This chapter's project, one that views the Mandelbrot set, gives you examples of some of the more advanced concepts you have been introduced to. The Mandelbrot set is the most spectacular example of fractals, which represents one of the hot scientific topics of recent years. With the applets in this chapter, you can view or generate an original Mandelbrot image and zoom in and out of it to produce new portions of the set.
Since the Mandelbrot set can take a while to generate-requiring millions of calculations-it gives you a chance to combine threads and image filters so you can view the set as it's being generated. You might also want to save the Mandelbrot images. The BmpClass, introduced in Part III, that converts a BMP formatted file into a Java image, is enhanced so you can save the Mandelbrot data as a BMP file. You can then view or modify it with any tool that can handle the BMP format. Finally, the chapter concludes by showing how you can auto-document the source of a Java class into a HTML file. This can be viewed by a browser and has links to other classes.
Since you have already been introduced to most aspects of Java, this chapter will jump straight into the project. Topics will be introduced as appropriate.
There are actually two applets in this chapter. The first applet, MandelApp, is used to generate a full Mandelbrot set. The tools and BMP file produced by this applet are input into the second applet, called MandelZoomApp. This applet displays a Mandelbrot set, then allows you to zoom (magnify) portions of the set so you can inspect its fractal qualities. You can also return to previous images and zoom into another area.
If you want to use the file-saving capabilities of this program, you need to run it from something that does not prevent file saving, such as the appletviewer program. You can run the program in a browser like Netscape, though; it will be able to do everything except save the images as files.
Table 14.1 lists the classes used in this chapter's applets. Most
of the classes are new, so their names are set in boldface type.
Existing classes that were modified have their names italicized.
| Class/Interface | Description |
| BmpImage | For BMP-Image conversion. |
| CalculatorFilter | ImageFilter that produces updates of images as they are generated. |
| CalculatorFilterNotify | Interface that defines ways an ImageFilter can receive data updates. |
| CalculatorImage | Used to tie a calculation object, an image, and a CalculatorFilter together. |
| CalculatorProducer | Interface that defines a mechanism for establishing how an ImageFilter can update a calculation class. |
| MandelApp | An Applet that produces a full Mandelbrot image and lets you save it to a file. |
| MandelEntry | Accessor class for keeping information about a Mandelbrot image. |
| Mandelbrot | A Thread that produces Mandelbrot data for the specified parameters. It implements CalculatorProducer to get started by a filter. It uses CalculatorFilterNotify to update a filter with new data. |
| MandelZoomApp | An Applet that displays the full Mandelbrot set and allows you to zoom in and out of the set. |
Because the Mandelbrot set can take quite a while to generate, it was designed by combining a calculation thread with an image filter so you can see the results as they are generated. However, understanding how the classes interrelate is a little tricky. Figure 14.1 shows the workflow involved in producing a Mandelbrot image. Understanding this flow is the key to understanding this project.
Figure 14.1 : Workflow of producing a Mandelbrot image.
The process begins when an applet displaying Mandelbrot sets constructs a Mandelbrot object. (In this project, the two Applet classes are MandelApp and MandelZoomApp.) The Mandelbrot object, in turn, creates an instance of the CalculatorImage class. The Mandelbrot set passes itself as a part of the CalculatorImage constructor. It is referenced as a CalculatorProducer object, an interface that the Mandelbrot class implements. This interface implementation will be used to communicate with the image filter.
In the next step, the applet requests a Mandelbrot image. This is initiated by calling the getImage() method of the Mandelbrot object, which in turn leads to a call to a like-named method of the CalculatorImage object. At this point, the CalculatorImage object first creates a color palette by using an instance of the ImageColorModel class, then creates a MemoryImageSource object. This object, which implements ImageProducer, produces an image initialized to all zeros (black); it's combined with an instance of the CalculatorFilter class to produce a FilteredImageSource.
When the MemoryImageSource object produces its empty image, it is passed to the CalculatorFilter, which takes the opportunity to produce the calculated image. It does this by kicking off the thread of the image to be calculated. The CalculatorFilter doesn't know that it is the Mandelbrot set that's calculated-it just knows that some calculation needs to occur in the CalculatorProducer object in which it has a reference.
Once the Mandelbrot thread is started, it begins the long calculations to produce a Mandelbrot set. Whenever it finishes a section of the set, it notifies the filter with new data through the CalculatorFilterNotify interface. The filter, in turn, lets the viewing applet know that it has new data to display by updating the corresponding ImageConsumer, which causes the applet's imageUpdate() method to be called. This causes a repaint, and the new image data to be displayed. This process repeats until the full image is created.
As you have probably observed, this is a complicated process. Although the mechanics of image processing were introduced in Part III, it doesn't hurt to have another example. The Calculator classes here are meant to provide a generic approach toward manipulating images that need long calculations. You can replace the Mandelbrot class with some other calculation thread that implements CalculatorProducer, and everything should work. A good exercise would be to replace Mandelbrot with another fractal calculation or some other scientific imaging calculation (I found that replacing Mandelbrot with a Julia fractal class calculation was very easy).
Before going into the internals of the classes that make up this project, it's worth spending a couple of moments to understand what's behind the images produced by the Mandelbrot class.
In the 1970s, Benoit Mandelbrot at IBM was using computers to study curves generated by iterations of complex formulas. He found that these curves had unusual characteristics, one of which is called self-similarity. The curves have a series of patterns that repeat themselves when inspected more closely.
One of the characteristics of the curves Mandelbrot studied was that they could be described as having a certain dimensional quality that Mandelbrot termed "fractal." One of the fractals that Mandelbrot was investigating is called a Julia set. By mapping the set in a certain way, Mandelbrot came across a set that turned out to include all the Julia sets-a kind of a master set that was deemed the Mandelbrot set. This set has several spectacular features, all of them beautiful. The most striking of these is its self-similarity and a extraordinary sensitivity to initial conditions. As you explore the Mandelbrot set, you will be amazed by both its seeming chaos and exquisite order.
Figure 14.2 shows the famous Mandelbrot set, produced by this chapter's MandelApp applet. The figures in this chapter show the kind of images that appear when you zoom into various places in this set. The Mandelbrot set is based on a seemingly simple iterated function, shown in Formula 14.1.
Figure 14.2 : The full Mandelbrot set image.
Formula 14.1. Formula for calculating the Mandelbrot set.
zn+1=zn2 + c
In Formula 14.1, z and c
are complex numbers. The Mandelbrot set is concerned with what
happens when z0 is zero and
c is set over a range of
values. The real part of c
is set to the x-axis, and the complex portion corresponds to the
y-axis. A color is mapped to each point based on how quickly the
corresponding value of c
causes the iteration to reach infinity. The process of "zooming"
in and out of the Mandelbrot set is equivalent to defining what
ranges of c are going to
be explored. It is amazing that something so simple can yield
patterns so sophisticated!
| Note |
If you are more interested in chaos and fractals, there are a lot of places to turn. Chaos by James Gleick (Penguin, 1987) is a layman's introduction to the ideas and discoveries that gave rise to chaos theory and the study of fractals. Mandelbrot's The Fractal Geometry of Nature (W.H. Freeman, 1983) lays out his ideas on fractals and nature. For a rigorous mathematical treatment of fractals, see the beautiful book Fractals Everywhere (Academic Press, 1988), written by one of the foremost figures in fractals, Michael Barnsley. Among other things, Barnsley is a major innovator on how to use fractal geometrics to achieve high rates of data compression. For a no-nonsense approach to writing programs that display fractals, see Fractal Programming in C by Roger T. Stevens (M&T Books, 1989). The algorithms for the Mandelbrot set were developed from this book. The C programs in this book map very easily to Java-except for the underlying graphics tools, which were developed for MS-DOS. However, the image calculation classes created in this chapter aim to fill this gap. With Stevens's book and these classes, you should be able to move his C code right over to Java and begin exploring the amazing world of fractals! |
There are two applets in this chapter. The first applet, MandelApp, generates the full Mandelbrot set. This will take a little while, depending on your computer; for example, on a 486DX2-50 pc, it takes a couple of minutes. When the image is complete, indicated by a message on the browser's status bar, you can save the image to a BMP formatted file by clicking anywhere on the applet's display area. The file will be called mandel.bmp. Remember to run this applet from a program, such as appletviewer, that lets applets write to disk.
The other applet, MandelAppZoom, is more full-featured. It begins by loading the Mandelbrot bitmap specified by an HTML applet parameter tag. The default mandel1 corresponds to a BMP file and a data file that specifies x-y parameter values-included on this book's CD-ROM.
Once the image is up, you can pick regions to zoom in on by clicking on a point in the image, then dragging the mouse to the endpoint of the region you want to display. Enter z or Z on the keyboard, and the applet creates the image representing the new region of the Mandelbrot set. The key to this applet is patience! The calculations can take a little while to set up and run. The applet tries to help your patience by updating the status bar to indicate what is going on. Furthermore, the image filter displays each column of the set as the calculations advance.
You might select a region that doesn't appear to have anything interesting to show when you zoom in on it. You can stop a calculation in the middle by entering a or A on the keyboard. The applet will take a moment to wrap up, but then you can proceed. When you are having problems finding an interesting region to look at, try increasing the size of the highlighted area. This will yield a bigger area that is generated, giving you a better feel for what should be inspected. You get the best results by working with medium-sized highlighted regions, rather than large or small ones.
Figures 14.3 to 14.6 show what some of the zoomed-in regions of the Mandelbrot set look like. Figure 14.3 is a large area picked above the black "circles" of the full Mandelbrot set; Figure 14.5 explores an area between two of the black areas. The richest displays seem to occur at the boundaries of the black areas. The black color indicates that the particular value takes a long time to reach infinity. Consequently, these are also the regions that take the longest to calculate. You get what you pay for!
Figure 14.3 : Zoom in over block regions of Figure 14.2.
Figure 14.4 : Zoom in of Figure 14.3.
The zoom applet maintains a cache of processed images so you can move back and forth among the processed images. Table 14.2 lists the text codes for using the zoom applet.
Figure 14.5 : Zoom in between black regions of Figure 14.2.
Figure 14.6 : Zoom in of Figure 14.5.
| Action | |
| Abort current Mandelbrot calculation. | |
| Go to previous image. | |
| Go to next image. | |
| Remove all but full image from memory. | |
| Go to next image. | |
| Go to previous image. | |
| Save the current image to a BMP file prefixed by tempMandel. | |
| Zoom in on currently highlighted region. |
The Mandelbrot class, shown in Listing 14.1, calculates the Mandelbrot set. It implements the Runnable interface, so it can run as a thread, and also implements the CalculatorProducer interface, so it can update an image filter of progress made in its calculations.
There are two constructors for the Mandelbrot class. The default constructor produces the full Mandelbrot set and takes the dimensions of the image to calculate. The Real and Imagine variables in the constructors and the run() method are used to map the x-y axis to the real and imaginary portions of c in Formula 14.1. The other constructor is used to zoom in on a user-defined mapping.
A couple of the other variables are worth noting. The variable maxIterations represents when to stop calculating a number. If this number, set to 512, is reached, then the starting value of c takes a long time to head toward infinity. The variable maxSize is a simpler indicator of how quickly the current value grows. How the current calculation is related to these variables is mapped to a specific color; the higher the number, the slower the growth. If you have a fast computer, you can adjust these variables to get a richer or duller expression of the Mandelbrot set.
Once the thread is started (by the CalculatorFilter object through the start() method), the run() method calculates the Mandelbrot values and stores a color corresponding to the growth rate of the current complex number into a pixel array. When a column is complete, it uses the CalculateFilterNotify to let the related filter know that new data has been produced. It also checks to see whether you want to abort the calculation. Note how it synchronizes the stopCalc boolean object in the run() and stop() methods.
The calculation can take a while to complete. Still, it takes only a couple of minutes on a 486-based pc. This performance is quite a testament to Java! With other interpreted, portable languages you would probably be tempted to use the reset button because the calculations would take so long. With Java you get fast visual feedback on how the set unfolds.
A good exercise is to save any partially developed Mandelbrot set; you can use the saveBMP() method here. You also need some kind of data file to indicate where the calculation was stopped.
Listing 14.1. The Mandelbrot class.
import java.awt.image.*;
import java.awt.Image;
import java.lang.*;
// Class for producing a Mandelbrot set image...
public class Mandelbrot implements Runnable, CalculatorProducer {
int width; // The dimensions of the image...
int height;
CalculateFilterNotify filter; // Keeps track of image production...
int pix[]; // Pixels used to construct image...
CalculatorImage img;
// General Mandelbrot parameters...
int numColors = 256;
int maxIterations = 512;
int maxSize = 4;
double RealMax,ImagineMax,RealMin,ImagineMin; // Define sizes to build...
private Boolean stopCalc = new Boolean(false); // Stop calculations...
// Create standard Mandelbrot set
public Mandelbrot(int width,int height) {
this.width = width;
this.height = height;
RealMax = 1.20; // Default starting sizes...
RealMin = -2.0;
ImagineMax = 1.20;
ImagineMin = -1.20;
}
// Create zoom of Mandelbrot set
public Mandelbrot(int width,int height,double RealMax,double RealMin,
double ImagineMax,double ImagineMin) {
this.width = width;
this.height = height;
this.RealMax = RealMax; // Default starting sizes...
this.RealMin = RealMin;
this.ImagineMax = ImagineMax;
this.ImagineMin = ImagineMin;
}
// Start producing the Mandelbrot set...
public Image getImage() {
img = new CalculatorImage(width,height,this);
return img.getImage();
}
// Start thread to produce data...
public void start(int pix[],CalculateFilterNotify filter) {
this.pix = pix;
this.filter = filter;
new Thread(this).start();
}
// See if user wants to stop before completion...
public void stop() {
synchronized (stopCalc) {
stopCalc = Boolean.TRUE;
}
System.out.println("GOT STOP!");
}
// Create data here...
public void run() {
// Establish Mandelbrot parameters...
double Q[] = new double[height];
// Pixdata is for image filter updates...
int pixdata[] = new int[height];
double P,diffP,diffQ, x, y, x2, y2;
int color, row, column,index;
System.out.println("RealMax = " + RealMax + " RealMin = " + RealMin +
" ImagineMax = " + ImagineMax + " ImagineMin = " + ImagineMin);
// Setup calculation parameters...
diffP = (RealMax - RealMin)/(width);
diffQ = (ImagineMax - ImagineMin)/(height);
Q[0] = ImagineMax;
color = 0;
// Setup delta parameters...
for (row = 1; row < height; row++)
Q[row] = Q[row-1] - diffQ;
P = RealMin;
// Start calculating!
for (column = 0; column < width; column++) {
for (row = 0; row < height; row++) {
x = y = x2 = y2 = 0.0;
color = 1;
while ((color < maxIterations) &&
((x2 + y2) < maxSize)) {
x2 = x * x;
y2 = y * y;
y = (2*x*y) + Q[row];
x = x2 - y2 + P;
++color;
}
// plot...
index = (row * width) + column;
pix[index] = (int)(color % numColors);
pixdata[row] = pix[index];
} // end row
// Update column after each iteration...
filter.dataUpdateColumn(column,pixdata);
P += diffP;
// See if we were told to stop...
synchronized (stopCalc) {
if (stopCalc == Boolean.TRUE) {
column = width;
System.out.println("RUN: Got stop calc!");
}
} // end sync
} // end col
// Tell filter that we're done producing data...
System.out.println("FILTER: Data Complete!");
filter.setComplete();
}
// Save the Mandelbrot set as a BMP file...
public void saveBMP(String filename) {
img.saveBMP(filename,pix);
}
}
The CalculateFilterNotify interface defines the methods needed to update an image filter that works with a calculation thread. As shown in Listing 14.2, the "data" methods are used for conveying a new batch of data to the filter. The setComplete() method indicates that the calculations are complete.
Listing 14.2. The CalculateFilterNotify interface.
/* Interface for defining methods for updating a
Calculator Filter... */
public interface CalculateFilterNotify {
public void dataUpdate(); // Update everything...
public void dataUpdateRow(int row); // Update one row...
public void dataUpdateColumn(int col,int pixdata[]); // Update one column...
public void setComplete();
}
The CalculatorProducer interface, as shown in Listing 14.3, defines the method called when a calculation filter is ready to kick off a thread that produces the data used to generate an image. The CalculateFilterNotify object passed to the start() method is called by the producer whenever new data is yielded.
Listing 14.3. The CalculatorProducer interface.
// Interface for a large calculation to produce image...
interface CalculatorProducer {
public void start(int pix[],CalculateFilterNotify cf);
}
The CalculatorFilter class in Listing 14.4 is a subclass of ImageFilter. Its purpose is to receive image data produced by some long calculation (like the Mandelbrot set) and update any consumer of the the new data's image. The CalculatorProducer, indicated by variable cp, is what produces the data.
Since the ImageFilter class was explained in detail in Part III, issues related to this class are not repeated here. However, a couple of things should be pointed out. When the image is first requested, the filter gets the dimensions the consumer wants by a call of the setDimensions() method. At this point, the CalculatorFilter will allocate a large array holding the color values for each pixel.
When the original ImageProducer is finished creating the original image, the filter's imageComplete() method will be called, but the filter needs to override this method. In this case, the CalculatorFilter will start the CalculatorProducer thread, passing it the pixel array to put in its updates. Whenever the CalculatorProducer has new data, it will call one of the four methods specified by the CalculateFilterNotify interface: dataUpdate(), dataUpdateRow(), dataUpdateColumn(), or setComplete(). (The dataUpdateColumn() method is called by the Mandelbrot calculation since it operates on a column basis.) In each of these cases, the filter updates the appropriate consumer pixels by using the setPixels() method, then calls the consumer's imageComplete() method to indicate the nature of the change. For the three "data" methods, the updates are only partial, so a SINGLEFRAMEDONE flag is sent. The setComplete() method, on the other hand, indicates that everything is complete, so it sets a STATICIMAGEDONE flag.
Listing 14.4. The CalculatorFilter class.
import java.awt.image.*;
import java.awt.Image;
import java.awt.Toolkit;
import java.lang.*;
public class CalculatorFilter extends ImageFilter
implements CalculateFilterNotify {
private ColorModel defaultRGBModel;
private int width, height;
private int pix[];
private boolean complete = false;
private CalculatorProducer cp;
private boolean cpStart = false;
public CalculatorFilter(ColorModel cm,CalculatorProducer cp) {
defaultRGBModel = cm;
this.cp = cp;
}
public void setDimensions(int width, int height) {
this.width = width;
this.height = height;
pix = new int[width * height];
consumer.setDimensions(width,height);
}
public void setColorModel(ColorModel model) {
consumer.setColorModel(defaultRGBModel);
}
public void setHints(int hints) {
consumer.setHints(ImageConsumer.RANDOMPIXELORDER);
}
public void resendTopDownLeftRight(ImageProducer p) {
}
public void setPixels(int x, int y, int w, int h,
ColorModel model, int pixels[],int off,int scansize) {
}
public void imageComplete(int status) {
if (!cpStart) {
cpStart = true;
dataUpdate(); // Show empty pixels...
cp.start(pix,this);
} // end if
if (complete)
consumer.imageComplete(ImageConsumer.STATICIMAGEDONE);
}
// Called externally to notify that more data has been created
// Notify consumer so they can repaint...
public void dataUpdate() {
consumer.setPixels(0,0,width,height,
defaultRGBModel,pix,0,width);
consumer.imageComplete(ImageConsumer.SINGLEFRAMEDONE);
}
// External call to update a specific pixel row...
public void dataUpdateRow(int row) {
// The key thing here is the second to last parameter (offset)
// which states where to start getting data from the pix array...
consumer.setPixels(0,row,width,1,
defaultRGBModel,pix,(width * row),width);
consumer.imageComplete(ImageConsumer.SINGLEFRAMEDONE);
}
// External call to update a specific pixel column...
public void dataUpdateColumn(int col,int pixdata[]) {
// The key thing here is the second to last parameter (offset)
// which states where to start getting data from the pix array...
consumer.setPixels(col,0,1,height,
defaultRGBModel,pixdata,0,1);
consumer.imageComplete(ImageConsumer.SINGLEFRAMEDONE);
}
// Called from external calculating program when data has
// finished being calculated...
public void setComplete() {
complete = true;
consumer.setPixels(0,0,width,height,
defaultRGBModel,pix,0,width);
consumer.imageComplete(ImageConsumer.STATICIMAGEDONE);
}
}
The CalculatorImage class, shown in Listing 14.5, is the glue between the CalculatorProducer class that produces the image data and the CalculatorFilter that manages it. When an image is requested with the getImage() method, the CalculatorImage creates a color palette through an instance of the ImageColorModel class, then creates a MemoryImageSource object. This ImageProducer object produces an image initialized to all zeros (black). It is combined with an instance of the CalculatorFilter class to produce a FilteredImageSource. When the createImage() method of the Toolkit is called, production of the calculated image begins.
The color palette is a randomly generated series of pixel values. Depending on your luck, these colors can be attractive or uninspiring. The createPalette() method is a good place to create a custom set of colors for this applet, if you want to have some control over its appearance. You should replace the random colors with hard-coded RGB values, and you might want to download a URL file that specifies a special color mapping.
Listing 14.5. The CalculatorImage class.
// This class takes a CalculatorProducer and sets up the
// environment for creating a calculated image. Ties the
// producer to the CalculatorFilter so incremental updates can
// be made...
public class CalculatorImage {
int width; // The dimensions of the image...
int height;
CalculatorProducer cp; // What produces the image data...
IndexColorModel palette; // The colors of the image...
// Create Palette only once per session...
static IndexColorModel prvPalette = null;
int numColors = 256; // Number of colors in palette...
// Use defines how big of an image they want...
public CalculatorImage(int width,int height,CalculatorProducer cp) {
this.width = width;
this.height = height;
this.cp = cp;
}
// Start producing the Calculator image...
public synchronized Image getImage() {
// Hook into the filter...
createPalette();
ImageProducer p = new FilteredImageSource(
new MemoryImageSource(width,height,palette,
(new int[width * height]),0,width),
new CalculatorFilter(palette,cp));
// Return the image...
return Toolkit.getDefaultToolkit().createImage(p);
}
// Create a 256 color palette...
// Use Default color model...
void createPalette() {
// Create palette only once per session...
if (prvPalette != null) {
palette = prvPalette;
return;
}
// Create a palette out of random RGB combinations...
byte blues[], reds[], greens[];
reds = new byte[numColors];
blues = new byte[numColors];
greens = new byte[numColors];
// First and last entries are black and white...
blues[0] = reds[0] = greens[0] = (byte)0;
blues[255] = reds[255] = greens[255] = (byte)255;
// Fill in other entries...
for ( int x = 1; x < 254; x++ ){
reds[x] = (byte)(255 * Math.random());
blues[x] = (byte)(255 * Math.random());
greens[x] = (byte)(255 * Math.random());
}
// Create Index Color Model...
palette = new IndexColorModel(8,256,reds,greens,blues);
prvPalette = palette;
}
// Save the image set as a BMP file...
public void saveBMP(String filename,int pix[]) {
try {
BmpImage.saveBitmap(filename,palette,
pix,width,height);
}
catch (IOException ioe) {
System.out.println("Error saving file!");
}
}
}
The MandelApp class, shown in Listing 14.6, creates and displays the full Mandelbrot set; the end result is shown in Figure 14.2. An instance of the Mandelbrot class is created in the init() method. Whenever the Mandelbrot calculation has produced some new data, it calls the ImageObserver-based method, imageUpdate(). This will probably result in the applet being repainted to show the new data. If the image is complete, an internal flag is set. After this, if you click the mouse, the image will be saved to a BMP formatted file called mandel.bmp.
Listing 14.6. The MandelApp class.
import java.awt.*;
import java.lang.*;
import java.applet.Applet;
// This applet displays the Mandlebrot set through
// use of the Mandelbrot class...
public class MandelApp extends Applet {
Image im; // Image that displays Mandelbrot set...
Mandelbrot m; // Creates the Mandelbrot image...
int NUMCOLS = 640; // Dimensions image display...
int NUMROWS = 350;
boolean complete = false;
// Set up the Mandelbrot set...
public void init() {
m = new Mandelbrot(NUMCOLS,NUMROWS);
im = m.getImage();
}
// Will get updates as set is being created.
// Repaint when they occur...
public boolean imageUpdate(Image im,int flags,
int x, int y, int w, int h) {
if ((flags & FRAMEBITS) != 0) {
showStatus("Calculating...");
repaint();
return true;
}
if ((flags & ALLBITS) != 0) {
showStatus("Image Complete!");
repaint();
complete = true;
return false;
}
return true;
}
// Paint on update...
public void update(Graphics g) {
paint(g);
}
public synchronized void paint(Graphics g) {
g.drawImage(im,0,0,this);
}
// Save Bitmap on mouse down when image complete...
public boolean mouseDown(Event evt,int x, int y) {
if (complete) {
showStatus("Save Bitmap...");
m.saveBMP("mandel.bmp");
showStatus("Bitmap saved!");
return true;
} // end if
return false;
}
}
Listing 14.7 shows the MandelZoomApp class, which represents this chapter's main applet; its function was described earlier, in the section "Using the Applets." See this section and Table 14.1 for how to use the applet.
The most interesting features in the code are the routines for marking the region to be highlighted. Each pixel on the displayed Mandelbrot image maps an x-y value to a real-imaginary value of the c value of the Mandelbrot formula shown in Formula 14.1. Whenever you move the cursor, the current real-imaginary values are shown in the browser's status bar. When you highlight an area to zoom in on, you are really picking a range of c values to be explored. All the double variables are used for tracking this range of values. These values are read in at initialization by the loadParameters() method to match the bitmap that's displayed. You can specify other Mandelbrot BMP files and corresponding data files by changing the filename parameter of the applet's <APPLET> tag.
The Zoom() method takes the currently highlighted range and brings up a new Mandelbrot image that corresponds to this range. It uses the same calculation-image filtering techniques that the MandelApp class does.
Listing 14.7. The MandelZoomApp class.
// This applet displays the Mandelbrot set bitmap specified
// in the APPLET tag parameters. You can then zoom and in
// and out of the bitmap by dragging a region to paint.
// And then clicking on the appropriate option...
// Z or z - Zoom
// S or s - Save.
public class MandelZoomApp extends Applet {
Image img;
boolean zoomOn = false;
double XLeft,XRight,YTop,YBottom,XDelta,YDelta;
double currentX,currentY;
double startX,startY,endX,endY; // Zooming coordinates...
Rectangle markingRectangle; // Zooming rectangle...
Mandelbrot m; // Creates the Mandelbrot image...
int NUMCOLS = 640; // Dimensions image display...
int NUMROWS = 350;
boolean complete = false;
// Array for keeping track of Mandelbrot entries...
MandelEntry me[];
int lastIndex; // Top of array...
int currentIndex;
// Set up the Mandelbrot set specified in the parameters...
public void init() {
img = null;
m = null;
// Get parameter of bitmap to display...
String filename;
if ((filename = getParameter("filename")) == null)
filename = "mandel1";
// Load the bitmap...
loadBitmap(filename);
// Initialize Mandelbrot array...
me = new MandelEntry[40];
me[0] = new MandelEntry(null,img,XLeft,XRight,YTop,YBottom);
lastIndex = 0;
currentIndex = 0;
}
// ZOOM onto Mandelbrot set if all is good...
void Zoom() {
// No Zooming if off or no rectangle...
if ((!zoomOn) || (markingRectangle == null)) {
showMsg("Nothing marked or Zooming disable...");
return;
} // end if
// See if Mandelbrot table is full...
if ((lastIndex + 1) >= me.length) {
showMsg("Mandelbrot table full. Clear with C before zooming");
return;
}
showMsg("ZOOM: SX=" + startX + " SY=" + startY + " EX=" + endX + " EY=" + endY);
// Load new Mandelbrot...
complete = false;
zoomOn = false;
markingRectangle = null; // Reset marking rectangle...
m = new Mandelbrot(NUMCOLS,NUMROWS,endX,startX,
endY,startY);
img = m.getImage();
// Store in Mandelbrot table...
XLeft = startX;
XRight = endX;
YTop = startY;
YBottom = endY;
XDelta = Math.abs(XRight - XLeft);
YDelta = Math.abs(YBottom - YTop);
++lastIndex;
me[lastIndex] = new MandelEntry(m,img,startX,endX,startY,endY);
currentIndex = lastIndex;
showMsg("Calculating...");
repaint();
}
// Paint on update...
public void update(Graphics g) {
paint(g);
}
public synchronized void paint(Graphics g) {
if (img == null)
return;
// Show image...
g.drawImage(img,0,0,this);
// Show marking rectangle if exists...
if (markingRectangle != null) {
g.drawRect(markingRectangle.x,markingRectangle.y,
markingRectangle.width,markingRectangle.height);
} // end if
}
// Will get updates as set is being created.
// Repaint when they occur...
public boolean imageUpdate(Image im,int flags,
int x, int y, int w, int h) {
if ((flags & FRAMEBITS) != 0) {
repaint();
return true;
}
if ((flags & ALLBITS) != 0) {
showMsg("Image Complete!");
repaint();
complete = true;
zoomOn = true;
return false;
}
return true;
}
// Load a bitmap and accompanying data file...
void loadBitmap(String filename) {
// Zoom is false unless both succeed...
zoomOn = false;
markingRectangle = null; // Reset marking rectangle...
// Load the bitmap...
try {
showMsg("Load image...");
ImageProducer producer = BmpImage.getImageProducer(
getDocumentBase(), filename + ".bmp");
img = createImage(producer);
showMsg("Image loaded...");
}
catch (AWTException e){
img = null;
showMsg("Cannot open file " + filename);
return;
}
// Load the zoom parameters.
// Turn Zoom on if all works...
try {
loadParameters(filename);
zoomOn = true;
complete = true;
}
catch (IOException e){
showMsg("Cannot load parameter data. " + e.getMessage());
}
}
// Load the parameters. Throw IO Exception...
public void loadParameters(String filename) throws IOException {
// Create URL for data...
URL u;
try {
u = new URL(getDocumentBase(),filename + ".dat");
}
catch (MalformedURLException e) {
showMsg("Bad Data URL");
throw new IOException("Bad URL");
}
// Now load the data by opening up a stream
// to the URL...
DataInputStream dis = new DataInputStream(
new BufferedInputStream(u.openStream() ) );
// Read only the first line...
String param = dis.readLine();
// Tokenize out the boundary values....
StringTokenizer s = new StringTokenizer(param,",");
try {
XLeft = Double.valueOf(s.nextToken()).doubleValue();
XRight = Double.valueOf(s.nextToken()).doubleValue();
YTop = Double.valueOf(s.nextToken()).doubleValue();
YBottom = Double.valueOf(s.nextToken()).doubleValue();
XDelta = Math.abs(XRight - XLeft);
YDelta = Math.abs(YBottom - YTop);
}
catch (NumberFormatException e) {
throw new IOException("Improperly formatted data...");
}
catch (NoSuchElementException e) {
throw new IOException("Improperly formatted data...");
}
}
// Track mouse to show fractal values and to
// mark area to zoom
public boolean handleEvent(Event evt) {
switch(evt.id) {
case Event.KEY_PRESS: {
// Z or z means Zoom
if ((evt.key == 'z') || (evt.key == 'Z'))
Zoom();
// S or s means Save
if ((evt.key == 's') || (evt.key == 'S'))
saveFile();
// A or a means Abort Zoom calculation...
if ((evt.key == 'a') || (evt.key == 'A')) {
if (m != null) {
showMsg("Aborting calculation...");
m.stop();
} // end if
}
// P or p means previous image...
if ((evt.key == 'p') || (evt.key == 'P'))
previousImage();
// B or b means previous image...
if ((evt.key == 'B') || (evt.key == 'b'))
previousImage();
// N or n means next image...
if ((evt.key == 'N') || (evt.key == 'n'))
nextImage();
// F or f means next image...
if ((evt.key == 'F') || (evt.key == 'f'))
nextImage();
// C or c means clear images
if ((evt.key == 'C') || (evt.key == 'c'))
clearImage();
return true;
}
// Mouse clicks. Start marking...
case Event.MOUSE_DOWN: {
startMarking(evt.x,evt.y);
return false;
}
case Event.MOUSE_DRAG: {
dragMarking(evt.x,evt.y);
return false;
}
case Event.MOUSE_UP: {
stopMarking(evt.x,evt.y);
return false;
}
case Event.MOUSE_MOVE: {
showPosition(evt.x,evt.y);
return false;
}
default:
return false;
}
}
// Save the image as a file...
void saveFile() {
// Don't save if we are loading...
if (!complete)
return;
// Get Mandelbrot reference, if exists...
Mandelbrot mb = me[currentIndex].getMandelbrot();
if (mb == null) {
showStatus("Cannot save. Not generated in this session");
return;
} // end if
// Generate the filename...
String filename = "tempMandel" + (currentIndex + 1) + ".bmp";
// Security test...
try {
System.getSecurityManager().checkWrite(filename);
}
catch (SecurityException e) {
showStatus("Write not permitted!");
return;
}
// Save the image...
showStatus("Saving image as " + filename + "...");
mb.saveBMP(filename);
showStatus("Image saved as " + filename);
}
// Routines for moving through Mandelbrot table...
// Load previous image...
void previousImage() {
// Nothing if we are loading...
if (!complete)
return;
// Do nothing if at top index...
if (currentIndex == 0) {
showMsg("At Top index");
return;
}
// Go to previous image...
reloadImage(currentIndex - 1);
}
// Load next image...
void nextImage() {
// Nothing if we are loading...
if (!complete)
return;
// Do nothing if at last index...
if (currentIndex == lastIndex) {
showMsg("At Last index");
return;
}
// Go to next image...
reloadImage(currentIndex + 1);
}
// Reload index from Mandelbrot array...
void reloadImage(int index) {
showMsg("Reloading image...");
currentIndex = index;
complete = true;
zoomOn = true;
markingRectangle = null; // Reset marking rectangle...
// Get data from Mandelbrot table...
img = me[currentIndex].getImage();
XLeft = me[currentIndex].getXLeft();
XRight = me[currentIndex].getXRight();
YTop = me[currentIndex].getYTop();
YBottom = me[currentIndex].getYBottom();
XDelta = Math.abs(XRight - XLeft);
YDelta = Math.abs(YBottom - YTop);
repaint();
}
// Remove everything but first image from stack...
void clearImage() {
for (int i = 1; i <= lastIndex; ++i)
me[i] = null;
// Go back to first image...
lastIndex = 0;
reloadImage(0);
}
// ************************************
// Routines for mouse tracking...
// ************************************
boolean TrackingOn = false;
int leftX,topY;
// Start marking a zoom rectangle, erase existing one...
void startMarking(int x,int y) {
// Get current positions... Clear marking if invalid...
if (!showPosition(x,y)) {
TrackingOn = false;
markingRectangle = null;
repaint();
return;
} // end if
// Else, start marking...
TrackingOn = true;
startX = currentX;
startY = currentY;
endX = currentX;
endY = currentY;
leftX = x;
topY = y;
// Set marking rectangle and repaint...
markingRectangle = new Rectangle(x,y,1,1);
repaint();
}
// Expand square of dragging unless invalid...
void dragMarking(int x,int y) {
// Get current positions... Clear marking if invalid...
boolean good = showPosition(x,y);
// See if other marking conditions hold.
// Such as going in a bad direction...
if (good) {
if ((!TrackingOn) || (x < leftX) || (y < topY))
good = false;
}
// Clear out if marking is bad...
if (!good) {
TrackingOn = false;
markingRectangle = null;
repaint();
return;
} // end if
// Set new marking rectangle and repaint...
endX = currentX;
endY = currentY;
markingRectangle = new Rectangle(leftX,topY,
x - leftX,y - topY);
repaint(leftX,topY,markingRectangle.width + 1,
markingRectangle.height + 1);
}
// Stop marking...
void stopMarking(int x,int y) {
showPosition(x,y);
TrackingOn = false;
// Kill if too small...
if (markingRectangle != null) {
if ((markingRectangle.width < 3) ||
(markingRectangle.height < 3)) {
markingRectangle = null;
} // end if
}
repaint();
}
// Show current position to status if an image has
// been prepared...
// Returns true if good position, else bad...
boolean showPosition(int x,int y) {
// Return if not ready to zoom...
if ((img == null) || (!zoomOn))
return false;
// See if we are in the display area...
int width = img.getWidth(this);
int height = img.getHeight(this);
if ((x > width) || y > height) {
showStatus("");
return false;
} // end if
currentX = XLeft + (XDelta * (((double)x)/((double)width)));
currentY = YTop + (YDelta * (((double)y)/((double)height)));
showStatus(currentX + " : " + currentY);
return true;
}
// Print a message to standard out and the status bar...
public void showMsg(String s) {
System.out.println(s);
showStatus(s);
}
}
A cache is maintained so that you can move back and forth between images. The cache is an array of MandelEntry accessor objects; the MandelEntry class is shown in Listing 14.8. The cache is set to store up to 40 images. If you fill up the cache, press C or c to clear the cache of everything but the full Mandelbrot set image. As an exercise, you might want to make the caching mechanism more sophisticated so that it can bring in existing files, delete individual images, and so forth.
Note that there is a little trick in the saveFile() method. It uses the SecurityManager to see whether file writes are allowed. This is a way of checking the browser's security before a write is attempted. If file writing is prohibited, a SecurityException is thrown. How this works will differ from browser to browser.
Listing 14.8. The MandelEntry class.
// Store Mandelbrot images and corresponding coordinates...
class MandelEntry {
Mandelbrot m;
Image img;
double XLeft,XRight,YTop,YBottom;
// Constructor: Store data...
public MandelEntry(Mandelbrot m,Image img,double XLeft,
double XRight,double YTop,double YBottom) {
this.m = m;
this.img = img;
this.XLeft = XLeft;
this.XRight = XRight;
this.YTop = YTop;
this.YBottom = YBottom;
}
// Accessor methods...
public Mandelbrot getMandelbrot() {
return m;
}
public Image getImage() {
return img;
}
public double getXLeft() {
return XLeft;
}
public double getXRight() {
return XRight;
}
public double getYTop() {
return YTop;
}
public double getYBottom() {
return YBottom;
}
}
The BmpImage class, introduced in Part III of this book, reads images stored in the BMP format and converts them into a form Java can use. In this chapter, more functions were added to the class so that it could write the BMP back out to a file (shown in Listing 14.9). It's basically the opposite of the reading process discussed in Part III.
Listing 14.9. Adding BMP saving to the BmpImage class.
import java.lang.String;
import java.io.*;
import java.net.*;
import java.awt.*;
import java.awt.image.*;
/**
* This is a class that reads and writes a
* BMP formatted file
*/
public class BmpImage
{
// ... EXISTING CODE GOES HERE!!!
/**
* Write out a bitmap...
* Current only supporting 8 bits per pixel...
* @String filename - The file to save it as...
* @IndexColorModel ICM - Palette to use
* @int pix[] - Pixels to save
* @int width - Width of data
* @int height - Height of data
*/
public static void saveBitmap(String filename,
IndexColorModel ICM, int pix[],
int width, int height) throws IOException {
// Create output stream...
BmpImage b = new BmpImage(filename);
DataOutputStream os = new DataOutputStream(
new BufferedOutputStream(
new FileOutputStream(filename) ) );
b.writeFileHeader(os,ICM,width,height);
b.write8bitWindowsHeader(os,ICM,width,height);
b.write8bitColorIndex(os,ICM);
b.write8bitData(os,pix,width,height);
os.close();
}
/**
* Write out the file header
* @DataOutputStream os - The output stream to write
* @IndexColorModel ICM - Palette to use
* @int width - Width of data
* @int height - Height of data
*/
public void writeFileHeader(DataOutputStream os,
IndexColorModel ICM,
int width, int height) throws IOException {
byte b[] = new byte[4];
// Write out magic code...
b[0] = 'B';
b[1] = 'M';
os.write(b,0,2);
// Calculate size and offset..
int paletteSize = (ICM.getMapSize() * 4);
int offset = 54 + paletteSize;
int fileSize = offset + (width * height);
// Write out size & offset...
pushVal(os,fileSize,4);
pushVal(os,0,4);
pushVal(os,offset,4);
}
/**
* Write the bitmap header out to Windows...
* @DataOutputStream os - The output stream to write
* @IndexColorModel ICM - Palette to use
* @int width - Width of data
* @int height - Height of data
*/
public void write8bitWindowsHeader(DataOutputStream os,
IndexColorModel ICM,
int width, int height) throws IOException {
pushVal(os,40,4); // Bytes in header
pushVal(os,width,4); // Size in pixels...
pushVal(os,height,4);
pushVal(os,1,2); // # Color Planes
pushVal(os,8,2); // Bits per pixel...
pushVal(os,0,4); // NO Compression...
pushVal(os,width * height,4); // Size of image...
// LATER PUT IN REAL DATA pixels/meter
pushVal(os,3790,4); // TBD: Horizontal Res pixels/meter
pushVal(os,3790,4); // TBD: Vertical Res pixels/meter
pushVal(os,ICM.getMapSize(),4); // Indexes in bitmap...
pushVal(os,ICM.getMapSize(),4); // Indexes in bitmap...
}
/**
* Write the bitmap header out to Windows...
* @DataOutputStream os - The output stream to write
* @IndexColorModel ICM - Palette to use
*/
public void write8bitColorIndex(DataOutputStream os,
IndexColorModel ICM) throws IOException {
// Create RGB array...
int paletteSize = ICM.getMapSize();
byte blues[] = new byte[paletteSize];
byte greens[] = new byte[paletteSize];
byte reds[] = new byte[paletteSize];
byte b[] = new byte[4];
// Copy RGB arrays...
ICM.getBlues(blues);
ICM.getGreens(reds);
ICM.getReds(reds);
// Write out palette...
for (int i = 0; i < paletteSize; ++i) {
b[0] = (byte)blues[i];
b[1] = (byte)greens[i];
b[2] = (byte)reds[i];
b[3] = (byte)0;
os.write(b,0,4);
} // end for
}
/**
* Write out data of bitmap...
* @DataOutputStream os - The output stream to write
* @IndexColorModel ICM - Palette to use
* @int pix[] - Pixels to save
* @int width - Width of data
* @int height - Height of data
*/
public void write8bitData(DataOutputStream os,
int pix[],int width, int height) throws IOException {
// Bytes b...
byte b[] = new byte[width];
for (int i = 0; i < 4; ++i)
b[i] = 0;
// Calculate padding
int padding = 0;
int overage = width % 4;
if (overage != 0)
padding = 4 - overage;
// Write out starting from bottom of height
int index,x,y;
for (y = (height - 1); y >= 0; -y) {
// Write out each row, send to big buffer...
index = (y * width);
for (x = 0; x < width; ++x,++index)
b[x] = (byte)pix[index];
// Write out a big block...
os.write(b,0,width);
// Send out padding...
if (padding != 0) {
for (int i = 0; i < 4; ++i)
b[i] = 0;
os.write(b,0,padding);
}
System.out.print("."); System.out.flush();
} // end y for
System.out.println("Write done!");
}
/**
* Write out integer to little endian stream...
* @DataOutputStream os - The output stream to write
* @int data - Data to convert
* @int len - Length of array to convert
*/
private void pushVal(DataOutputStream os,
int data,int len) throws IOException {
byte b[] = new byte[len];
for (int i = 0; i < len; ++i) {
b[i] = (byte)(data >> (i * 8));
}
os.write(b,0,len);
}
The last thing covered in this chapter is how to auto-document your code. The tool javadoc, provided with the JDK, can take a properly formatted file and convert it into an HTML file, complete with links to the classes it references (assuming those classes are also run through javadoc). The BmpImage.java is such a file; its HTML output from javadoc is shown in Figure 14.7 and is included on this book's CD-ROM.
Figure 14.7 : BmpImage HTML after being run through javadoc.
Comments that should appear in the HTML are marked by appearing between /** and */, as shown at the beginning of the source code in Listing 14.9. The javadoc tool figures out a lot of things on its own, such the superclass, what external classes are used, and the individual parts of a method or variable declaration. You can specify additional information for each method by preceding certain keywords with an @. These keywords include param, returns, and exception for documenting parameters, return values, and exceptions thrown, respectively. For example, here is the declaration for getImageProducer():
/**
* A method to retreive an ImageProducer given just a BMP URL.
* @param context contains the base URL (from getCodeBase() or such)
* @returns an ImageProducer
* @exception AWTException on stream or bitmap data errors
*/
Look at the HTML to see what this looks like.
You will need to place the HTML output in the right directory for everything to work properly. You can also document an entire package by passing the package name to javadoc.
The major work of this book began in Part II with a series of discussions on how to use the AWT package. The spreadsheet applet was used to show how to incrementally build an applet using AWT. Since AWT is the basis for constructing the user interface of your Java applets, you need to know the package well. While constructing the spreadsheet, you also learned the subtleties of the java.io package and how to create exception handlers. By the end of Part II, you had seen most of the basics of Java applet programming.
Part III took everything a step further. You discovered the underlying classes behind applets and images and saw how threads can be used to enhance your application. Part III concluded with showing you how AWT, the applet classes, images, and threads could be brought together to create a Catalog applet, whose key element was a background image loader running as a thread. Although this applet was not a final product, it could-combined with the client/server mechanisms of Part IV-be the basis for producing a serious catalog application for use on the World Wide Web.
In Part IV, you incorporated the lessons of the previous chapters to create the most complex application of the book. You saw how to use the Java network classes to create a client-server application, and how to use native methods to take full advantage of a particular platform's features. The client applet demonstrated how Java could be used to represent data as it changes in real time. The election applet in Part IV was just the beginning of what you can create with Java client-server technology.
Part V allowed you to focus on some of the more advanced features of Java. You saw how HotJava, although still in its infancy, has features that indicate the future of browsers and Java programming. You also saw how to use Java's image classes to create advanced animation and image-processing applets. With a knowledge of these advanced imaging techniques, you can now use Java to produce images more sophisticated than just a banner moving across the screen.
You have been given the tools to write great Java applets for the Internet, the intranet, or anywhere else Java calls. Go for it!