribute(QwtScaleEngine::Symmetric))
        interval = interval.symmetrize(reference());

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

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

    stepSize = divideInterval(interval.width(), qwtMax(maxNumSteps, 1));

    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(), QwtScaleEngine::subDivide()
*/
QwtScaleDiv PowerScaleEngine::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 PowerScaleEngine::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
        // explicitly 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 PowerScaleEngine::buildMajorTicks(
    const QwtDoubleInterval &interval, double stepSize) const
{
    int numTicks = qRound(interval.width() / stepSize) + 1;
    if ( numTicks > 10000 )
        numTicks = 10000;

    QwtValueList ticks;

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

    return ticks;
}

void PowerScaleEngine::buildMinorTicks(
    const QwtValueList& majorTicks,
    int maxMinSteps, double stepSize,
    QwtValueList &minorTicks,
    QwtValueList &mediumTicks) const
{
    double minStep = divideInterval(stepSize, maxMinSteps);
    if (minStep == 0.0)
        return;

    // # ticks per interval
    int numTicks = (int)::ceil(qwtAbs(stepSize / minStep)) - 1;

    // Do the minor steps fit into the interval?
    if ( QwtScaleArithmetic::compareEps((numTicks +  1) * qwtAbs(minStep),
        qwtAbs(stepSize), stepSize) > 0)
    {
        numTicks = 1;
        minStep = stepSize * 0.5;
    }

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

    // calculate minor ticks

    for (int i = 0; i < (int)majorTicks.count(); i++)
    {
        double val = majorTicks[i];
        for (int k = 0; k < numTicks; 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 PowerScaleEngine::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);
}

//! Create a clone of the transformation
QwtScaleTransformation *PowerScaleTransformation::copy() const
{
	return new PowerScaleTransformation(d_engine);
}

PowerScaleTransformation::~PowerScaleTransformation() {}

/*
 * Transform a value between 2 linear intervals
 *
 * \param s value related to the interval [s1, s2]
 * \param s1 first border of scale interval
 * \param s2 second border of scale interval
 * \param p1 first border of target interval
 * \param p2 second border of target interval
 */
double PowerScaleTransformation::xForm(
    double s, double s1, double s2, double p1, double p2) const
{
	return p1 + (p2 - p1) / (pow(s2, nth_power) - pow(s1, nth_power)) * (pow(s, nth_power) - pow(s1, nth_power));
}

/*
 * Transform a value from a linear to a power scale interval
 *
 * \param p value related to the linear interval [p1, p2]
 * \param p1 first border of linear interval
 * \param p2 second border of linear interval
 * \param s1 first border of logarithmic interval
 * \param s2 second border of logarithmic interval
 */
double PowerScaleTransformation::invXForm(double p, double p1, double p2,
    double s1, double s2) const
{
	return pow((p - p1) / (p2 - p1) * (pow(s2, nth_power) - pow(s1, nth_power)), 1.0/nth_power) * s1;
}