qwt_scale_engine.cpp

/* -*- mode: C++ ; c-file-style: "stroustrup" -*- *****************************
 * Qwt Widget Library
 * Copyright (C) 1997   Josef Wilgen
 * Copyright (C) 2002   Uwe Rathmann
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the Qwt License, Version 1.0
 *****************************************************************************/

#include "qwt_scale_engine.h"
#include "qwt_math.h"
#include "qwt_scale_map.h"
#include <qalgorithms.h>
#include <qmath.h>
#include <float.h>

#if QT_VERSION < 0x040601
#define qFabs(x) ::fabs(x)
#define qExp(x) ::exp(x)
#endif

static inline double qwtLog( double base, double value )
{
    return log( value ) / log( base );
}

static inline QwtInterval qwtLogInterval( double base, const QwtInterval &interval )
{
    return QwtInterval( qwtLog( base, interval.minValue() ),
            qwtLog( base, interval.maxValue() ) );
}

static inline QwtInterval qwtPowInterval( double base, const QwtInterval &interval ) 
{
    return QwtInterval( qPow( base, interval.minValue() ),
            qPow( base, interval.maxValue() ) );
}


#if 1

// this version often doesn't find the best ticks: f.e for 15: 5, 10
static double qwtStepSize( double intervalSize, int maxSteps, uint base )
{
    const double minStep = 
        QwtScaleArithmetic::divideInterval( intervalSize, maxSteps, base );

    if ( minStep != 0.0 )
    {
        // # ticks per interval
        const int numTicks = qCeil( qAbs( intervalSize / minStep ) ) - 1;

        // Do the minor steps fit into the interval?
        if ( qwtFuzzyCompare( ( numTicks +  1 ) * qAbs( minStep ),
            qAbs( intervalSize ), intervalSize ) > 0 )
        {
            // The minor steps doesn't fit into the interval
            return 0.5 * intervalSize;
        }
    }

    return minStep;
}

#else

static double qwtStepSize( double intervalSize, int maxSteps, uint base )
{
    if ( maxSteps <= 0 )
        return 0.0;

    if ( maxSteps > 2 )
    {
        for ( int numSteps = maxSteps; numSteps > 1; numSteps-- )
        {
            const double stepSize = intervalSize / numSteps;

            const double p = ::floor( ::log( stepSize ) / ::log( base ) );
            const double fraction = qPow( base, p );

            for ( uint n = base; n > 1; n /= 2 )
            {
                if ( qFuzzyCompare( stepSize, n * fraction ) )
                    return stepSize;

                if ( n == 3 && ( base % 2 ) == 0 )
                {
                    if ( qFuzzyCompare( stepSize, 2 * fraction ) )
                        return stepSize;
                }
            }
        }
    }

    return intervalSize * 0.5;
}

#endif

static const double _eps = 1.0e-6;

/*!
  Ceil a value, relative to an interval

  \param value Value to be ceiled
  \param intervalSize Interval size

  \return Rounded value

  \sa floorEps()
*/
double QwtScaleArithmetic::ceilEps( double value,
    double intervalSize )
{
    const double eps = _eps * intervalSize;

    value = ( value - eps ) / intervalSize;
    return ::ceil( value ) * intervalSize;
}

/*!
  Floor a value, relative to an interval

  \param value Value to be floored
  \param intervalSize Interval size

  \return Rounded value
  \sa floorEps()
*/
double QwtScaleArithmetic::floorEps( double value, double intervalSize )
{
    const double eps = _eps * intervalSize;

    value = ( value + eps ) / intervalSize;
    return ::floor( value ) * intervalSize;
}

/*!
  \brief Divide an interval into steps

  \f$stepSize = (intervalSize - intervalSize * 10e^{-6}) / numSteps\f$

  \param intervalSize Interval size
  \param numSteps Number of steps
  \return Step size
*/
double QwtScaleArithmetic::divideEps( double intervalSize, double numSteps )
{
    if ( numSteps == 0.0 || intervalSize == 0.0 )
        return 0.0;

    return ( intervalSize - ( _eps * intervalSize ) ) / numSteps;
}

/*!
  Calculate a step size for a given interval

  \param intervalSize Interval size
  \param numSteps Number of steps
  \param base Base for the division ( usually 10 )

  \return Calculated step size
 */
double QwtScaleArithmetic::divideInterval( 
    double intervalSize, int numSteps, uint base ) 
{
    if ( numSteps <= 0 )
        return 0.0;

    const double v = QwtScaleArithmetic::divideEps( intervalSize, numSteps );
    if ( v == 0.0 )
        return 0.0;

    const double lx = qwtLog( base, qFabs( v ) );
    const double p = ::floor( lx );

    const double fraction = qPow( base, lx - p );

    uint n = base;
    while ( ( n > 1 ) && ( fraction <= n / 2 ) )
        n /= 2;

    double stepSize = n * qPow( base, p );
    if ( v < 0 )
        stepSize = -stepSize;

    return stepSize;
}

class QwtScaleEngine::PrivateData
{
public:
    PrivateData():
        attributes( QwtScaleEngine::NoAttribute ),
        lowerMargin( 0.0 ),
        upperMargin( 0.0 ),
        referenceValue( 0.0 ),
        base( 10 ),
        transform( NULL )
    {