Creating figures 
There are some basic elements here: a grid, axes, a graph, points and a line. Our goal is to develop some classes that can be easily reused to create illustrations like this. 
Figure API ANCHOR
Let's think about what we'll need to draw this figure.
In fact, each of the items above will be an object. ANCHOR BoundingBox
The viewing rectangle will be important for setting up the change of coordinates and for drawing both the grid and the graph. We will create a class BoundingBox to help us pass the information around easily.
public class BoundingBox { public double llx, lly, urx, ury; public BoundingBox(double lowerLeftX, double lowerLeftY, double upperRightX, double upperRightY) { llx = lowerLeftX; lly = lowerLeftY; urx = upperRightX; ury = upperRightY; } }
Notice that all a BoundingBox does is store information. ANCHOR FigurePanel
We will create an extension of JPanel, called FigurePanel, in a moment. Let's think about what we want out of it.
public FigurePanel(double llx, double lly, double urx, double ury) { bbox = new BoundingBox(llx, lly, urx, ury); }ANCHOR FigurePanel's paintComponent method
Here we will simply determine the AffineTransform and ask the grid and graph to draw themselves on the Graphics2D.
public void paintComponent(Graphics gfx) { super.paintComponent(gfx); Rectangle size = getBounds(); if (size.width != width  size.height != height  transform == null) { width = size.width; height = size.height; float ratioX = (float) (width / (bbox.urx  bbox.llx)); float ratioY = (float) (height/(bbox.ury  bbox.lly)); transform = new AffineTransform(); transform.scale(ratioX, ratioY); transform.translate(bbox.llx, bbox.ury); } Graphics2D g = (Graphics2D) gfx; g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON); g.setRenderingHint(RenderingHints.KEY_STROKE_CONTROL, RenderingHints.VALUE_STROKE_PURE); for (int i = 0; i < plotables.size(); i++) ((Plotable) plotables.elementAt(i)).plot(g, bbox, transform); }ANCHOR What is a plotable?
The graphical elements will simply contain code for drawing themselves. We will have them extend a class called Plotable.
Axes GraphicalEllipse GraphicalFunction GraphicalLine GraphicalPoint GridANCHOR Plotable
import java.awt.*; import java.awt.geom.*; public abstract class Plotable { Color color = Color.black; public abstract void plot(Graphics2D g, BoundingBox bbox, AffineTransform transform); public void setColor(Color c) { color = c; } }ANCHOR How do we extend Plotable?
Here is Grid.java:
import java.awt.*; import java.awt.geom.*; public class Grid extends Plotable { public void plot(Graphics2D g, BoundingBox bbox, AffineTransform transform) { GeneralPath path = new GeneralPath(); int minX = (int) Math.floor(Math.min(bbox.llx, bbox.urx)); int maxX = (int) Math.ceil(Math.max(bbox.llx, bbox.urx)); for (int x = minX; x <= maxX; x++) { path.moveTo(x, (float) bbox.lly); path.lineTo(x, (float) bbox.ury); } int minY = (int) Math.floor(Math.min(bbox.lly, bbox.ury)); int maxY = (int) Math.ceil(Math.max(bbox.lly, bbox.ury)); for (int y = minY; y <= maxY; y++) { path.moveTo((float) bbox.llx, y); path.lineTo((float) bbox.urx, y); } g.setPaint(color); g.draw(transform.createTransformedShape(path)); } }
Notice that this arrangement allows us to concentrate on drawing the grid in this class without worrying about the other details. ANCHOR GraphicalPoint.java
Here is CubicPoint.java:
import java.awt.*; import java.awt.geom.*; public class GraphicalPoint extends Plotable implements Moveable { public static final int CIRCLE = 0; public static final int SQUARE = 1; int style = CIRCLE; double size = 2; public double x, y; Shape shape; public GraphicalPoint(double xp, double yp) { x = xp; y = yp; } public void setPoint(double xp, double yp) { x = xp; y = yp; } public void setSize(double s) { size = s; } public void setStyle(int s) { style = s; } public void plot(Graphics2D g, BoundingBox bbox, AffineTransform transform) { Point2D.Double point = new Point2D.Double(x, y); transform.transform(point, point); if (style == CIRCLE) shape = new Ellipse2D.Double(point.x  size, point.y  size, 2*size, 2*size); else shape = new Rectangle2D.Double(point.x  size, point.y  size, 2*size, 2*size); g.setPaint(color); g.fill(shape); g.setPaint(Color.black); g.draw(shape); } }ANCHOR Let's draw a simple figure ANCHOR Graphing functions
We first need to model a function
public interface Function { public double valueAt(double x, double[] params); }
For instance, here is the method in an implementation of Function.
public double valueAt(double x, double[] params) { return x*x*x+params[0]*x; }ANCHOR GraphicalFunction
import java.awt.*; import java.awt.geom.*; public class GraphicalFunction extends Plotable { Function function; Stroke stroke; int steps = 50; double[] params; double x0, x1; boolean domainSet = false; public GraphicalFunction(Function f, double[] p) { function = f; params = p; stroke = new BasicStroke(1f); } public void setSteps(int s) { steps = s; } public void setStroke(Stroke s) { stroke = s; } public void setDomain(double xp0, double xp1) { domainSet = true; x0 = xp0; x1 = xp1; } public void plot(Graphics2D g, BoundingBox bbox, AffineTransform transform) { if (!domainSet) { x0 = bbox.llx; x1 = bbox.urx; } double stepsize = (x1  x0)/steps; GeneralPath path = new GeneralPath(); Point2D.Float point = new Point2D.Float((float) x0, (float) function.valueAt(x0, params)); transform.transform(point, point); path.moveTo(point.x, point.y); for (int i = 1; i <= steps; i++) { double x = x0 + i*stepsize; point = new Point2D.Float((float) x, (float) function.valueAt(x, params)); transform.transform(point, point); path.lineTo(point.x, point.y); } g.setPaint(color); Stroke savedStroke = g.getStroke(); g.setStroke(stroke); g.draw(path); g.setStroke(savedStroke); } }ANCHOR Let's add a function ADDANCHOR package ANCHOR Putting everything into a package
By now, we have quite a few classes that work together to create illustrations. Let's see how to bundle them together into a package.
Our classes are:
Axes FigurePanel Grid GraphicalPoint BoundingBox GraphicalPoint PlotableANCHOR To create a package called figure:
package figure;
In a bash shell, use export CLASSPATH=..
In a windows terminal window, use set CLASSPATH=..
java figure.SimpleFigure
We can set up our figure package to allow for interactive diagrams.
LineMover.java ANCHOR Get the figure package
Download the figure package and unpack it using the command tar xzvf figure.tgz ADDANCHOR applets ANCHOR Applets An example
Note: 

Note: 

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Here is an example of how an application, our CubicGraph from Chapter 3, can be converted to an applet.

CubicGraph.java 
LineMoverApplet.java 
lineMover.htmlLASTANCHOR Testing the applet
You can test the applet using a program called appletviewer:
appletviewer lineMover.html