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/*
Copyright (C) 1998 Jürgen Hochwald <juergen.hochwald@privat.kkf.net>
Copyright (C) 2003 Charles Samuels <charles@kde.org>
This library 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.
This library 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 General Public License
along with this library; see the file COPYING. If not, write to
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
Boston, MA 02110-1301, USA.
*/
#include <stdio.h>
#include "spline.h"
const bool Spline::natural=false;
Spline::Spline()
{
yp1=0.0;
ypn=0.0;
mRecalc = true;
}
Spline::Spline(const Spline ©)
{
operator=(copy);
}
Spline &Spline::operator =(const Spline ©)
{
mPoints = copy.mPoints;
mRecalc = copy.mRecalc;
yp1 = copy.yp1;
ypn = copy.ypn;
return *this;
}
Spline::~Spline()
{
}
void Spline::add(double x, double y)
{
Group g = { x, y, 0.0 };
mPoints.push_back(g);
mRecalc=true;
}
std::vector<double> Spline::points(int count) const
{
std::vector<double> points;
if (count == numPoints())
{
for (int i=0; i < count; ++i)
{
points.push_back(mPoints[i].y);
}
}
else
{
double min = mPoints[0].x;
double max = mPoints[numPoints()-1].x;
double dcount = double(count);
for (int i=0; i<count; ++i)
{
points.push_back(spline( (max-min)/dcount*i + min));
}
}
return points;
}
void Spline::calcSpline()
{
const int np=numPoints();
double *u = new double[np];
if (natural)
{
mPoints[0].y2 = u[0] = 0.0;
}
else
{
mPoints[0].y2 = -0.5;
u[0] =
(3.0/(mPoints[1].x-mPoints[0].x))*((mPoints[1].y-mPoints[0].y)
/ (mPoints[1].x-mPoints[0].x)-yp1);
}
double sig,p,qn,un;
for (int i=1; i<=np-2; i++)
{
sig=(mPoints[i].x-mPoints[i-1].x) / (mPoints[i+1].x-mPoints[i-1].x);
p = sig*mPoints[i-1].y2+2.0;
mPoints[i].y2 = (sig-1.0)/p;
u[i] =
(mPoints[i+1].y - mPoints[i].y) / (mPoints[i+1].x-mPoints[i].x)
- (mPoints[i].y - mPoints[i-1].y) / (mPoints[i].x - mPoints[i-1].x);
u[i] = (6.0*u[i] / (mPoints[i+1].x - mPoints[i-1].x) - sig *u[i-1])/p;
}
if (natural)
{
qn = un = 0.0;
}
else
{
qn = 0.5;
un =
(3.0 / (mPoints[np-1].x - mPoints[np-2].x))
* (ypn - (mPoints[np-1].y - mPoints[np-2].y)
/ (mPoints[np-1].x - mPoints[np-2].x));
}
mPoints[np-1].y2 = (un - qn * u[np-2]) / (qn*mPoints[np-2].y2 +1.0 );
for (int i=np-2; i>=0; i--)
{
mPoints[i].y2 = mPoints[i].y2 * mPoints[i+1].y2+u[i];
}
mRecalc = false;
delete [] u;
}
double Spline::spline(double xarg) const
{
if (numPoints()==0) return 0.0;
if (numPoints()==1) return mPoints[0].y;
if (mRecalc) calcSpline();
int klo=0;
int khi=numPoints()-1;
int k;
while (khi-klo > 1)
{
k = khi+klo;
if (k % 2)
k = (k+1) / 2;
else
k = k/2;
if (mPoints[k].x > xarg) khi=k;
else klo=k;
}
double h = mPoints[khi].x - mPoints[klo].x;
if (h==0)
{
// failed
return 0.0;
}
double a = (mPoints[khi].x - xarg) / h;
double b = (xarg - mPoints[klo].x) / h;
return
a * mPoints[klo].y + b*mPoints[khi].y
+ ((a*a*a-a) * mPoints[klo].y2
+ (b*b*b-b) * mPoints[khi].y2) * (h*h) / 6.0;
}
double Spline::x(int num) const
{
if (numPoints()<num) return 0.0;
return mPoints[num].x;
}
double Spline::y(int num) const
{
if (numPoints()<num) return 0.0;
return mPoints[num].y;
}
void Spline::clear()
{
mPoints.resize(0);
ypn=0.0;
yp1=0.0;
mRecalc=true;
}
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