qwt_curve_fitter.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_curve_fitter.h"
#include "qwt_math.h"
#include "qwt_spline.h"
#include <qstack.h>
#include <qvector.h>

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

//! Constructor
QwtCurveFitter::QwtCurveFitter()
{
}

//! Destructor
QwtCurveFitter::~QwtCurveFitter()
{
}

class QwtSplineCurveFitter::PrivateData
{
public:
    PrivateData():
        fitMode( QwtSplineCurveFitter::Auto ),
        splineSize( 250 )
    {
    }

    QwtSpline spline;
    QwtSplineCurveFitter::FitMode fitMode;
    int splineSize;
};

//! Constructor
QwtSplineCurveFitter::QwtSplineCurveFitter()
{
    d_data = new PrivateData;
}

//! Destructor
QwtSplineCurveFitter::~QwtSplineCurveFitter()
{
    delete d_data;
}

/*!
  Select the algorithm used for building the spline

  \param mode Mode representing a spline algorithm
  \sa fitMode()
*/
void QwtSplineCurveFitter::setFitMode( FitMode mode )
{
    d_data->fitMode = mode;
}

/*!
  \return Mode representing a spline algorithm
  \sa setFitMode()
*/
QwtSplineCurveFitter::FitMode QwtSplineCurveFitter::fitMode() const
{
    return d_data->fitMode;
}

/*!
  Assign a spline

  \param spline Spline
  \sa spline()
*/
void QwtSplineCurveFitter::setSpline( const QwtSpline &spline )
{
    d_data->spline = spline;
    d_data->spline.reset();
}

/*!
  \return Spline
  \sa setSpline()
*/
const QwtSpline &QwtSplineCurveFitter::spline() const
{
    return d_data->spline;
}

/*!
  \return Spline
  \sa setSpline()
*/
QwtSpline &QwtSplineCurveFitter::spline()
{
    return d_data->spline;
}

/*!
   Assign a spline size ( has to be at least 10 points )

   \param splineSize Spline size
   \sa splineSize()
*/
void QwtSplineCurveFitter::setSplineSize( int splineSize )
{
    d_data->splineSize = qMax( splineSize, 10 );
}

/*!
  \return Spline size
  \sa setSplineSize()
*/
int QwtSplineCurveFitter::splineSize() const
{
    return d_data->splineSize;
}

/*!
  Find a curve which has the best fit to a series of data points

  \param points Series of data points
  \return Curve points
*/
QPolygonF QwtSplineCurveFitter::fitCurve( const QPolygonF &points ) const
{
    const int size = points.size();
    if ( size <= 2 )
        return points;

    FitMode fitMode = d_data->fitMode;
    if ( fitMode == Auto )
    {
        fitMode = Spline;

        const QPointF *p = points.data();
        for ( int i = 1; i < size; i++ )
        {
            if ( p[i].x() <= p[i-1].x() )
            {
                fitMode = ParametricSpline;
                break;
            }
        };
    }

    if ( fitMode == ParametricSpline )
        return fitParametric( points );
    else
        return fitSpline( points );
}

QPolygonF QwtSplineCurveFitter::fitSpline( const QPolygonF &points ) const
{
    d_data->spline.setPoints( points );
    if ( !d_data->spline.isValid() )
        return points;

    QPolygonF fittedPoints( d_data->splineSize );

    const double x1 = points[0].x();
    const double x2 = points[int( points.size() - 1 )].x();
    const double dx = x2 - x1;
    const double delta = dx / ( d_data->splineSize - 1 );

    for ( int i = 0; i < d_data->splineSize; i++ )
    {
        QPointF &p = fittedPoints[i];

        const double v = x1 + i * delta;
        const double sv = d_data->spline.value( v );

        p.setX( v );
        p.setY( sv );
    }
    d_data->spline.reset();

    return fittedPoints;
}

QPolygonF QwtSplineCurveFitter::fitParametric( const QPolygonF &points ) const
{
    int i;
    const int size = points.size();

    QPolygonF fittedPoints( d_data->splineSize );
    QPolygonF splinePointsX( size );
    QPolygonF splinePointsY( size );

    const QPointF *p = points.data();
    QPointF *spX = splinePointsX.data();
    QPointF *spY = splinePointsY.data();

    double param = 0.0;
    for ( i = 0; i < size; i++ )
    {
        const double x = p[i].x();
        const double y = p[i].y();
        if ( i > 0 )
        {
            const double delta = qSqrt( qwtSqr( x - spX[i-1].y() )
                      + qwtSqr( y - spY[i-1].y() ) );
            param += qMax( delta, 1.0 );
        }
        spX[i].setX( param );
        spX[i].setY( x );
        spY[i].setX( param );
        spY[i].setY( y );
    }

    d_data->spline.setPoints( splinePointsX );
    if ( !d_data->spline.isValid() )
        return points;

    const double deltaX =
        splinePointsX[size - 1].x() / ( d_data->splineSize - 1 );
    for ( i = 0; i < d_data->splineSize; i++ )
    {
        const double dtmp = i * deltaX;
        fittedPoints[i].setX( d_data->spline.value( dtmp ) );
    }

    d_data->spline.setPoints( splinePointsY );
    if ( !d_data->spline.isValid() )
        return points;

    const double deltaY =
        splinePointsY[size - 1].x() / ( d_data->splineSize - 1 );
    for ( i = 0; i < d_data->splineSize; i++ )
    {
        const double dtmp = i * deltaY;
        fittedPoints[i].setY( d_data->spline.value( dtmp ) );
    }

    return fittedPoints;
}

class QwtWeedingCurveFitter::PrivateData
{
public:
    PrivateData():
        tolerance( 1.0 ),
        chunkSize( 0 )
    {
    }

    double tolerance;
    uint chunkSize;
};

class QwtWeedingCurveFitter::Line
{
public:
    Line( int i1 = 0, int i2 = 0 ):
        from( i1 ),
        to( i2 )
    {
    }

    int from;
    int to;
};

/*!
   Constructor

   \param tolerance Tolerance
   \sa setTolerance(), tolerance()
*/
QwtWeedingCurveFitter::QwtWeedingCurveFitter( double tolerance )
{
    d_data = new PrivateData;
    setTolerance( tolerance );
}

//! Destructor
QwtWeedingCurveFitter::~QwtWeedingCurveFitter()
{
    delete d_data;
}

/*!
 Assign the tolerance

 The tolerance is the maximum distance, that is acceptable
 between the original curve and the smoothed curve.

 Increasing the tolerance will reduce the number of the
 resulting points.

 \param tolerance Tolerance

 \sa tolerance()
*/
void QwtWeedingCurveFitter::setTolerance( double tolerance )
{
    d_data->tolerance = qMax( tolerance, 0.0 );
}

/*!
  \return Tolerance
  \sa setTolerance()
*/
double QwtWeedingCurveFitter::tolerance() const
{
    return d_data->tolerance;
}

/*!
 Limit the number of points passed to a run of the algorithm

 The runtime of the Douglas Peucker algorithm increases non linear
 with the number of points. For a chunk size > 0 the polygon
 is split into pieces passed to the algorithm one by one.

 \param numPoints Maximum for the number of points passed to the algorithm

 \sa chunkSize()
*/
void QwtWeedingCurveFitter::setChunkSize( uint numPoints )
{
    if ( numPoints > 0 )
        numPoints = qMax( numPoints, 3U );

    d_data->chunkSize = numPoints;
}

/*!
  
  \return Maximum for the number of points passed to a run 
          of the algorithm - or 0, when unlimited
  \sa setChunkSize()
*/
uint QwtWeedingCurveFitter::chunkSize() const
{
    return d_data->chunkSize;
}

/*!
  \param points Series of data points
  \return Curve points
*/
QPolygonF QwtWeedingCurveFitter::fitCurve( const QPolygonF &points ) const
{
    QPolygonF fittedPoints;

    if ( d_data->chunkSize == 0 )
    {
        fittedPoints = simplify( points );
    }
    else
    {
        for ( int i = 0; i < points.size(); i += d_data->chunkSize )
        {
            const QPolygonF p = points.mid( i, d_data->chunkSize );
            fittedPoints += simplify( p );
        }
    }

    return fittedPoints;
}

QPolygonF QwtWeedingCurveFitter::simplify( const QPolygonF &points ) const
{
    const double toleranceSqr = d_data->tolerance * d_data->tolerance;

    QStack<Line> stack;
    stack.reserve( 500 );

    const QPointF *p = points.data();
    const int nPoints = points.size();

    QVector<bool> usePoint( nPoints, false );

    stack.push( Line( 0, nPoints - 1 ) );

    while ( !stack.isEmpty() )
    {
        const Line r = stack.pop();

        // initialize line segment
        const double vecX = p[r.to].x() - p[r.from].x();
        const double vecY = p[r.to].y() - p[r.from].y();

        const double vecLength = qSqrt( vecX * vecX + vecY * vecY );

        const double unitVecX = ( vecLength != 0.0 ) ? vecX / vecLength : 0.0;
        const double unitVecY = ( vecLength != 0.0 ) ? vecY / vecLength : 0.0;

        double maxDistSqr = 0.0;
        int nVertexIndexMaxDistance = r.from + 1;
        for ( int i = r.from + 1; i < r.to; i++ )
        {
            //compare to anchor
            const double fromVecX = p[i].x() - p[r.from].x();
            const double fromVecY = p[i].y() - p[r.from].y();

            double distToSegmentSqr;
            if ( fromVecX * unitVecX + fromVecY * unitVecY < 0.0 )
            {
                distToSegmentSqr = fromVecX * fromVecX + fromVecY * fromVecY;
            }
            else
            {
                const double toVecX = p[i].x() - p[r.to].x();
                const double toVecY = p[i].y() - p[r.to].y();
                const double toVecLength = toVecX * toVecX + toVecY * toVecY;

                const double s = toVecX * ( -unitVecX ) + toVecY * ( -unitVecY );
                if ( s < 0.0 )
                {
                    distToSegmentSqr = toVecLength;
                }
                else
                {
                    distToSegmentSqr = qFabs( toVecLength - s * s );
                }
            }

            if ( maxDistSqr < distToSegmentSqr )
            {
                maxDistSqr = distToSegmentSqr;
                nVertexIndexMaxDistance = i;
            }
        }
        if ( maxDistSqr <= toleranceSqr )
        {
            usePoint[r.from] = true;
            usePoint[r.to] = true;
        }
        else
        {
            stack.push( Line( r.from, nVertexIndexMaxDistance ) );
            stack.push( Line( nVertexIndexMaxDistance, r.to ) );
        }
    }

    QPolygonF stripped;
    for ( int i = 0; i < nPoints; i++ )
    {
        if ( usePoint[i] )
            stripped += p[i];
    }

    return stripped;
}