qt_demoe/third/3rd_qwt/qwt_spline.cpp

385 lines
8.3 KiB
C++

/* -*- 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_spline.h"
#include "qwt_math.h"
class QwtSpline::PrivateData
{
public:
PrivateData():
splineType( QwtSpline::Natural )
{
}
QwtSpline::SplineType splineType;
// coefficient vectors
QVector<double> a;
QVector<double> b;
QVector<double> c;
// control points
QPolygonF points;
};
static int lookup( double x, const QPolygonF &values )
{
#if 0
//qLowerBound/qHigherBound ???
#endif
int i1;
const int size = values.size();
if ( x <= values[0].x() )
i1 = 0;
else if ( x >= values[size - 2].x() )
i1 = size - 2;
else
{
i1 = 0;
int i2 = size - 2;
int i3 = 0;
while ( i2 - i1 > 1 )
{
i3 = i1 + ( ( i2 - i1 ) >> 1 );
if ( values[i3].x() > x )
i2 = i3;
else
i1 = i3;
}
}
return i1;
}
//! Constructor
QwtSpline::QwtSpline()
{
d_data = new PrivateData;
}
/*!
Copy constructor
\param other Spline used for initialization
*/
QwtSpline::QwtSpline( const QwtSpline& other )
{
d_data = new PrivateData( *other.d_data );
}
/*!
Assignment operator
\param other Spline used for initialization
\return *this
*/
QwtSpline &QwtSpline::operator=( const QwtSpline & other )
{
*d_data = *other.d_data;
return *this;
}
//! Destructor
QwtSpline::~QwtSpline()
{
delete d_data;
}
/*!
Select the algorithm used for calculating the spline
\param splineType Spline type
\sa splineType()
*/
void QwtSpline::setSplineType( SplineType splineType )
{
d_data->splineType = splineType;
}
/*!
\return the spline type
\sa setSplineType()
*/
QwtSpline::SplineType QwtSpline::splineType() const
{
return d_data->splineType;
}
/*!
\brief Calculate the spline coefficients
Depending on the value of \a periodic, this function
will determine the coefficients for a natural or a periodic
spline and store them internally.
\param points Points
\return true if successful
\warning The sequence of x (but not y) values has to be strictly monotone
increasing, which means <code>points[i].x() < points[i+1].x()</code>.
If this is not the case, the function will return false
*/
bool QwtSpline::setPoints( const QPolygonF& points )
{
const int size = points.size();
if ( size <= 2 )
{
reset();
return false;
}
d_data->points = points;
d_data->a.resize( size - 1 );
d_data->b.resize( size - 1 );
d_data->c.resize( size - 1 );
bool ok;
if ( d_data->splineType == Periodic )
ok = buildPeriodicSpline( points );
else
ok = buildNaturalSpline( points );
if ( !ok )
reset();
return ok;
}
/*!
\return Points, that have been by setPoints()
*/
QPolygonF QwtSpline::points() const
{
return d_data->points;
}
//! \return A coefficients
const QVector<double> &QwtSpline::coefficientsA() const
{
return d_data->a;
}
//! \return B coefficients
const QVector<double> &QwtSpline::coefficientsB() const
{
return d_data->b;
}
//! \return C coefficients
const QVector<double> &QwtSpline::coefficientsC() const
{
return d_data->c;
}
//! Free allocated memory and set size to 0
void QwtSpline::reset()
{
d_data->a.resize( 0 );
d_data->b.resize( 0 );
d_data->c.resize( 0 );
d_data->points.resize( 0 );
}
//! True if valid
bool QwtSpline::isValid() const
{
return d_data->a.size() > 0;
}
/*!
Calculate the interpolated function value corresponding
to a given argument x.
\param x Coordinate
\return Interpolated coordinate
*/
double QwtSpline::value( double x ) const
{
if ( d_data->a.size() == 0 )
return 0.0;
const int i = lookup( x, d_data->points );
const double delta = x - d_data->points[i].x();
return( ( ( ( d_data->a[i] * delta ) + d_data->b[i] )
* delta + d_data->c[i] ) * delta + d_data->points[i].y() );
}
/*!
\brief Determines the coefficients for a natural spline
\return true if successful
*/
bool QwtSpline::buildNaturalSpline( const QPolygonF &points )
{
int i;
const QPointF *p = points.data();
const int size = points.size();
double *a = d_data->a.data();
double *b = d_data->b.data();
double *c = d_data->c.data();
// set up tridiagonal equation system; use coefficient
// vectors as temporary buffers
QVector<double> h( size - 1 );
for ( i = 0; i < size - 1; i++ )
{
h[i] = p[i+1].x() - p[i].x();
if ( h[i] <= 0 )
return false;
}
QVector<double> d( size - 1 );
double dy1 = ( p[1].y() - p[0].y() ) / h[0];
for ( i = 1; i < size - 1; i++ )
{
b[i] = c[i] = h[i];
a[i] = 2.0 * ( h[i-1] + h[i] );
const double dy2 = ( p[i+1].y() - p[i].y() ) / h[i];
d[i] = 6.0 * ( dy1 - dy2 );
dy1 = dy2;
}
//
// solve it
//
// L-U Factorization
for ( i = 1; i < size - 2; i++ )
{
c[i] /= a[i];
a[i+1] -= b[i] * c[i];
}
// forward elimination
QVector<double> s( size );
s[1] = d[1];
for ( i = 2; i < size - 1; i++ )
s[i] = d[i] - c[i-1] * s[i-1];
// backward elimination
s[size - 2] = - s[size - 2] / a[size - 2];
for ( i = size - 3; i > 0; i-- )
s[i] = - ( s[i] + b[i] * s[i+1] ) / a[i];
s[size - 1] = s[0] = 0.0;
//
// Finally, determine the spline coefficients
//
for ( i = 0; i < size - 1; i++ )
{
a[i] = ( s[i+1] - s[i] ) / ( 6.0 * h[i] );
b[i] = 0.5 * s[i];
c[i] = ( p[i+1].y() - p[i].y() ) / h[i]
- ( s[i+1] + 2.0 * s[i] ) * h[i] / 6.0;
}
return true;
}
/*!
\brief Determines the coefficients for a periodic spline
\return true if successful
*/
bool QwtSpline::buildPeriodicSpline( const QPolygonF &points )
{
int i;
const QPointF *p = points.data();
const int size = points.size();
double *a = d_data->a.data();
double *b = d_data->b.data();
double *c = d_data->c.data();
QVector<double> d( size - 1 );
QVector<double> h( size - 1 );
QVector<double> s( size );
//
// setup equation system; use coefficient
// vectors as temporary buffers
//
for ( i = 0; i < size - 1; i++ )
{
h[i] = p[i+1].x() - p[i].x();
if ( h[i] <= 0.0 )
return false;
}
const int imax = size - 2;
double htmp = h[imax];
double dy1 = ( p[0].y() - p[imax].y() ) / htmp;
for ( i = 0; i <= imax; i++ )
{
b[i] = c[i] = h[i];
a[i] = 2.0 * ( htmp + h[i] );
const double dy2 = ( p[i+1].y() - p[i].y() ) / h[i];
d[i] = 6.0 * ( dy1 - dy2 );
dy1 = dy2;
htmp = h[i];
}
//
// solve it
//
// L-U Factorization
a[0] = qSqrt( a[0] );
c[0] = h[imax] / a[0];
double sum = 0;
for ( i = 0; i < imax - 1; i++ )
{
b[i] /= a[i];
if ( i > 0 )
c[i] = - c[i-1] * b[i-1] / a[i];
a[i+1] = qSqrt( a[i+1] - qwtSqr( b[i] ) );
sum += qwtSqr( c[i] );
}
b[imax-1] = ( b[imax-1] - c[imax-2] * b[imax-2] ) / a[imax-1];
a[imax] = qSqrt( a[imax] - qwtSqr( b[imax-1] ) - sum );
// forward elimination
s[0] = d[0] / a[0];
sum = 0;
for ( i = 1; i < imax; i++ )
{
s[i] = ( d[i] - b[i-1] * s[i-1] ) / a[i];
sum += c[i-1] * s[i-1];
}
s[imax] = ( d[imax] - b[imax-1] * s[imax-1] - sum ) / a[imax];
// backward elimination
s[imax] = - s[imax] / a[imax];
s[imax-1] = -( s[imax-1] + b[imax-1] * s[imax] ) / a[imax-1];
for ( i = imax - 2; i >= 0; i-- )
s[i] = - ( s[i] + b[i] * s[i+1] + c[i] * s[imax] ) / a[i];
//
// Finally, determine the spline coefficients
//
s[size-1] = s[0];
for ( i = 0; i < size - 1; i++ )
{
a[i] = ( s[i+1] - s[i] ) / ( 6.0 * h[i] );
b[i] = 0.5 * s[i];
c[i] = ( p[i+1].y() - p[i].y() )
/ h[i] - ( s[i+1] + 2.0 * s[i] ) * h[i] / 6.0;
}
return true;
}