de.quippy.javamod.multimedia.mod.mixer.interpolation

Class CubicSpline

java.lang.Object

de.quippy.javamod.multimedia.mod.mixer.interpolation.CubicSpline

public class CubicSpline
extends Object

Since:

15.06.2006 This code is adopted from the great Mod Plug Tracker by Olivier Lapicque ------------------------------------------------------------------------------------------------ cubic spline interpolation doc, (derived from "digital image warping", g. wolberg) interpolation polynomial: f(x) = A3*(x-floor(x))**3 + A2*(x-floor(x))**2 + A1*(x-floor(x)) + A0 with Y = equispaced data points (dist=1), YD = first derivates of data points and IP = floor(x) the A[0..3] can be found by solving A0 = Y[IP] A1 = YD[IP] A2 = 3*(Y[IP+1]-Y[IP])-2.0*YD[IP]-YD[IP+1] A3 = -2.0 * (Y[IP+1]-Y[IP]) + YD[IP] - YD[IP+1] with the first derivates as YD[IP] = 0.5 * (Y[IP+1] - Y[IP-1]); YD[IP+1] = 0.5 * (Y[IP+2] - Y[IP]) the coefs becomes A0 = Y[IP] A1 = YD[IP] = 0.5 * (Y[IP+1] - Y[IP-1]); A2 = 3.0 * (Y[IP+1]-Y[IP])-2.0*YD[IP]-YD[IP+1] = 3.0 * (Y[IP+1] - Y[IP]) - 0.5 * 2.0 * (Y[IP+1] - Y[IP-1]) - 0.5 * (Y[IP+2] - Y[IP]) = 3.0 * Y[IP+1] - 3.0 * Y[IP] - Y[IP+1] + Y[IP-1] - 0.5 * Y[IP+2] + 0.5 * Y[IP] = -0.5 * Y[IP+2] + 2.0 * Y[IP+1] - 2.5 * Y[IP] + Y[IP-1] = Y[IP-1] + 2 * Y[IP+1] - 0.5 * (5.0 * Y[IP] + Y[IP+2]) A3 = -2.0 * (Y[IP+1]-Y[IP]) + YD[IP] + YD[IP+1] = -2.0 * Y[IP+1] + 2.0 * Y[IP] + 0.5 * (Y[IP+1] - Y[IP-1]) + 0.5 * (Y[IP+2] - Y[IP]) = -2.0 * Y[IP+1] + 2.0 * Y[IP] + 0.5 * Y[IP+1] - 0.5 * Y[IP-1] + 0.5 * Y[IP+2] - 0.5 * Y[IP] = 0.5 * Y[IP+2] - 1.5 * Y[IP+1] + 1.5 * Y[IP] - 0.5 * Y[IP-1] = 0.5 * (3.0 * (Y[IP] - Y[IP+1]) - Y[IP-1] + YP[IP+2]) then interpolated data value is (horner rule) out = (((A3*x)+A2)*x+A1)*x+A0 this gives parts of data points Y[IP-1] to Y[IP+2] of part x**3 x**2 x**1 x**0 Y[IP-1] -0.5 1 -0.5 0 Y[IP] 1.5 -2.5 0 1 Y[IP+1] -1.5 2 0.5 0 Y[IP+2] 0.5 -0.5 0 0 --------------------------------------------------------------------------------------------------

Author:

Daniel Becker

Field Summary

Fields

Modifier and Type	Field and Description
static int[]	lut
static int	SPLINE_FRACMASK
static int	SPLINE_FRACSHIFT
static int	SPLINE_QUANTBITS

Method Summary

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

SPLINE_QUANTBITS

public static final int SPLINE_QUANTBITS

See Also:

Constant Field Values

SPLINE_FRACSHIFT

public static final int SPLINE_FRACSHIFT

See Also:

Constant Field Values

SPLINE_FRACMASK

public static final int SPLINE_FRACMASK

See Also:

Constant Field Values

lut

public static final int[] lut