/*
* NaturalSpline.
*
* JavaZOOM : jlgui@javazoom.net
* http://www.javazoom.net
*
*-----------------------------------------------------------------------
* This program 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 program 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 this program; if not, write to the Free Software
* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*----------------------------------------------------------------------
*/
package plugins.audioPlayer.javazoom.jlgui.player.amp.equalizer.ui;
import java.awt.Polygon;
public class NaturalSpline extends ControlCurve
{
public final int STEPS = 12;
public NaturalSpline()
{
super();
}
/*
* calculates the natural cubic spline that interpolates y[0], y[1], ...
* y[n] The first segment is returned as C[0].a + C[0].b*u + C[0].c*u^2 +
* C[0].d*u^3 0<=u <1 the other segments are in C[1], C[2], ... C[n-1]
*/
Cubic[] calcNaturalCubic(int n, int[] x)
{
float[] gamma = new float[n + 1];
float[] delta = new float[n + 1];
float[] D = new float[n + 1];
int i;
/*
* We solve the equation [2 1 ] [D[0]] [3(x[1] - x[0]) ] |1 4 1 | |D[1]|
* |3(x[2] - x[0]) | | 1 4 1 | | . | = | . | | ..... | | . | | . | | 1 4
* 1| | . | |3(x[n] - x[n-2])| [ 1 2] [D[n]] [3(x[n] - x[n-1])]
*
* by using row operations to convert the matrix to upper triangular and
* then back sustitution. The D[i] are the derivatives at the knots.
*/
gamma[0] = 1.0f / 2.0f;
for (i = 1; i < n; i++)
{
gamma[i] = 1 / (4 - gamma[i - 1]);
}
gamma[n] = 1 / (2 - gamma[n - 1]);
delta[0] = 3 * (x[1] - x[0]) * gamma[0];
for (i = 1; i < n; i++)
{
delta[i] = (3 * (x[i + 1] - x[i - 1]) - delta[i - 1]) * gamma[i];
}
delta[n] = (3 * (x[n] - x[n - 1]) - delta[n - 1]) * gamma[n];
D[n] = delta[n];
for (i = n - 1; i >= 0; i--)
{
D[i] = delta[i] - gamma[i] * D[i + 1];
}
/* now compute the coefficients of the cubics */
Cubic[] C = new Cubic[n];
for (i = 0; i < n; i++)
{
C[i] = new Cubic((float) x[i], D[i], 3 * (x[i + 1] - x[i]) - 2 * D[i] - D[i + 1], 2 * (x[i] - x[i + 1]) + D[i] + D[i + 1]);
}
return C;
}
/**
* Return a cubic spline.
*/
public Polygon getPolyline()
{
Polygon p = new Polygon();
if (pts.npoints >= 2)
{
Cubic[] X = calcNaturalCubic(pts.npoints - 1, pts.xpoints);
Cubic[] Y = calcNaturalCubic(pts.npoints - 1, pts.ypoints);
// very crude technique - just break each segment up into steps lines
int x = (int) Math.round(X[0].eval(0));
int y = (int) Math.round(Y[0].eval(0));
p.addPoint(x, boundY(y));
for (int i = 0; i < X.length; i++)
{
for (int j = 1; j <= STEPS; j++)
{
float u = j / (float) STEPS;
x = Math.round(X[i].eval(u));
y = Math.round(Y[i].eval(u));
p.addPoint(x, boundY(y));
}
}
}
return p;
}
}