pldtik.c

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//      Determine tick spacing and mode (fixed or floating) of
//      numeric axis labels.
//
// Copyright (C) 2004-2014 Alan W. Irwin
//
// This file is part of PLplot.
//
// PLplot is free software; you can redistribute it and/or modify
// it under the terms of the GNU Library General Public License as published
// by the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// PLplot 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 Library General Public License for more details.
//
// You should have received a copy of the GNU Library General Public License
// along with PLplot; if not, write to the Free Software
// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
//

#include "plplotP.h"

//--------------------------------------------------------------------------
// void pldtik()
//
// Determine tick spacing: works out a "nice" interval (if tick == 0) such
// that there are between 3 and 7.5 major tick intervals in the input
// range vmin to vmax.  The recommended number of subticks is returned in
// "nsubt" unless the routine is entered with a non-zero value of "nsubt".
// n.b. big change: now returns only positive values of tick and nsubt
//--------------------------------------------------------------------------

void
pldtik( PLFLT vmin, PLFLT vmax, PLFLT *tick, PLINT *nsubt, PLBOOL ld )
{
    PLFLT t1, t2, tick_reasonable;
    PLINT np, ns;
    // Unnecessarily set factor to quiet -O3 -Wuninitialized warnings.
    PLFLT factor = 0.0;


    if ( ld )
    {
        // Check suitable units for tick spacing
        pldtfac( vmin, vmax, &factor, NULL );

        *tick = *tick / factor;
        vmin  = vmin / factor;
        vmax  = vmax / factor;
    }

// Magnitude of min/max difference to get tick spacing

    t1 = (PLFLT) log10( ABS( vmax - vmin ) );
    np = (PLINT) floor( t1 );
    t1 = t1 - np;

// Get tick spacing.

    if ( t1 > 0.7781512503 )
    {
        t2 = 2.0;
        ns = 4;
    }
    else if ( t1 > 0.4771212549 )
    {
        t2 = 1.0;
        ns = 5;
    }
    else if ( t1 > 0.1760912591 )
    {
        t2 = 5.0;
        ns = 5;
        np = np - 1;
    }
    else
    {
        t2 = 2.0;
        ns = 4;
        np = np - 1;
    }

// Now compute reasonable tick spacing

    tick_reasonable = t2 * pow( 10.0, (double) np );
    if ( *tick == 0 )
    {
        *tick = t2 * pow( 10.0, (double) np );
    }
    else
    {
        *tick = ABS( *tick );
        if ( *tick < 1.e-4 * tick_reasonable )
        {
            plexit( "pldtik: magnitude of specified tick spacing is much too small" );
            return;
        }
    }
    if ( *nsubt == 0 )
        *nsubt = ns;

    *nsubt = ABS( *nsubt );

    if ( ld )
    {
        *tick = *tick * factor;
    }
}

//--------------------------------------------------------------------------
// PLFLT pldtfac()
//
// Calculate factor to convert a date/time interval in seconds
// into a more natural units (minutes, hours, days, week, years).
// Also optionally calculate the sensible start time for counting ticks
// from (e.g. beginning of day, beginning of year).
// Used to calculate sensible tick and label spacings.
//--------------------------------------------------------------------------
void
pldtfac( PLFLT vmin, PLFLT vmax, PLFLT *factor, PLFLT *start )
{
    PLFLT diff;
    PLINT year, month, day, hour, min;
    PLFLT sec;

    diff = vmax - vmin;

    if ( start != NULL )
    {
        plbtime( &year, &month, &day, &hour, &min, &sec, vmin );
    }

    if ( diff < 3.0 * 60.0 )
    {
        // Seconds
        *factor = 1.0;
        if ( start != NULL )
        {
            sec = 0.;
            plctime( year, month, day, hour, min, sec, start );
        }
    }
    else if ( diff < 3.0 * 60.0 * 60.0 )
    {
        // Minutes
        *factor = 60.0;
        if ( start != NULL )
        {
            sec = 0.;
            min = 0;
            plctime( year, month, day, hour, min, sec, start );
        }
    }
    else if ( diff < 3.0 * 60.0 * 60.0 * 24.0 )
    {
        // Hours
        *factor = 60.0 * 60.0;
        if ( start != NULL )
        {
            sec  = 0.;
            min  = 0;
            hour = 0;
            plctime( year, month, day, hour, min, sec, start );
        }
    }
    else if ( diff < 3.0 * 60.0 * 60.0 * 24.0 * 7.0 )
    {
        // Days
        *factor = 60.0 * 60.0 * 24.0;
        if ( start != NULL )
        {
            sec  = 0.;
            min  = 0;
            hour = 0;
            plctime( year, month, day, hour, min, sec, start );
        }
    }
    else if ( diff < 3.0 * 60.0 * 60.0 * 24.0 * 365 )
    {
        // Weeks
        *factor = 60.0 * 60.0 * 24.0 * 7.0;
        if ( start != NULL )
        {
            sec  = 0.;
            min  = 0;
            hour = 0;
            plctime( year, month, day, hour, min, sec, start );
        }
    }
    else
    {
        // Years
        *factor = 60.0 * 60.0 * 24.0 * 365.25;
        if ( start != NULL )
        {
            sec   = 0.;
            min   = 0;
            hour  = 0;
            day   = 0;
            month = 0;
            plctime( year, month, day, hour, min, sec, start );
        }
    }
}

//--------------------------------------------------------------------------
// void pldprec()
//
// Determine precision: the output variable "mode" is set to 0 if labels
// are to be written in floating-point format, or to 1 if they are to be
// written in scientific format.  For mode = 1, the exponent will be
// placed at:
//
//      top left        for vertical axis on left
//      top right       for vertical axis on right
//      bottom right    for horizontal axis
//
// The digmax flag can be set by the user, and represents the maximum
// number of digits a label may occupy including sign and decimal point.
// digmin, calculated internally, is the maximum number of digits
// labels at vmin and vmax would occupy if floating point.
// If digmax<0, it is disregarded,
// and if digmax=0 the default value is used.  For digmax>0, mode=1 is
// chosen if there is insufficient room for the label within the specified
// # of digits (digmin > digfix, where digfix is determined from digmax with
// fuzz factors).
//
// In the case of mode=0, the actual # of digits will become too large
// when the magnitude of the labels become too large.  The mode=1 case
// offers the greatest precision for the smallest field length.
//
// The determination of maximum length for fixed point quantities is
// complicated by the fact that very long fixed point representations look
// much worse than the same sized floating point representation.  Further,
// a fixed point number with a large negative exponent will actually gain
// in precision when written as floating point.  Thus we use certain fuzz
// factors to get 'digfix' from 'digmax', however it will always be true
// that digfix<=digmax.
//
// Finally, if 'digmax' is set, 'prec' is reduced in size if necessary so
// that the labels fit the requested field length, where prec is the number of
// places after the decimal place.
//--------------------------------------------------------------------------

#define MIN_FLTDIG    3         // disregarded if fractional part is 0
#define DIGMAX_DEF    5

void
pldprec( PLFLT vmin, PLFLT vmax, PLFLT tick, PLINT lf,
         PLINT *mode, PLINT *prec, PLINT digmax, PLINT *scale )
{
    PLFLT chosen, notchosen, vmod, t0;
    PLINT msd, notmsd, np, digmin, digfix;

    *mode  = 0;
    *scale = 0;

    // Default xdigmax, ydigmax and zdigmax set in c_plinit so this is
    // only an emergency measure in case of some internal PLplot
    // logic error.
    if ( digmax == 0 )
        digmax = DIGMAX_DEF;
    // No modification of digfix from digmax value.
    digfix = digmax;
// Choose vmin or vmax depending on magnitudes of vmin and vmax.
    chosen    = ( ABS( vmax ) >= ABS( vmin ) ) ? vmax : vmin;
    notchosen = ( ABS( vmax ) >= ABS( vmin ) ) ? vmin : vmax;
// Magnitute of chosen to get number of significant digits

    if ( ABS( chosen ) > 0. )
    {
        vmod = ABS( chosen );
        t0   = (PLFLT) log10( vmod );
        msd  = (PLINT) floor( t0 );
    }
    else
    {
        // this branch occurs only when 0. --- 0. range put in
        vmod = 1.;
        t0   = (PLFLT) log10( vmod );
        msd  = (PLINT) floor( t0 );
    }

    if ( ABS( notchosen ) > 0. )
        notmsd = (PLINT) floor( (PLFLT) log10( ABS( notchosen ) ) );
    else
        notmsd = msd;
    // Autoselect the mode flag
    // 'digmin' is the minimum number of places taken up by the label

    if ( msd >= 0 )
    {
        // n.b. no decimal point in the minimal case
        digmin = msd + 1;
    }
    else
    {
        // adjust digmin to account for leading 0 and decimal point
        digmin = -msd + 2;
    }
// adjust digmin to account for sign on the chosen end of axis or sign on the
// nonchosen end of axis if notmsd = msd or (msd <= 0 and notmsd < 0)
// For the latter case the notchosen label starts with "-0."
// For checking for the latter case, the notmsd < 0 condition is redundant
// since notmsd <= msd always and the equal part is selected by the first
// condition.
//
    if ( chosen < 0. || ( notchosen < 0. && ( notmsd == msd || msd <= 0 ) ) )
        digmin = digmin + 1;

    if ( digmin > digfix && !lf )
    {
        *mode  = 1;
        *scale = msd;
    }

// Establish precision.
// It must be fine enough to resolve the tick spacing

    np = (PLINT) floor( log10( ABS( tick ) ) );

    if ( *mode != 0 )
        *prec = msd - np;
    else
        *prec = MAX( -np, 0 );

// One last hack required: if exponent < 0, i.e. number has leading '0.',
// it's better to change to floating point form if the number of digits
// is insufficient to represent the tick spacing.
//
    if ( *mode == 0 && digmax > 0 && !lf )
    {
        if ( t0 < 0.0 )
        {
            if ( digmax - 2 - *prec < 0 )
            {
                *mode  = 1;
                *scale = msd;
            }
        }
        else
            *prec = MAX( MIN( *prec, digmax - msd - 1 ), 0 );
    }
    if ( *mode != 0 )
    {
        *prec = msd - np;
        *prec = MAX( MIN( *prec, MAX( digmax - 1, MIN_FLTDIG ) ), 0 );
    }
}