org.apache.xmlgraphics/batik-awt-util/1.13 : org/apache/batik/ext/awt/image/rendered/TurbulencePatternRed.java

TurbulencePatternRed
http://xmlgraphics.apache.org/batik/batik-awt-util/: Batik AWT utilities (Apache Software Foundation)
The Apache Software License, Version 2.0
/*

   Licensed to the Apache Software Foundation (ASF) under one or more
   contributor license agreements.  See the NOTICE file distributed with
   this work for additional information regarding copyright ownership.
   The ASF licenses this file to You under the Apache License, Version 2.0
   (the "License"); you may not use this file except in compliance with
   the License.  You may obtain a copy of the License at

       http://www.apache.org/licenses/LICENSE-2.0

   Unless required by applicable law or agreed to in writing, software
   distributed under the License is distributed on an "AS IS" BASIS,
   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   See the License for the specific language governing permissions and
   limitations under the License.

 */

package org.apache.batik.ext.awt.image.rendered;

import java.awt.Rectangle;
import java.awt.color.ColorSpace;
import java.awt.geom.AffineTransform;
import java.awt.geom.Rectangle2D;
import java.awt.image.ColorModel;
import java.awt.image.DataBuffer;
import java.awt.image.DataBufferInt;
import java.awt.image.DirectColorModel;
import java.awt.image.SinglePixelPackedSampleModel;
import java.awt.image.WritableRaster;
This class creates a RenderedImage in conformance to the one
defined for the feTurbulence filter of the SVG specification.  What
follows is my high-level description of how the noise is generated.
This is not contained in the SVG spec, just the algorithm for
doing it.  This is provided in the hope that someone will figure
out a clever way to accelerate parts of the function.
gradient contains a long list of random unit vectors.  For each
point we are to generate noise for we do two things.  first we use
the latticeSelector to 'co-mingle' the integer portions of x and y
(this allows us to have a one-dimensional array of gradients that
appears 2 dimensional, by using the co-mingled index).
We do this for [x,y], [x+1,y], [x,y+1], and [x+1, y+1], this gives
us the four gradient vectors that surround the point (b00, b10, ...)
Next we construct the four vectors from the grid points (where the
gradient vectors are defined) [these are rx0, rx1, ry0, ry1].
We then take the dot product between the gradient vectors and the
grid point vectors (this gives the portion of the grid point vector
that projects along the gradient vector for each grid point).
These four dot projects are then combined with linear interpolation.
The weight factor for the linear combination is the result of applying
the 's' curve function to the fractional part of x and y (rx0, ry0).
The S curve function get's it's name because it looks a bit like as
'S' from 0->1.
Author:     Vincent Hardy,     Thomas DeWeese
Version: $Id: TurbulencePatternRed.java 1808001 2017-09-11 09:51:29Z ssteiner $/**
 * This class creates a RenderedImage in conformance to the one
 * defined for the feTurbulence filter of the SVG specification.  What
 * follows is my high-level description of how the noise is generated.
 * This is not contained in the SVG spec, just the algorithm for
 * doing it.  This is provided in the hope that someone will figure
 * out a clever way to accelerate parts of the function.
 *
 * gradient contains a long list of random unit vectors.  For each
 * point we are to generate noise for we do two things.  first we use
 * the latticeSelector to 'co-mingle' the integer portions of x and y
 * (this allows us to have a one-dimensional array of gradients that
 * appears 2 dimensional, by using the co-mingled index).
 *
 * We do this for [x,y], [x+1,y], [x,y+1], and [x+1, y+1], this gives
 * us the four gradient vectors that surround the point (b00, b10, ...)
 *
 * Next we construct the four vectors from the grid points (where the
 * gradient vectors are defined) [these are rx0, rx1, ry0, ry1].
 *
 * We then take the dot product between the gradient vectors and the
 * grid point vectors (this gives the portion of the grid point vector
 * that projects along the gradient vector for each grid point).
 * These four dot projects are then combined with linear interpolation.
 * The weight factor for the linear combination is the result of applying
 * the 's' curve function to the fractional part of x and y (rx0, ry0).
 * The S curve function get's it's name because it looks a bit like as
 * 'S' from 0-&gt;1.
 *
 * @author     <a href="mailto:vincent.hardy@eng.sun.com">Vincent Hardy</a>
 * @author     <a href="mailto:DeWeese@apache.org">Thomas DeWeese</a>
 * @version $Id: TurbulencePatternRed.java 1808001 2017-09-11 09:51:29Z ssteiner $ */
public final class TurbulencePatternRed extends AbstractRed {
    Inner class to store tile stitching info.
#see
/**
     * Inner class to store tile stitching info.
     * #see
     */
    static final class StitchInfo {
        Width of the integer lattice tile
/**
         * Width of the integer lattice tile
         */
        int width;

        Height of the integer lattice tile
/**
         * Height of the integer lattice tile
         */
        int height;

        Value beyond which values are wrapped on
the x-axis.
See Also: noise2Stitch.noise2Stitch/**
         * Value beyond which values are wrapped on
         * the x-axis.
         * @see TurbulencePatternRed#noise2Stitch
         */
        int wrapX;

        Value beyond which values are wrapped on
the y-axis.
See Also: noise2Stitch.noise2Stitch/**
         * Value beyond which values are wrapped on
         * the y-axis.
         * @see TurbulencePatternRed#noise2Stitch
         */
        int wrapY;

        Default constructor
/**
         * Default constructor
         */
        StitchInfo(){
        }

        Copy constructor
/**
         * Copy constructor
         */
        StitchInfo(StitchInfo stitchInfo){
            this.width = stitchInfo.width;
            this.height = stitchInfo.height;
            this.wrapX = stitchInfo.wrapX;
            this.wrapY = stitchInfo.wrapY;
        }

        final void assign(StitchInfo stitchInfo) {
            this.width  = stitchInfo.width;
            this.height = stitchInfo.height;
            this.wrapX  = stitchInfo.wrapX;
            this.wrapY  = stitchInfo.wrapY;
        }

        /*
         * Adjustst the StitchInfo for when the frequency has been
         * doubled.
         *
         *  width = tileWidth*baseFrequencyX
         *  height = tileHeight*baseFrequencyY
         *  minY = tileY*baseFrequencyY + PerlinN
         *  wrapX = tileX*baseFrequencyX + PerlinN + width
         *  wrapY = tileY*baseFrequencyY + PerlinN + height
         *
         */
        final void doubleFrequency(){
            width *= 2;
            height *= 2;
            wrapX *= 2;
            wrapY *= 2;
            wrapX -= PerlinN;
            wrapY -= PerlinN;
        }
    }

    Used when stitching is on
/**
     * Used when stitching is on
     */
    private StitchInfo stitchInfo = null;

    Identity transform, default used when null input in the constructor.
/**
     * Identity transform, default used when null input in the constructor.
     */
    private static final AffineTransform IDENTITY = new AffineTransform();

     x-axis base frequency for the noise function along the x-axis
/**
     *  x-axis base frequency for the noise function along the x-axis
     */
    private double baseFrequencyX;

    y-axis base frequency for the noise function along the y-axis
/**
     * y-axis base frequency for the noise function along the y-axis
     */
    private double baseFrequencyY;

    Number of octaves in the noise function
/**
     * Number of octaves in the noise function
     */
    private int numOctaves;

    Starting number for the pseudo random number generator
/**
     * Starting number for the pseudo random number generator
     */
    private int seed;

    Defines the tile for the turbulence function, if non-null turns
on stitching, so frequencies are adjusted to avoid
discontinuities in case frequencies do not match tile
boundaries.
/**
     * Defines the tile for the turbulence function, if non-null turns
     * on stitching, so frequencies are adjusted to avoid
     * discontinuities in case frequencies do not match tile
     * boundaries.
     */
    private Rectangle2D tile;

    Defines the tile for the turbulence function
/**
     * Defines the tile for the turbulence function
     */
    private AffineTransform txf;

    Defines whether the filter performs a fractal noise or a turbulence function
/**
     * Defines whether the filter performs a fractal noise or a turbulence function
     */
    private boolean isFractalNoise;

    List of channels that the generator produces.
/**
     * List of channels that the generator produces.
     */
    private int[] channels;

    // To avoid doing an inverse transform on each pixel, transform
    // the image space unit vectors and process how much of a delta
    // this is in filter space.
    double[] tx = {1, 0};
    double[] ty = {0, 1};

    Produces results in the range [1, 2**31 - 2].
Algorithm is: r = (a * r) mod m
where a = 16807 and m = 2**31 - 1 = 2147483647
See [Park & Miller], CACM vol. 31 no. 10 p. 1195, Oct. 1988
To test: the algorithm should produce the result 1043618065
as the 10,000th generated number if the original seed is 1.
/**
     * Produces results in the range [1, 2**31 - 2].
     * Algorithm is: r = (a * r) mod m
     * where a = 16807 and m = 2**31 - 1 = 2147483647
     * See [Park & Miller], CACM vol. 31 no. 10 p. 1195, Oct. 1988
     * To test: the algorithm should produce the result 1043618065
     * as the 10,000th generated number if the original seed is 1.
     */
    private static final int RAND_m = 2147483647; /* 2**31 - 1 */
    private static final int RAND_a = 16807; /* 7**5; primitive root of m */
    private static final int RAND_q = 127773; /* m / a */
    private static final int RAND_r = 2836; /* m % a */

    private static final int BSize = 0x100;
    private static final int BM = 0xff;
    private static final double PerlinN = 0x1000;
    private final int[] latticeSelector = new int[BSize + 1];
    private final double[] gradient = new double[(BSize+1)*8];

    public double getBaseFrequencyX(){
        return baseFrequencyX;
    }

    public double getBaseFrequencyY(){
        return baseFrequencyY;
    }

    public int getNumOctaves(){
        return numOctaves;
    }

    public int getSeed(){
        return seed;
    }

    public Rectangle2D getTile(){
        return (Rectangle2D)tile.clone();
    }

    public boolean isFractalNoise(){
        return isFractalNoise;
    }

    public boolean[] getChannels(){
        boolean[] channels = new boolean[4];
        for (int channel : this.channels) channels[channel] = true;

        return channels;
    }

    public final int setupSeed(int seed) {
        if (seed <= 0) seed = -(seed % (RAND_m - 1)) + 1;
        if (seed > RAND_m - 1) seed = RAND_m - 1;
        return seed;
    }

    public final int random(int seed) {
      int result = RAND_a * (seed % RAND_q) - RAND_r * (seed / RAND_q);
        if (result <= 0) result += RAND_m;
        return result;
    }

    private void initLattice(int seed) {
        double u, v, s;
        int i, j, k, s1, s2;
        seed = setupSeed(seed);

        for(k = 0; k < 4; k++){
            for(i = 0; i < BSize; i++){
                u = (((seed = random(seed)) % (BSize + BSize)) - BSize);
                v = (((seed = random(seed)) % (BSize + BSize)) - BSize);

                s = 1/Math.sqrt(u*u + v*v);
                gradient[i*8 + k*2    ] = u*s;
                gradient[i*8 + k*2 + 1] = v*s;
            }
        }

        for(i = 0; i < BSize; i++)
            latticeSelector[i] = i;

        while(--i > 0){
            k = latticeSelector[i];
            j = (seed = random(seed)) % BSize;
            latticeSelector[i] = latticeSelector[j];
            latticeSelector[j] = k;

            // Now we apply the lattice to the gradient array, this
            // lets us avoid one of the lattice lookups.
            s1 = i<<3;
            s2 = j<<3;
            for (j=0; j<8; j++) {
                s = gradient[s1+j];
                gradient[s1+j] = gradient[s2+j];
                gradient[s2+j] = s;
            }
        }
        latticeSelector[BSize] = latticeSelector[0];
        for (j=0; j<8; j++)
            gradient[(BSize*8)+j] = gradient[j];
    }


    private static final double s_curve(final double t) {
        return (t * t * (3 - 2 * t) );
    }

    private static final double lerp(double t, double a, double b) {
        return ( a + t * (b - a) );
    }

    Generate a pixel of noise corresponding to the point vec0,vec1.
See class description for a high level discussion of method.
This handles cases where channels <= 4.
Params: noise – The place to put the generated noise.
vec0 –  The X coordiate to generate noise for
vec1 –  The Y coordiate to generate noise for/**
     * Generate a pixel of noise corresponding to the point vec0,vec1.
     * See class description for a high level discussion of method.
     * This handles cases where channels <= 4.
     * @param noise The place to put the generated noise.
     * @param vec0  The X coordiate to generate noise for
     * @param vec1  The Y coordiate to generate noise for
     */
    private final void noise2(final double[] noise, double vec0, double vec1) {
        int b0, b1;
        final int i, j;
        final double rx0, rx1, ry0, ry1, sx, sy;

        vec0 += PerlinN;
        b0 = ((int)vec0)&BM;

        i = latticeSelector[b0];
        j = latticeSelector[b0+1];

        rx0 = vec0 - (int)vec0;
        rx1 = rx0 - 1.0;
        sx  = s_curve(rx0);

        vec1 += PerlinN;
        b0 = (int)vec1;

        // The gradient array already has the latticeSelector applied
        // to it, So we can avoid doing the last lookup.
        b1 = ((j + b0)&BM)<<3;
        b0 = ((i + b0)&BM)<<3;

        ry0 = vec1 - (int)vec1;
        ry1 = ry0 - 1.0;
        sy = s_curve(ry0);

        switch (channels.length) {
            // Intentionally use 'fall through' in switch statement.
        case 4:
            noise[3] =
                lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+6] + ry0*gradient[b0+7],
                          rx1*gradient[b1+6] + ry0*gradient[b1+7]),
                     lerp(sx,
                          rx0*gradient[b0+8+6] + ry1*gradient[b0+8+7],
                          rx1*gradient[b1+8+6] + ry1*gradient[b1+8+7]));
        case 3:
            noise[2] =
                lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+4] + ry0*gradient[b0+5],
                          rx1*gradient[b1+4] + ry0*gradient[b1+5]),
                     lerp(sx,
                          rx0*gradient[b0+8+4] + ry1*gradient[b0+8+5],
                          rx1*gradient[b1+8+4] + ry1*gradient[b1+8+5]));
        case 2:
            noise[1] =
                lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+2] + ry0*gradient[b0+3],
                          rx1*gradient[b1+2] + ry0*gradient[b1+3]),
                     lerp(sx,
                          rx0*gradient[b0+8+2] + ry1*gradient[b0+8+3],
                          rx1*gradient[b1+8+2] + ry1*gradient[b1+8+3]));
        case 1:
            noise[0] =
                lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+0] + ry0*gradient[b0+1],
                          rx1*gradient[b1+0] + ry0*gradient[b1+1]),
                     lerp(sx,
                          rx0*gradient[b0+8+0] + ry1*gradient[b0+8+1],
                          rx1*gradient[b1+8+0] + ry1*gradient[b1+8+1]));
        }
    }

    This version of the noise function implements stitching.
If any of the lattice is on the right or bottom edge, the
function uses the the latice on the other side of the
tile, i.e., the left or right edge.
Params: noise – The place to put the generated noise.
vec0 –  The X coordiate to generate noise for
vec1 –  The Y coordiate to generate noise for
stitchInfo – The stitching information for the noise function./**
     * This version of the noise function implements stitching.
     * If any of the lattice is on the right or bottom edge, the
     * function uses the the latice on the other side of the
     * tile, i.e., the left or right edge.
     * @param noise The place to put the generated noise.
     * @param vec0  The X coordiate to generate noise for
     * @param vec1  The Y coordiate to generate noise for
     * @param stitchInfo The stitching information for the noise function.
     */
    private final void noise2Stitch(final double[] noise,
                                    final double vec0, final double vec1,
                                    final StitchInfo stitchInfo){
        int b0, b1;
        final int i, j, b00, b10, b01, b11;
        double t;
        final double rx0, rx1, ry0, ry1, sx, sy;

        t = vec0  + PerlinN;
        b0 = ((int)t);
        b1 = b0+1;
        // Stitch lattice tile x coordinates
        if (b1 >= stitchInfo.wrapX) {
            if (b0 >= stitchInfo.wrapX) {
                b0 -= stitchInfo.width;
                b1 -= stitchInfo.width;
            } else {
                b1 -= stitchInfo.width;
            }
        }
        i = latticeSelector[b0&BM];
        j = latticeSelector[b1&BM];

        rx0 = t - (int)t;
        rx1 = rx0 - 1.0;
        sx = s_curve(rx0);

        t = vec1 + PerlinN;
        b0 = ((int)t);
        b1 = b0+1;
        // Stitch lattice tile y coordinates
        if (b1 >= stitchInfo.wrapY) {
            if (b0 >= stitchInfo.wrapY) {
                b0 -= stitchInfo.height;
                b1 -= stitchInfo.height;
            } else {
                b1 -= stitchInfo.height;
            }
        }
        // In this case we still need to keep all four indexes since
        // we may have split y across the stitch boundry, in which
        // case b0 and b1 do not have a fixed offset from one another.
        // We still avoid a latticeSelector lookup for each index though...
        b00 = ((i + b0)&BM)<<3;
        b10 = ((j + b0)&BM)<<3;
        b01 = ((i + b1)&BM)<<3;
        b11 = ((j + b1)&BM)<<3;

        ry0 = t - (int)t;
        ry1 = ry0 - 1.0;
        sy = s_curve(ry0);

        switch (channels.length) {
            // Intentionally use 'fall through' in switch statement.
        case 4:
            noise[3] =
                lerp(sy,
                     lerp(sx,
                          rx0*gradient[b00+6] + ry0*gradient[b00+7],
                          rx1*gradient[b10+6] + ry0*gradient[b10+7]),
                     lerp(sx,
                          rx0*gradient[b01+6] + ry1*gradient[b01+7],
                          rx1*gradient[b11+6] + ry1*gradient[b11+7]));
        case 3:
            noise[2] =
                lerp(sy,
                     lerp(sx,
                          rx0*gradient[b00+4] + ry0*gradient[b00+5],
                          rx1*gradient[b10+4] + ry0*gradient[b10+5]),
                     lerp(sx,
                          rx0*gradient[b01+4] + ry1*gradient[b01+5],
                          rx1*gradient[b11+4] + ry1*gradient[b11+5]));
        case 2:
            noise[1] =
                lerp(sy,
                     lerp(sx,
                          rx0*gradient[b00+2] + ry0*gradient[b00+3],
                          rx1*gradient[b10+2] + ry0*gradient[b10+3]),
                     lerp(sx,
                          rx0*gradient[b01+2] + ry1*gradient[b01+3],
                          rx1*gradient[b11+2] + ry1*gradient[b11+3]));
        case 1:
            noise[0] =
                lerp(sy,
                     lerp(sx,
                          rx0*gradient[b00+0] + ry0*gradient[b00+1],
                          rx1*gradient[b10+0] + ry0*gradient[b10+1]),
                     lerp(sx,
                          rx0*gradient[b01+0] + ry1*gradient[b01+1],
                          rx1*gradient[b11+0] + ry1*gradient[b11+1]));
        }
    }

    This is the heart of the turbulence calculation. It returns
'turbFunctionResult', as defined in the spec.  This is
special case for 4 bands of output.
Params: pointX – x coordinate of the point to process.
pointY – y coordinate of the point to process.
fSum – array used to avoid reallocating double array for each pixel
Returns: The ARGB pixel value./**
     * This is the heart of the turbulence calculation. It returns
     * 'turbFunctionResult', as defined in the spec.  This is
     * special case for 4 bands of output.
     *
     * @param pointX x coordinate of the point to process.
     * @param pointY y coordinate of the point to process.
     * @param fSum array used to avoid reallocating double array for each pixel
     * @return The ARGB pixel value.
     */
    private final int turbulence_4(double pointX,
                                   double pointY,
                                   final double[] fSum) {
        double n, ratio = 255;
        int i, j, b0, b1, nOctave;
        double px, py, rx0, rx1, ry0, ry1, sx, sy;

        pointX *= baseFrequencyX;
        pointY *= baseFrequencyY;
        fSum[0] = fSum[1] = fSum[2] = fSum[3] = 0;

        for (nOctave = numOctaves; nOctave > 0; nOctave--){
            px = pointX+PerlinN;

            b0 = ((int)px)&BM;
            i = latticeSelector[b0 ];
            j = latticeSelector[b0+1];

            rx0 = px - (int)px;
            rx1 = rx0 - 1.0;
            sx  = s_curve(rx0);

            py = pointY+PerlinN;
            b0 = ((int)py) & BM;
            b1 = (b0+1) & BM;

            b1 = ((j + b0)&BM)<<3;
            b0 = ((i + b0)&BM)<<3;

            ry0 = py - (int)py;
            ry1 = ry0 - 1.0;
            sy = s_curve(ry0);

            n = lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+0] + ry0*gradient[b0+1],
                          rx1*gradient[b1+0] + ry0*gradient[b1+1]),
                     lerp(sx,
                          rx0*gradient[b0+8+0] + ry1*gradient[b0+8+1],
                          rx1*gradient[b1+8+0] + ry1*gradient[b1+8+1]));

            if (n<0) fSum[0] -= (n * ratio);
            else     fSum[0] += (n * ratio);

            n = lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+2] + ry0*gradient[b0+3],
                          rx1*gradient[b1+2] + ry0*gradient[b1+3]),
                     lerp(sx,
                          rx0*gradient[b0+8+2] + ry1*gradient[b0+8+3],
                          rx1*gradient[b1+8+2] + ry1*gradient[b1+8+3]));

            if (n<0) fSum[1] -= (n * ratio);
            else     fSum[1] += (n * ratio);

            n = lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+4] + ry0*gradient[b0+5],
                          rx1*gradient[b1+4] + ry0*gradient[b1+5]),
                     lerp(sx,
                          rx0*gradient[b0+8+4] + ry1*gradient[b0+8+5],
                          rx1*gradient[b1+8+4] + ry1*gradient[b1+8+5]));

            if (n<0) fSum[2] -= (n * ratio);
            else     fSum[2] += (n * ratio);

            n = lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+6] + ry0*gradient[b0+7],
                          rx1*gradient[b1+6] + ry0*gradient[b1+7]),
                     lerp(sx,
                          rx0*gradient[b0+8+6] + ry1*gradient[b0+8+7],
                          rx1*gradient[b1+8+6] + ry1*gradient[b1+8+7]));
            if (n<0) fSum[3] -= (n * ratio);
            else     fSum[3] += (n * ratio);

            ratio *= .5;
            pointX *= 2;
            pointY *= 2;
        }

        i = (int)fSum[0];
        if ((i & 0xFFFFFF00) == 0) j  = i<<16;
        else                       j  = ((i & 0x80000000) != 0)?0:0xFF0000;

        i = (int)fSum[1];
        if ((i & 0xFFFFFF00) == 0) j |= i<<8;
        else                       j |= ((i & 0x80000000) != 0)?0:0xFF00;

        i = (int)fSum[2];
        if ((i & 0xFFFFFF00) == 0) j |= i;
        else                       j |= ((i & 0x80000000) != 0)?0:0xFF;

        i = (int)fSum[3];
        if ((i & 0xFFFFFF00) == 0) j |= i<<24;
        else                       j |= ((i & 0x80000000) != 0)?0:0xFF000000;
        return j;
    }


    This is the heart of the turbulence calculation. It returns
'turbFunctionResult', as defined in the spec.
Params: rgb – array for the four color components
pointX – x coordinate of the point to process.
pointY – y coordinate of the point to process.
fSum – array used to avoid reallocating double array for each pixel
noise – array used to avoid reallocating double array for
       each pixel/**
     * This is the heart of the turbulence calculation. It returns
     * 'turbFunctionResult', as defined in the spec.
     * @param rgb array for the four color components
     * @param pointX x coordinate of the point to process.
     * @param pointY y coordinate of the point to process.
     * @param fSum array used to avoid reallocating double array for each pixel
     * @param noise array used to avoid reallocating double array for
     *        each pixel
     */
    private final void turbulence(final int[] rgb,
                                  double pointX,
                                  double pointY,
                                  final double[] fSum,
                                  final double[] noise) {
        fSum[0] = fSum[1] = fSum[2] = fSum[3] = 0;
        double ratio = 255;
        pointX *= baseFrequencyX;
        pointY *= baseFrequencyY;
        switch (channels.length) {
        case 4:
            for(int nOctave = 0; nOctave < numOctaves; nOctave++){
                noise2(noise, pointX, pointY);

                if (noise[0]<0) fSum[0] -= (noise[0] * ratio);
                else            fSum[0] += (noise[0] * ratio);
                if (noise[1]<0) fSum[1] -= (noise[1] * ratio);
                else            fSum[1] += (noise[1] * ratio);
                if (noise[2]<0) fSum[2] -= (noise[2] * ratio);
                else            fSum[2] += (noise[2] * ratio);
                if (noise[3]<0) fSum[3] -= (noise[3] * ratio);
                else            fSum[3] += (noise[3] * ratio);
                ratio *= .5;
                pointX *= 2;
                pointY *= 2;
            }

            rgb[0] = (int)fSum[0];
            if ((rgb[0] & 0xFFFFFF00) != 0)
                rgb[0] = ((rgb[0] & 0x80000000) != 0)?0:255;
            rgb[1] = (int)fSum[1];
            if ((rgb[1] & 0xFFFFFF00) != 0)
                rgb[1] = ((rgb[1] & 0x80000000) != 0)?0:255;
            rgb[2] = (int)fSum[2];
            if ((rgb[2] & 0xFFFFFF00) != 0)
                rgb[2] = ((rgb[2] & 0x80000000) != 0)?0:255;
            rgb[3] = (int)fSum[3];
            if ((rgb[3] & 0xFFFFFF00) != 0)
                rgb[3] = ((rgb[3] & 0x80000000) != 0)?0:255;
            break;
        case 3:
            for(int nOctave = 0; nOctave < numOctaves; nOctave++){
                noise2(noise, pointX, pointY);

                if (noise[2]<0) fSum[2] -= (noise[2] * ratio);
                else            fSum[2] += (noise[2] * ratio);
                if (noise[1]<0) fSum[1] -= (noise[1] * ratio);
                else            fSum[1] += (noise[1] * ratio);
                if (noise[0]<0) fSum[0] -= (noise[0] * ratio);
                else            fSum[0] += (noise[0] * ratio);
                ratio *= .5;
                pointX *= 2;
                pointY *= 2;
            }
            rgb[2] = (int)fSum[2];
            if ((rgb[2] & 0xFFFFFF00) != 0)
                rgb[2] = ((rgb[2] & 0x80000000) != 0)?0:255;
            rgb[1] = (int)fSum[1];
            if ((rgb[1] & 0xFFFFFF00) != 0)
                rgb[1] = ((rgb[1] & 0x80000000) != 0)?0:255;
            rgb[0] = (int)fSum[0];
            if ((rgb[0] & 0xFFFFFF00) != 0)
                rgb[0] = ((rgb[0] & 0x80000000) != 0)?0:255;
            break;
        case 2:
            for(int nOctave = 0; nOctave < numOctaves; nOctave++){
                noise2(noise, pointX, pointY);

                if (noise[1]<0) fSum[1] -= (noise[1] * ratio);
                else            fSum[1] += (noise[1] * ratio);
                if (noise[0]<0) fSum[0] -= (noise[0] * ratio);
                else            fSum[0] += (noise[0] * ratio);
                ratio *= .5;
                pointX *= 2;
                pointY *= 2;
            }

            rgb[1] = (int)fSum[1];
            if ((rgb[1] & 0xFFFFFF00) != 0)
                rgb[1] = ((rgb[1] & 0x80000000) != 0)?0:255;
            rgb[0] = (int)fSum[0];
            if ((rgb[0] & 0xFFFFFF00) != 0)
                rgb[0] = ((rgb[0] & 0x80000000) != 0)?0:255;
            break;
        case 1:
            for(int nOctave = 0; nOctave < numOctaves; nOctave++){
                noise2(noise, pointX, pointY);

                if (noise[0]<0) fSum[0] -= (noise[0] * ratio);
                else            fSum[0] += (noise[0] * ratio);
                ratio *= .5;
                pointX *= 2;
                pointY *= 2;
            }

            rgb[0] = (int)fSum[0];
            if ((rgb[0] & 0xFFFFFF00) != 0)
                rgb[0] = ((rgb[0] & 0x80000000) != 0)?0:255;
            break;
        }
    }

    This is the heart of the turbulence calculation. It returns
'turbFunctionResult', as defined in the spec.
Params: rgb – array for the four color components
pointX – x coordinate of the point to process.
pointY – y coordinate of the point to process.
fSum – array used to avoid reallocating double array for each pixel
noise – array used to avoid reallocating double array for
each pixel
stitchInfo – The stitching information for the noise function/**
     * This is the heart of the turbulence calculation. It returns
     * 'turbFunctionResult', as defined in the spec.
     * @param rgb array for the four color components
     * @param pointX x coordinate of the point to process.
     * @param pointY y coordinate of the point to process.
     * @param fSum array used to avoid reallocating double array for each pixel
     * @param noise array used to avoid reallocating double array for
     * each pixel
     * @param stitchInfo The stitching information for the noise function
     */
    private final void turbulenceStitch(final int[] rgb,
                                        double pointX, double pointY,
                                        final double[] fSum,
                                        final double[] noise,
                                        StitchInfo stitchInfo){
        double ratio = 1;
        pointX *= baseFrequencyX;
        pointY *= baseFrequencyY;
        fSum[0] = fSum[1] = fSum[2] = fSum[3] = 0;
        switch (channels.length) {
        case 4:
            for(int nOctave = 0; nOctave < numOctaves; nOctave++){
                noise2Stitch(noise, pointX, pointY, stitchInfo);

                if (noise[3]<0) fSum[3] -= (noise[3] * ratio);
                else            fSum[3] += (noise[3] * ratio);
                if (noise[2]<0) fSum[2] -= (noise[2] * ratio);
                else            fSum[2] += (noise[2] * ratio);
                if (noise[1]<0) fSum[1] -= (noise[1] * ratio);
                else            fSum[1] += (noise[1] * ratio);
                if (noise[0]<0) fSum[0] -= (noise[0] * ratio);
                else            fSum[0] += (noise[0] * ratio);
                ratio  *= .5;
                pointX *= 2;
                pointY *= 2;

                stitchInfo.doubleFrequency();
            }
            rgb[3] = (int)(fSum[3] * 255);
            if ((rgb[3] & 0xFFFFFF00) != 0)
                rgb[3] = ((rgb[3] & 0x80000000) != 0)?0:255;
            rgb[2] = (int)(fSum[2] * 255);
            if ((rgb[2] & 0xFFFFFF00) != 0)
                rgb[2] = ((rgb[2] & 0x80000000) != 0)?0:255;
            rgb[1] = (int)(fSum[1] * 255);
            if ((rgb[1] & 0xFFFFFF00) != 0)
                rgb[1] = ((rgb[1] & 0x80000000) != 0)?0:255;
            rgb[0] = (int)(fSum[0] * 255);
            if ((rgb[0] & 0xFFFFFF00) != 0)
                rgb[0] = ((rgb[0] & 0x80000000) != 0)?0:255;
            break;
        case 3:
            for(int nOctave = 0; nOctave < numOctaves; nOctave++){
                noise2Stitch(noise, pointX, pointY, stitchInfo);
                if (noise[2]<0) fSum[2] -= (noise[2] * ratio);
                else            fSum[2] += (noise[2] * ratio);
                if (noise[1]<0) fSum[1] -= (noise[1] * ratio);
                else            fSum[1] += (noise[1] * ratio);
                if (noise[0]<0) fSum[0] -= (noise[0] * ratio);
                else            fSum[0] += (noise[0] * ratio);
                ratio  *= .5;
                pointX *= 2;
                pointY *= 2;

                stitchInfo.doubleFrequency();
            }
            rgb[2] = (int)(fSum[2] * 255);
            if ((rgb[2] & 0xFFFFFF00) != 0)
                rgb[2] = ((rgb[2] & 0x80000000) != 0)?0:255;
            rgb[1] = (int)(fSum[1] * 255);
            if ((rgb[1] & 0xFFFFFF00) != 0)
                rgb[1] = ((rgb[1] & 0x80000000) != 0)?0:255;
            rgb[0] = (int)(fSum[0] * 255);
            if ((rgb[0] & 0xFFFFFF00) != 0)
                rgb[0] = ((rgb[0] & 0x80000000) != 0)?0:255;
            break;
        case 2:
            for(int nOctave = 0; nOctave < numOctaves; nOctave++){
                noise2Stitch(noise, pointX, pointY, stitchInfo);
                if (noise[1]<0) fSum[1] -= (noise[1] * ratio);
                else            fSum[1] += (noise[1] * ratio);
                if (noise[0]<0) fSum[0] -= (noise[0] * ratio);
                else            fSum[0] += (noise[0] * ratio);
                ratio  *= .5;
                pointX *= 2;
                pointY *= 2;

                stitchInfo.doubleFrequency();
            }
            rgb[1] = (int)(fSum[1] * 255);
            if ((rgb[1] & 0xFFFFFF00) != 0)
                rgb[1] = ((rgb[1] & 0x80000000) != 0)?0:255;
            rgb[0] = (int)(fSum[0] * 255);
            if ((rgb[0] & 0xFFFFFF00) != 0)
                rgb[0] = ((rgb[0] & 0x80000000) != 0)?0:255;
            break;
        case 1:
            for(int nOctave = 0; nOctave < numOctaves; nOctave++){
                noise2Stitch(noise, pointX, pointY, stitchInfo);
                if (noise[0]<0) fSum[0] -= (noise[0] * ratio);
                else            fSum[0] += (noise[0] * ratio);
                ratio  *= .5;
                pointX *= 2;
                pointY *= 2;

                stitchInfo.doubleFrequency();
            }
            rgb[0] = (int)(fSum[0] * 255);
            if ((rgb[0] & 0xFFFFFF00) != 0)
                rgb[0] = ((rgb[0] & 0x80000000) != 0)?0:255;
            break;
        }
    }

    This is the heart of the turbulence calculation. It returns
'turbFunctionResult', as defined in the spec.  This handles the
case where we are generating 4 channels of noise.
Params: pointX – x coordinate of the point to process.
pointY – y coordinate of the point to process.
fSum – array used to avoid reallocating double array for each pixel
Returns: The ARGB pixel/**
     * This is the heart of the turbulence calculation. It returns
     * 'turbFunctionResult', as defined in the spec.  This handles the
     * case where we are generating 4 channels of noise.
     * @param pointX x coordinate of the point to process.
     * @param pointY y coordinate of the point to process.
     * @param fSum array used to avoid reallocating double array for each pixel
     * @return The ARGB pixel
     */
    private final int turbulenceFractal_4( double pointX,
                                           double pointY,
                                           final double[] fSum) {
        int b0, b1, nOctave, i, j;
        double px, py, rx0, rx1, ry0, ry1, sx, sy, ratio = 127.5;

        pointX *= baseFrequencyX;
        pointY *= baseFrequencyY;
        fSum[0] = fSum[1] = fSum[2] = fSum[3] = 127.5;

        for (nOctave = numOctaves; nOctave > 0; nOctave--){
            px = pointX+PerlinN;

            b0 = ((int)px)&BM;
            i = latticeSelector[b0 ];
            j = latticeSelector[b0+1];

            rx0 = px - (int)px;
            rx1 = rx0 - 1.0;
            sx  = s_curve(rx0);

            py = pointY+PerlinN;
            b0 = ((int)py) & BM;
            b1 = (b0+1) & BM;

            b1 = ((j + b0)&BM)<<3;
            b0 = ((i + b0)&BM)<<3;

            ry0 = py - (int)py;
            ry1 = ry0 - 1.0;
            sy = s_curve(ry0);

            fSum[0] += lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+0] + ry0*gradient[b0+1],
                          rx1*gradient[b1+0] + ry0*gradient[b1+1]),
                     lerp(sx,
                          rx0*gradient[b0+8+0] + ry1*gradient[b0+8+1],
                          rx1*gradient[b1+8+0] + ry1*gradient[b1+8+1]))*ratio;

            fSum[1] += lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+2] + ry0*gradient[b0+3],
                          rx1*gradient[b1+2] + ry0*gradient[b1+3]),
                     lerp(sx,
                          rx0*gradient[b0+8+2] + ry1*gradient[b0+8+3],
                          rx1*gradient[b1+8+2] + ry1*gradient[b1+8+3]))*ratio;

            fSum[2] += lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+4] + ry0*gradient[b0+5],
                          rx1*gradient[b1+4] + ry0*gradient[b1+5]),
                     lerp(sx,
                          rx0*gradient[b0+8+4] + ry1*gradient[b0+8+5],
                          rx1*gradient[b1+8+4] + ry1*gradient[b1+8+5]))*ratio;

            fSum[3] += lerp(sy,
                     lerp(sx,
                          rx0*gradient[b0+6] + ry0*gradient[b0+7],
                          rx1*gradient[b1+6] + ry0*gradient[b1+7]),
                     lerp(sx,
                          rx0*gradient[b0+8+6] + ry1*gradient[b0+8+7],
                          rx1*gradient[b1+8+6] + ry1*gradient[b1+8+7]))*ratio;

            ratio  *= .5;
            pointX *= 2;
            pointY *= 2;
        }

        i = (int)fSum[0];
        if ((i & 0xFFFFFF00) == 0) j  = i<<16;
        else                       j  = ((i & 0x80000000) != 0)?0:0xFF0000;

        i = (int)fSum[1];
        if ((i & 0xFFFFFF00) == 0) j |= i<<8;
        else                       j |= ((i & 0x80000000) != 0)?0:0xFF00;

        i = (int)fSum[2];
        if ((i & 0xFFFFFF00) == 0) j |= i;
        else                       j |= ((i & 0x80000000) != 0)?0:0xFF;

        i = (int)fSum[3];
        if ((i & 0xFFFFFF00) == 0) j |= i<<24;
        else                       j |= ((i & 0x80000000) != 0)?0:0xFF000000;
        return j;
    }

    This is the heart of the turbulence calculation. It returns
'turbFunctionResult', as defined in the spec.
Params: rgb – array for the four color components
pointX – x coordinate of the point to process.
pointY – y coordinate of the point to process.
fSum – array used to avoid reallocating double array for each pixel
noise – array used to avoid reallocating double array for
each pixel/**
     * This is the heart of the turbulence calculation. It returns
     * 'turbFunctionResult', as defined in the spec.
     * @param rgb array for the four color components
     * @param pointX x coordinate of the point to process.
     * @param pointY y coordinate of the point to process.
     * @param fSum array used to avoid reallocating double array for each pixel
     * @param noise array used to avoid reallocating double array for
     * each pixel
     */
    private final void turbulenceFractal(final int[] rgb,
                                         double pointX,
                                         double pointY,
                                         final double[] fSum,
                                         final double[] noise){
        double ratio = 127.5;
        int    nOctave;
        fSum[0] = fSum[1] = fSum[2] = fSum[3] = 127.5;
        pointX *= baseFrequencyX;
        pointY *= baseFrequencyY;
        for(nOctave = numOctaves; nOctave > 0; nOctave--){
            noise2(noise, pointX, pointY);

            switch (channels.length) {
            case 4:
                fSum[3] += (noise[3] * ratio);
            case 3:
                fSum[2] += (noise[2] * ratio);
            case 2:
                fSum[1] += (noise[1] * ratio);
            case 1:
                fSum[0] += (noise[0] * ratio);
            }

            ratio  *= .5;
            pointX *= 2;
            pointY *= 2;
        }

        switch (channels.length) {
        case 4:
            rgb[3] = (int)fSum[3];
            if ((rgb[3] & 0xFFFFFF00) != 0)
                rgb[3] = ((rgb[3] & 0x80000000) != 0)?0:255;
        case 3:
            rgb[2] = (int)fSum[2];
            if ((rgb[2] & 0xFFFFFF00) != 0)
                rgb[2] = ((rgb[2] & 0x80000000) != 0)?0:255;
        case 2:
            rgb[1] = (int)fSum[1];
            if ((rgb[1] & 0xFFFFFF00) != 0)
                rgb[1] = ((rgb[1] & 0x80000000) != 0)?0:255;
        case 1:
            rgb[0] = (int)fSum[0];
            if ((rgb[0] & 0xFFFFFF00) != 0)
                rgb[0] = ((rgb[0] & 0x80000000) != 0)?0:255;
        }
    }

    This is the heart of the turbulence calculation. It returns
'turbFunctionResult', as defined in the spec.
Params: rgb – array for the four color components
pointX – x coordinate of the point to process.
pointY – y coordinate of the point to process.
fSum – array used to avoid reallocating double array for each pixel
noise – array used to avoid reallocating double array for
each pixel
stitchInfo – The stitching information for the noise function/**
     * This is the heart of the turbulence calculation. It returns
     * 'turbFunctionResult', as defined in the spec.
     * @param rgb array for the four color components
     * @param pointX x coordinate of the point to process.
     * @param pointY y coordinate of the point to process.
     * @param fSum array used to avoid reallocating double array for each pixel
     * @param noise array used to avoid reallocating double array for
     * each pixel
     * @param stitchInfo The stitching information for the noise function
     */
    private final void turbulenceFractalStitch(final int[] rgb,
                                               double pointX,
                                               double pointY,
                                               final double[] fSum,
                                               final double[] noise,
                                               StitchInfo stitchInfo){
        double ratio = 127.5;
        int    nOctave;
        fSum[0] = fSum[1] = fSum[2] = fSum[3] = 127.5;
        pointX *= baseFrequencyX;
        pointY *= baseFrequencyY;
        for(nOctave = numOctaves; nOctave > 0; nOctave--){
            noise2Stitch(noise, pointX, pointY, stitchInfo);

            switch (channels.length) {
            case 4:
                fSum[3] += (noise[3] * ratio);
            case 3:
                fSum[2] += (noise[2] * ratio);
            case 2:
                fSum[1] += (noise[1] * ratio);
            case 1:
                fSum[0] += (noise[0] * ratio);
            }

            ratio  *= .5;
            pointX *= 2;
            pointY *= 2;
            stitchInfo.doubleFrequency();
        }

        switch (channels.length) {
        case 4:
            rgb[3] = (int)fSum[3];
            if ((rgb[3] & 0xFFFFFF00) != 0)
                rgb[3] = ((rgb[3] & 0x80000000) != 0)?0:255;
        case 3:
            rgb[2] = (int)fSum[2];
            if ((rgb[2] & 0xFFFFFF00) != 0)
                rgb[2] = ((rgb[2] & 0x80000000) != 0)?0:255;
        case 2:
            rgb[1] = (int)fSum[1];
            if ((rgb[1] & 0xFFFFFF00) != 0)
                rgb[1] = ((rgb[1] & 0x80000000) != 0)?0:255;
        case 1:
            rgb[0] = (int)fSum[0];
            if ((rgb[0] & 0xFFFFFF00) != 0)
                rgb[0] = ((rgb[0] & 0x80000000) != 0)?0:255;
        }
    }

    Generates a Perlin noise pattern into dest Raster.
Params: dest – Raster to fill with the pattern./**
     * Generates a Perlin noise pattern into dest Raster.
     * @param dest Raster to fill with the pattern.
     */
    public WritableRaster copyData(WritableRaster dest) {
        //
        // First, check input arguments
        //
        if(dest==null)
            throw new IllegalArgumentException
                ("Cannot generate a noise pattern into a null raster");


        int w = dest.getWidth();
        int h = dest.getHeight();

        // Access the integer buffer for the destination Raster
        DataBufferInt dstDB = (DataBufferInt)dest.getDataBuffer();
        SinglePixelPackedSampleModel sppsm;
        int minX = dest.getMinX();
        int minY = dest.getMinY();
        sppsm = (SinglePixelPackedSampleModel)dest.getSampleModel();
        int dstOff = dstDB.getOffset() +
            sppsm.getOffset(minX - dest.getSampleModelTranslateX(),
                            minY - dest.getSampleModelTranslateY());

        final int[] destPixels = dstDB.getBankData()[0];
        int dstAdjust = sppsm.getScanlineStride() - w;

        // Generate pixel pattern now
        int i, end, dp=dstOff;
        final int[] rgb = new int[4];
        final double[] fSum = {0, 0, 0, 0};
        final double[] noise = {0, 0, 0, 0};

        final double tx0, tx1, ty0, ty1;
        tx0 = tx[0];
        tx1 = tx[1];
        // Update for y step, (note we substract all the stuff we
        // added while going across the scan line).
        ty0 = ty[0]-(w*tx0);
        ty1 = ty[1]-(w*tx1);

        double[] p = {minX, minY};
        txf.transform(p, 0, p, 0, 1);
        double point_0 = p[0];
        double point_1 = p[1];

        if(isFractalNoise){
            if(stitchInfo == null){
                if (channels.length == 4) {
                    for(i=0; i<h; i++){
                        for(end=dp+w; dp<end; dp++) {
                            destPixels[dp] = turbulenceFractal_4
                                (point_0, point_1, fSum);
                            point_0 += tx0;
                            point_1 += tx1;
                        }
                        point_0 += ty0;
                        point_1 += ty1;
                        dp += dstAdjust;
                    }
                } else {
                    for(i=0; i<h; i++){
                        for(end=dp+w; dp<end; dp++){
                            turbulenceFractal(rgb, point_0, point_1, fSum, noise);

                            // Write RGB value.
                            destPixels[dp] = ((rgb[3]<<24) |
                                              (rgb[0]<<16) |
                                              (rgb[1]<<8)  |
                                              (rgb[2]   ));
                            point_0 += tx0;
                            point_1 += tx1;
                        }
                        point_0 += ty0;
                        point_1 += ty1;
                        dp += dstAdjust;
                    }
                }
            }
            else{
                StitchInfo si = new StitchInfo();
                for(i=0; i<h; i++){
                    for(end=dp+w; dp<end; dp++){
                        si.assign(this.stitchInfo);
                        turbulenceFractalStitch(rgb, point_0, point_1,
                                                fSum, noise, si);

                        // Write RGB value.
                        destPixels[dp] = ((rgb[3]<<24) |
                                          (rgb[0]<<16) |
                                          (rgb[1]<<8)  |
                                          (rgb[2]   ));
                        point_0 += tx0;
                        point_1 += tx1;
                    }
                    point_0 += ty0;
                    point_1 += ty1;
                    dp += dstAdjust;
                }
            }
        }
        else{ // Loop for turbulence noise
            if(stitchInfo == null){
                if (channels.length == 4) {
                    for(i=0; i<h; i++){
                        for(end=dp+w; dp<end; dp++){
                            destPixels[dp] = turbulence_4
                                (point_0, point_1, fSum);

                            point_0 += tx0;
                            point_1 += tx1;
                        }
                        point_0 += ty0;
                        point_1 += ty1;
                        dp += dstAdjust;
                    }
                } else {
                    for(i=0; i<h; i++){
                        for(end=dp+w; dp<end; dp++){
                            turbulence(rgb, point_0, point_1, fSum, noise);

                            // Write RGB value.
                            destPixels[dp] = ((rgb[3]<<24) |
                                              (rgb[0]<<16) |
                                              (rgb[1]<<8)  |
                                              (rgb[2]   ));
                            point_0 += tx0;
                            point_1 += tx1;
                        }
                        point_0 += ty0;
                        point_1 += ty1;
                        dp += dstAdjust;
                    }
                }
            }
            else{
                StitchInfo si = new StitchInfo();
                for(i=0; i<h; i++){
                    for(end=dp+w; dp<end; dp++){
                        si.assign(this.stitchInfo);
                        turbulenceStitch(rgb, point_0, point_1,
                                         fSum, noise, si);

                        // Write RGB value.
                        destPixels[dp] = ((rgb[3]<<24) |
                                          (rgb[0]<<16) |
                                          (rgb[1]<<8)  |
                                          (rgb[2]   ));
                        point_0 += tx0;
                        point_1 += tx1;
                    }
                    point_0 += ty0;
                    point_1 += ty1;
                    dp += dstAdjust;
                }
            }
        }

        return dest;
    }

    Params: baseFrequencyX – x-axis base frequency for the noise
function along the x-axis
baseFrequencyY – y-axis base frequency for the noise
       function along the x-axis
numOctaves – number of octaves in the noise
       function. Positive integral value.
seed – starting number for the pseudo random number generator
isFractalNoise – defines whether the filter performs a
       fractal noise or a turbulence function.
tile – defines the tile size. May be null if stitchTiles
       is false. Otherwise, should not be null.
txf – The affine transform from device to user space.
cs – The Colorspace to output.
alpha – True if the data should have an alpha channel./**
     * @param baseFrequencyX x-axis base frequency for the noise
     * function along the x-axis
     * @param baseFrequencyY y-axis base frequency for the noise
     *        function along the x-axis
     * @param numOctaves number of octaves in the noise
     *        function. Positive integral value.
     * @param seed starting number for the pseudo random number generator
     * @param isFractalNoise defines whether the filter performs a
     *        fractal noise or a turbulence function.
     * @param tile defines the tile size. May be null if stitchTiles
     *        is false. Otherwise, should not be null.
     * @param txf The affine transform from device to user space.
     * @param cs The Colorspace to output.
     * @param alpha True if the data should have an alpha channel.
     */
    public TurbulencePatternRed(double baseFrequencyX,
                                double baseFrequencyY,
                                int     numOctaves,
                                int     seed,
                                boolean isFractalNoise,
                                Rectangle2D tile,
                                AffineTransform txf,
                                Rectangle       devRect,
                                ColorSpace      cs,
                                boolean         alpha) {
        this.baseFrequencyX = baseFrequencyX;
        this.baseFrequencyY = baseFrequencyY;
        this.seed = seed;
        this.isFractalNoise = isFractalNoise;
        this.tile = tile;
        this.txf  = txf;

        if(this.txf == null)
            this.txf = IDENTITY;

        int nChannels = cs.getNumComponents();
        if (alpha) nChannels++;
        channels = new int[nChannels];
        for(int i=0; i<channels.length; i++)
            channels[i] = i;

        txf.deltaTransform(tx, 0, tx, 0, 1);
        txf.deltaTransform(ty, 0, ty, 0, 1);

        double[] vecX = {.5, 0};
        double[] vecY = {0, .5};
        txf.deltaTransform(vecX, 0, vecX, 0, 1);
        txf.deltaTransform(vecY, 0, vecY, 0, 1);

        //
        // Now, limit the number of octaves so that we do not get frequencies
        // below half a pixel.
        //
        // If d is the distance between to pixels in user space, then,
        // numOctavesMax = -(log2(d) + log2(bf))
        // along one axis.
        //
        // The maximum distance along each axis is processed by
        // computing the inverse transform of 'maximum' vectors from
        // device space to the filter space and determining the
        // maximum component along each axis.

        double dx = Math.max(Math.abs(vecX[0]), Math.abs(vecY[0]));
        int maxX = -(int)Math.round((Math.log(dx) + Math.log(baseFrequencyX))/
                                    Math.log(2));

        double dy = Math.max(Math.abs(vecX[1]), Math.abs(vecY[1]));
        int maxY = -(int)Math.round((Math.log(dy) + Math.log(baseFrequencyY))/
                                    Math.log(2));

        this.numOctaves = numOctaves > maxX? maxX : numOctaves;
        this.numOctaves = this.numOctaves > maxY? maxY : this.numOctaves;

        if(this.numOctaves < 1 && numOctaves > 1)
            this.numOctaves = 1;

        if (this.numOctaves > 8)
            // beyond 8 octaves there is no significant contribution
            // to the output pixel (contribution is halved for each
            // octave so after 8 we are contributing less than half a
            // code value _at_best_).
            this.numOctaves = 8;

        if (tile != null) {
            //
            // Adjust frequencies to the tile size
            //
            double lowFreq = Math.floor(tile.getWidth()*baseFrequencyX)/tile.getWidth();
            double highFreq = Math.ceil(tile.getWidth()*baseFrequencyX)/tile.getWidth();
            if(baseFrequencyX/lowFreq < highFreq/baseFrequencyX)
                this.baseFrequencyX = lowFreq;
            else
                this.baseFrequencyX = highFreq;

            lowFreq = Math.floor(tile.getHeight()*baseFrequencyY)/tile.getHeight();
            highFreq = Math.ceil(tile.getHeight()*baseFrequencyY)/tile.getHeight();
            if(baseFrequencyY/lowFreq < highFreq/baseFrequencyY)
                this.baseFrequencyY = lowFreq;
            else
                this.baseFrequencyY = highFreq;

            //
            // Now, process the initial latice grid size to compute the minimum
            // and maximum latice values on each axis.
            //
            stitchInfo = new StitchInfo();
            stitchInfo.width = ((int)(tile.getWidth()*this.baseFrequencyX));
            stitchInfo.height = ((int)(tile.getHeight()*this.baseFrequencyY));
            stitchInfo.wrapX = ((int)(tile.getX()*this.baseFrequencyX +
                                      PerlinN + stitchInfo.width));
            stitchInfo.wrapY = ((int)(tile.getY()*this.baseFrequencyY +
                                      PerlinN + stitchInfo.height));

            // Protect agains zero frequencies.  Setting values to 1
            // will not affect the result of the computations.
            if(stitchInfo.width == 0) stitchInfo.width = 1;
            if(stitchInfo.height == 0) stitchInfo.height = 1;

            // System.out.println( "minLatticeX = " + minLatticeX +
            //                    " minLatticeY = " + minLatticeY +
            //                     " maxLatticeX = " + maxLatticeX +
            //                     " maxLatticeY = " + maxLatticeY);
        }

        initLattice(seed);

        ColorModel cm;
        if (alpha)
            cm = new DirectColorModel
                (cs, 32, 0x00FF0000, 0x0000FF00, 0x000000FF, 0xFF000000,
                 false, DataBuffer.TYPE_INT);
        else
            cm = new DirectColorModel
                (cs, 24, 0x00FF0000, 0x0000FF00, 0x000000FF, 0x0,
                 false, DataBuffer.TYPE_INT);

        int tileSize = AbstractTiledRed.getDefaultTileSize();
        init((CachableRed)null, devRect, cm,
             cm.createCompatibleSampleModel(tileSize, tileSize),
             0, 0, null);
    }

}
Author:	Vincent Hardy, Thomas DeWeese
Version:	$Id: TurbulencePatternRed.java 1808001 2017-09-11 09:51:29Z ssteiner $
Params:	pointX – x coordinate of the point to process. pointY – y coordinate of the point to process. fSum – array used to avoid reallocating double array for each pixel
Returns:	The ARGB pixel value.
/

org.apache.xmlgraphics/ batik-awt-util/ 1.13/ org/apache/batik/ext/awt/image/rendered/TurbulencePatternRed.java
