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Java Tutorial

Java is an object-oriented programming language with a built-in application programming interface (API) that can handle graphics and user interfaces and that can be used to create applications or applets. Because of its rich set of API's, similar to Macintosh and Windows, and its platform independence, Java can also be thought of as a platform in itself. Java also has standard libraries for doing mathematics.

Much of the syntax of Java is the same as C and C++. One major difference is that Java does not have pointers. However, the biggest difference is that you must write object oriented code in Java. Procedural pieces of code can only be embedded in objects. In the following we assume that the reader has some familiarity with a programming language. In particular, some familiarity with the syntax of C/C++ is useful.

In Java we distinguish between applications, which are programs that perform the same functions as those written in other programming languages, and applets, which are programs that can be embedded in a Web page and accessed over the Internet. Our initial focus will be on writing applications. When a program is compiled, a byte code is produced that can be read and executed by any platform that can run Java.

To use this tutorial you should run and study each program as you read along, so that you can see how added features affect the programs.

Objects

Object-oriented programming focuses on constructs called "objects." An object consists of data and functions known as methods which use or change the data. (Methods are similar to procedures or functions in other languages.) Objects of the same kind are said to have the same type or be in the same class. A class defines what data can be in an object, and what operations are performed by the methods. One or more objects can be created or "instantiated" from a class. The structure of a Java program consists of various objects exchanging messages. The keyword class defines a blueprint for objects with similar properties. In our first example we define the class Particle.

public class Particle
{
   double x, y, vx, vy, mass;
}

This class does not do anything (because it has no methods), but it can be used to describe a particle by its position, velocity, and mass. For simplicity, we will consider only two dimensions.

Constructors

Every class has at least one constructor, a method which has the same name as the class. A constructor initializes a new object belonging to the class.

public class Particle
{
   double x, y, vx, vy, mass; // these variables can be used by any method in the class

   // example of constructor method
   public Particle(double x, double y, double vx, double vy, double mass)
   {

      /* Use this keyword to make explicit that a method
         is accessing its own variables. */
      this.x = x; // set instance variable x equal to value of x in parameter list
      this.y = y;
      this.vx = vx;
      this.vy = vy;
      this.mass = mass;
   }
}

The constructor Particle creates an object of the Particle class by specifying five parameters: the initial position and velocity of a particle and the value of its mass. We say that Particle is the constructor for the Particle class.

We have used the following properties of Java:

  • Variable Declaration - The types of all variables must be declared. The primitive types are byte, short, int, long (8, 16, 32, and 64 bit integer variables, respectively), float and double (32 and 64-bit floating point variables), boolean (true or false), and char. Boolean is a distinct type rather than just another way of using integers. Strings are not a primitive type, but are instances of the String class. Because they are so common, string literals may appear in quotes just as in other languages. Summary of primitive data types;
  • Naming Conventions - Java distinguishes between upper and lower case variables. The convention is to capitalize the first letter of a class name. If the class name consists of several words, they are run together with successive words capitalized within the name (instead of using underscores to separate the names). The name of the constructor is the same as the name of the class. All keywords (words that are part of the language and cannot be redefined) are written in lower case;
  • Instance variables and methods can be accessed from any method within the class. The x in the argument list of the above constructor refers to the local value of the parameter which is set when Particle is called. We use the this keyword to refer to those variables defined for the entire class in contrast to those defined locally within a method and those that are arguments to a method. In the above example, this.x refers to the variable x which is defined just after the first line of the class definition. After we have introduced multiple constructors, we show a more illustrative example of the this keyword;
  • Classes are effectively new programmer-defined types; each class defines data (fields) and methods to manipulate the data. Fields in the class are template for the instance variables that are created when objects are instantiated (created) from that class. A new set of instance variables is created each time that an object is instantiated from the class;
  • The members of a class (variables and methods) are accessed by referring to an object created from the class using the dot operator. For example, suppose that a class Particle contains and instance variable x and a method step. If an object of this class is named p, then the instance variable in p would be accessed as p.x and the method accessed as p.step;
  • A semicolon is used to terminate individual statements;
  • Comments - There are three comment styles in Java. A single line comment starts with // and can be included anywhere in the program. Multiple line comments begin with /* and end with */; these are also useful for commenting out a portion of the text on a line. Finally, text enclosed within /** ... */ serves to generate documentation using the javadoc command;
  • Assignments - Java uses the C/C++ shortcuts.

Multiple Constructors

public class Particle
{
   double x, y, vx, vy, mass;

   // examples of multiple constructors

   public Particle()
   {
      this(0.0,0.0);
   }

   public Particle(double x, double y)
   {
      this(x,y,1.0);
   }

   public Particle(double x, double y, double m)
   {
      this(x,y,0.0,0.0,m);
   }

   public Particle(double x, double y, double vx, double vy)
   {
      this(x,y,vx,vy,1.0);
   }

   public Particle(double x, double y, double vx, double vy, double mass)
   {
      this.x = x;
      this.y = y;
      this.vx = vx;
      this.vy = vy;
      this.mass = mass;
   }
}

The multiple constructors (all named Particle) are distinguished only by the number of arguments. The constructors can be defined in any order. Hence, the keyword this in the first constructor refers to the next in the sequence because the latter has two arguments. The first constructor has no arguments and creates a particle of unit mass at the origin; the next is defined with two arguments: the spatial coordinates of the particle. The second constructor in turn references the third constructor which uses the spatial coordinates and the mass. The third and fourth constructors each refer to the final constructors which uses all five arguments. (The order of the constructors is unimportant.) Once the Particle class with its multiple constructors is defined, any class can call the constructor Particle using the number of arguments appropriate to that application. The advantage of having multiple constructors is that applications that use a particular constructor are unaffected by later additions made to the class Particle, whether variables or methods. For example, adding acceleration as an argument does not affect applications that rely only on the definitions given above.

Using multiple constructors is called method overloading -- the method name is used to specify more than one method. The rule for overloading is that the argument lists for all of the different methods must be unique, including the number of arguments and/or the types of the arguments.

All classes have at least one implicit constructor method. If no constructor is defined explicitly, the compiler creates one with no arguments.

We next give an example of a Particle class with methods for computing the weight of a particle and its distance from the origin. We will omit the velocity components for now.

public class Particle
{
   double x, y, mass;

   public Particle()
   {
   }

   public Particle(double x, double y)
   {
      this(x,y,1);
   }

   public Particle(double x, double y, double mass)
   {
      this.x = x; this.y = y; this.mass = mass;
   }

   public double getWeight()
   {
      return 9.8*mass;
   }

   public double distanceFromOrigin()
   {
      return Math.sqrt(x*x + y*y);
   }
}

The fundamental parts of a method are its name, arguments, return type, and the body. Methods can be created only as part of a class. By convention, variable and method names begin with a lower case letter.

The keyword return followed by an expression returns the value of the expression to the caller of the method. The type of the expression must be the same as specified by the method. (Note that a constructor does not return a value and hence no type is specified.) A method can return only the value of a single expression.

The method distanceFromOrigin in the class Particle computes the distance of a particle from the origin using the particle coordinates x and y. The square root function Math.sqrt in this calculation is part of the Math class, a library of mathematical functions which consists of a collection of static methods. We will postpone a discussion of such classes, but their use is clear from the context.

A program consists of one or more class definitions, each of which should be in separate files. The name of the file should be the same as the name of the class, for example, MyApplication.java. One of these classes must define a method main.

The following program creates two objects of type Particle.

public class MyApplication
{
   public static void main(String[] args)
   {

      /* Need an instance of class Particle - a particle object;
      assign it to the variable a which is of type Particle. */

      Particle a = new Particle(1.0,1.0);
      System.out.println("Distance of particle a from origin = " + a.distanceFromOrigin());
      System.out.println("Mass of particle a = " + a.mass);
      Particle b = new Particle();
      b.x = 2.0;
      b.y = 3.0;
      b.mass = 3;
      System.out.println("Distance of particle b from origin = " + b.distanceFromOrigin());
      System.out.println("Mass of particle b = " + b.mass);
      System.out.println("Weight of particle b = " + b.getWeight());
   }
}

The first statement in main declares a to be a Particle and uses the new keyword to instantiate an object. These two operations could have been done separately in two lines as illustrated for Particle b. Note that Java already defines primitive data types such as int and double.

If a program has more than one class, one and only one of the classes must define main().

The statement System.out.println() allows us to print the argument to the standard output with a call to the System class. System.out is an object used for sending output to the screen and println is a method that this object invokes.


Public and Private Variables

Java uses three explicit keywords and one implied keyword to set the boundaries in a class: public, private, and protected. The default access specifier for the names of variables and methods is “package visibility” or “friendly,” which means that all the other classes in the current package have access to them. (Packages are Java's way of grouping classes to make libraries and will be discussed later.) The access specifier public means that the variables and methods are available from any package; private implies that the variables and methods can only be accessed inside methods of the same class. The keyword protected indicates additional access to variables and methods that are available to subclasses. We will clarify its meaning when we discuss inheritance.

One reason to make a variable private is to restrict access to it. Access becomes an issue for threading which refers to the sequence of execution of program code. For example, we would want to avoid changing the value of a variable while another portion of the code is trying to read it. Make x private and see what happens when you run MyApplication.

If we declare x, y, and mass as private variables, we have to include explicit methods in Particle to allow another class to access the variable information in Particle. For simplicity, we will consider only the variables x and mass. Our Particle class becomes:

public class Particle
{
   private double x;
   private double mass;

   public Particle(double x)
   {
      this(x, 1.0);
   }

   public Particle(double x, double mass)
   {
      this.x = x;
      this.mass = mass;
   }

   public double getX()
   {
      return x;
   }

   public void setX(double newX)
   {
      x = newX;
   }

   public double getWeight()
   {
      return 9.8*mass;
   }

   public double distanceFromOrigin()
   {
      return Math.abs(x);
   }
}

Note the new methods getX and setX. They are used in the following.

public class MyApplication
{
   public static void main(String[] args)
   {
      Particle p = new Particle(10.0, 2.0);
      System.out.println("Distance of particle from origin = " + p.distanceFromOrigin());
      System.out.println("x-coordinate = " + p.getX()); // would have written p.x if x were public
      System.out.println(weight = " + p.getWeight());
      p.setX(3.0);    // change value of x
      System.out.println("new x-coordinate = " + p.getX());
      System.out.println("new distance from origin = " + p.distanceFromOrigin());
   }
}

In the following, we will not make variables such as x and y private, because they will be used in so many classes.

Using the Particle class

We now redefine the class Particle to include a method to compute the distance between two particles. The application that follows creates two particles and gives their mutual separation.

public class Particle
{
   double x, y, mass;

   public Particle(double x, double y)
   {
      this(x, y, 1.0);
   }

   public Particle(double x, double y, double mass)
   {
      this.x = x;
      this.y = y;
      this.mass = mass;
   }

   public double distanceFrom(Particle a)
   {
      double r2 = Math.pow(this.x - a.x, 2) + Math.pow(this.y - a.y,2);
      return Math.sqrt(r2);
   }

   public double distanceFromOrigin()
   {
      return Math.sqrt(x*x + y*y);
   }
}

public class MyApplication
{
   public static void main(String[] args)
   {

      Particle a = new Particle(5.0, 7.0);
      Particle b = new Particle(1.0, 2.0);
      System.out.println("Distance of a from b = " + a.distanceFrom(b));
      System.out.println("Distance of b from a = " + b.distanceFrom(a));
   }
}

Extending a class

Object oriented programming allows the user to reuse existing code rather than rewrite it. Classes have a hierarchical relationship, allowing the user to extend or modify the behavior of classes derived from base classes using inheritance. For example, we can expand the Particle class to include charged particles. The new class ChargedParticle will combine all the behavior and functionality of Particle with the ability to have a charge. We can implement ChargedParticle as an extension of Particle as shown below.

public class ChargedParticle extends Particle
{
   // magnitude of electron charge in Coulombs
   public static final double ELQ = 1.602e-19;
   private int charge;

   public ChargedParticle(double x,double y, double mass, int charge)
   {
      super(x, y, mass);       // constructor for Particle
      this.charge = charge;
   }

   public int getCharge()
   {
      return charge*ELQ;
   }

   public void setCharge(int newCharge)
   {
      charge = newCharge;
   }

   public static int netCharge(ChargedParticle a, ChargedParticle b)
   {
      return a.charge + b.charge;
   }
}

An example of the use of this new class is given below.

public class MyApplication
{
   public static void main(String[] args)
   {

   // particle charge is expressed in units of electron charge
   ChargedParticle a = new ChargedParticle(10.0,0,0,1);
   System.out.println("distance of a from origin = " + a.distanceFromOrigin());
   System.out.println("charge of a = " + a.getCharge());
   System.out.println("charge of a in coulombs = " + ChargedParticle.ELQ*a.getCharge());
   ChargedParticle b = new ChargedParticle(-5.0,0,0,-1);
   System.out.println("distance of b from origin: " +  b.distanceFromOrigin());
   System.out.println("charge of b = " + b.getCharge());
   System.out.println("net charge of a and b = " + ChargedParticle.netCharge(a,b));
   b.setCharge(3);
   System.out.println("new charge of b = " + b.getCharge());
   System.out.println("net charge of a and b = " + ChargedParticle.netCharge(a,b));
   }
}

Note how the (named) constant ELQ, the charge of an electron, has been introduced:

  • The keyword super refers to the constructor of the base class, in this case Particle. An inherited subclass contains all the members of the superclass except the private ones. Thus a derived class can receive the same messages as a base class;
  • A variable declared final is a constant. Its value must be specified when it is declared and this value cannot be changed. The static keyword means that there is only one copy of this variable, regardless of the number of instances of the class that are created. (A better name is class variable.) The C convention of using CAPITAL letters for constants will be used whenever it will not cause confusion;
  • The method setCharge defines the behavior of a particular object. In contrast, the static method netCharge belongs to the class and not to a particular instantiation of the class. To call a static method we use the class name rather than an instance name. Thus, to call the method netCharge we use ChargedParticle.netCharge(a,b) not a.netCharge(a,b). A static method is equivalent to a global function in C.

Static methods (class methods) and static variables, belong to a class and not a given instance of the class. The following example illustrates the nature of static variables:

public class StaticTest
{
   public static int x = 0;
   public int y = 0;

   public String getCoordinates()
   {
      return "x = " + x + ", y = " + y;
   }

   public static void main(String[] args)
   {
      StaticTest a = new StaticTest();
      StaticTest b = new StaticTest();
      a.x = 5;     // static variable
      a.y = 12;    // instance variable
      System.out.println(a.getCoordinates());      // outputs 5, 12
      b.x = 7;
      b.y = 13;
      System.out.println(a.getCoordinates());      // outputs 7, 12
      System.out.println(b.getCoordinates());      // outputs 7, 13
      StaticTest.x = 2;
      System.out.println(a.getCoordinates());      // outputs 2, 12
      System.out.println(b.getCoordinates());      // outputs 2, 13
   }
}

The (static) x member belongs to class Test and hence belongs to a and b. There is only one variable x and thus the value of x is always the one most recently specified. In contrast, y belongs to the instances a and b of the class Test and hence a.y and b.y are distinct variables. The String type is unique among all classes because it is the only class to support an operator: the + operator can be used to concatenate strings. When a number is concatenated with a string, the number is converted to a string. Because a String variable is an object, it has methods.

Arrays

An array is a special object containing a group of contigious memory locations that have the same name and the same type and a separate variable containing an integer constant equal to the number of array elements. The elements of Java arrays are numbered starting from 0. An array must be created before it can be used. We first declare a reference or "handle" to an array that permits Java to locate the object in memory when it is needed. Then we create an array object to assign to the reference using the new operator. For example, we can write

double x[];    // create an array reference
x = new double[5];    // create array object

Or we can create an array reference and an array object on a single line:

double x[] = new double[5];

The number of elements in the array x is x.length. The elements of the array are written as x[0], x[1], x[2], x[3], x[4]. An array object may be created and initialized when its reference is declared. For example,

double x[] = {1.0, 1.4, 1.6, 1.8, 3.0};

It is a good idea to declare array sizes using named constants (final variables) so that the length of the arrays can be easily changed.

final int ARRAY_SIZE = 1000;
double x[] = new double[ARRAY_SIZE];

A two-dimensional array is implemented by creating a one-dimensional array each of whose elements is also an array. We first declare a reference to an array of arrays and then create the individual arrays associated with each element. For example

double x[][];   / create reference to an array of arrays

Then we can write for example,

x = new double[3][5]; create array objects

Methods and Scope

The general form of a method definition is

return-value-type method-name(parameter list)
{
   declarations and statements
   (return statement)
}

The return-value-type is the data type of the result returned by the method to the caller. If no value is returned, the return-value-type is void. If the return-value-type is not void, then there must be a return statement.

The parameter-list is a comma-separated list containing the parameters received by the method whenever it is called. A type must be declared for every parameter in the list. If the parameter-list is empty, the parentheses is still required.

Variables that are used within a method and that are not accessible by calling methods are local variables.

Java programs communicate with their methods using pass-by-value. The method works with a copy of the original argument, not the argument itself which means that the method cannot modify the original argument even if it modifies the parameter. A program that illustrates pass-by-value os shown below.

public class TestPassByValue
{
   public static void main(String[] args)
   {
      // instantiate a TestPassByValue object
      TestPassByValue t = new TestPassByValue();
      int i = 1;    // local variable
      System.out.println("value of i before test = " + i);
      // pass value of local variable
      int j = t.test(i);
      System.out.println("value of i after test = " + i);
      System.out.println("value of j = " + j);
      j = t.test2(j);
      System.out.println("value of i after test2 = " + i);
      System.out.println("value of j after test2 = " + j);
   }

   public int test (int i)
   {
      i = ++i;   // same as i = i + 1;
      System.out.println("value of i in test = " + i);
      return i;
   }

   public int test2 (int k)
   {
      int i = k;   // i refers to instance variable
      System.out.println("value of k = " + k);
      i = ++i;
      System.out.println("value of i in test2 = " + i);
      return i;
    }
}

Variables have either class scope or block scope. Methods and the instance variables of a class have class scope. Class scope begins at the opening left brace and ends at the closing right brace of the class definition. Class scope allows any method in the class to directly invoke any other method in the class and to directly access any instance variable of the class. In effect, instance variables are global variables within a class. Instance variables can be used to communicate between methods in a class or to retain information between calls of a given method in the class.

A block is a compound statement and consists of all the statements between an opening and closing brace. Variables defined inside a block have block scope. Variables defined within a block have block scope and are visible within the block; they are not visible outside the block.

A variable can have the same name as an instance variable as an instance variable or method in the class in which the method is defined. In this case the instance variable is hidden from the method by the local variable. Example:

public class Point
{
   // define instance data
   public double x,y;   // instance variables

   // define constructors

   public Point()
   {
      x = 1;  // same variables as instance variables
      y = 1;
   }

   public Point (double x, double y)
   {
      this.x = x;  // this.x refers to instance variable
      this.y = y;
      this.x++;
      System.out.println("this.x = " + this.x);
      System.out.println("x = " + x);    // parameter variable
   }

   public Point (double x, double y, boolean dummy)
   {
      x++;
      System.out.println("x = " + x);
   }
}

public class TestPoint
{
   public static void main(String[] args)
   {

      /* Need an instance of class Particle - a particle object;
      assign it to the variable a which is of type Particle. */

      Point a = new Point(2.0,1.0);
      System.out.println("x = " + a.x);
      Point b = new Point();
      b.x = 3.0;
      System.out.println("xb = " + b.x);
   }
}

Simple Graphics

A powerful feature of Java is its ability to do graphics relatively simply. We next introduce several methods in the Particle class to draw a representation of the particle.

import java.awt.*;
public class Particle
{
   double x,y;
   Color color;    // part of AWT package

   public Particle(double x, double y)
   {
      // constructor with color variable
      this.x = x;
      this.y = y;
      color = Color.blue;        // define default color
   }

   // Draw representation of particle in given graphics context
   public void draw(Graphics g)
   {
      Color oldColor = g.getColor();
      g.setColor(color);
      g.fillOval((int)x, (int)y, 12, 12);
      g.setColor(oldColor);
   }

   public Color getColor()
   {
      return color;
   }

   public void setColor(Color newColor)
   {
      color = newColor;
   }

   public void move(double dx, double dy)
   {
      x += dx;     // same as x = x + dx;
      y += dy;
   }
}

The import statement allows us to use the Java libraries. The notation java.awt.* means that all the classes in the java.awt package can be used. This package implements the Java Abstract Window Toolkit (AWT) and contains all the classes and interfaces necessary for creating a user interface. Packages are a way of grouping a collection of related classes. A description of all the packages is given at the Sun Web site.

We have used the java.awt.Graphics class which provides drawing and painting methods. The method draw has an argument g of type Graphics. Think of g as a part of the screen (a bit map) where painting will take place and the methods that are associated with it.

The four principal elements need to create a GUI include:

  • Components - A component is a visual object containing text or graphics that can respond to keyboard or mouse inputs. Examples of components include buttons, labels, text boxes, check boxes, and lists. A blank component is known as a canvas, which can be used as a drawing area for text or graphics. All components inherit a common set of methods, the most common of which is paint.
  • Ccontainer - A container is a graphical object that can hold components or other containers. The most important type of container is a Frame.
  • Layout Manager - A layout manager is automatically associated with each container when it is created, but the layout manager can be changed. Examples include BorderLayout, BoxLayout, GridLayout.
  • Event Handlers - Events, such as the click of a mouse, are handled by creating listener classes which implement listener interfaces. The standard listener interfaces are in java.awt.event.

The following simple class draws the particle:

import java.awt.*;
public class ParticleDrawer extends Frame
{
   public static void main(String[] args)
   {
      // Create new frame
      ParticleDrawer frame = new ParticleDrawer();
   }

   // Construct ParticleDrawer frame
   public ParticleDrawer()
   {
      // predefined methods
      setSize(512, 342);    // units of coordinate system in pixels
      setVisible(true);
   }

   // Paint particles
   public void paint(Graphics g)
   {
      Particle p = new Particle(3.1, 4.1);
      p.draw(g);
      p.move(26.5, 35.8);
      p.setColor(Color.red);
      p.draw(g);
   }
}

A frame is a very simple window, with a border, a place for a title, and a close window button.

Note how the {paint method is used. It is not called directly. Instead, whenever the frame is shown, the paint method is called. In addition, if one covers the frame with another window, the paint method will be called again when the frame is uncovered. To directly call the paint method, use the repaint() method.

As an example we draw the trajectory of a projectile. To do so we add to Particle the method step to integrate the equations of motion for one time step. The arguments of step are the time step and the Force on the particle, which is defined in another class. We also add other useful methods.

public class Particle
{
   private double x,y,vx,vy,ax,ay;
   private double mass = 1.0;
   private boolean firststep = true;

   public Particle(double x, double y, double vx, double vy)
   {
      this.x = x;
      this.y = y;
      this.vx = vx;
      this.vy = vy;
   }

   public double getMass()
   {
      return mass;
   }

   public void setMass(double mass)
   {
      this.mass = mass;
   }

   public double getX()
   {
      return x;
   }

   public double getY()
   {
      return y;
   }

   public double getVx()
   {
      return vx;
   }

   public double getVy()
   {
      return vy;
   }

   public double getAx()
   {
      return ax;
   }

   public double getAy()
   {
      return ay;
   }

   public void setX(double x)
   {
      this.x = x;
   }

   public void setY(double y)
   {
      this.y = y;
   }

   public void setVx(double vx)
   {
      this.vx = vx;
   }

   public void setVy(double vy)
   {
      this.vy = vy;
   }

   public void step(double dt, Force f)
   {
      if (firststep)
      {
         ax = f.getfx(x,y,vx,vy,this)/mass;  // acceleration at beginning of interval
         ay = f.getfy(x,y,vx,vy,this)/mass;
         firststep = false;
      }
      // Euler-Richardson algorithm
      double vxm = vx + 0.5*ax*dt;  // velocity at middle of interval
      double vym = vy + 0.5*ay*dt;
      double xm = x + 0.5*vx*dt;    // position at middle of interval
      double ym = y + 0.5*vy*dt;
      double axm = f.getfx(xm,ym,vxm,vym,this)/mass;
      double aym = f.getfy(xm,ym,vxm,vym,this)/mass;
      vx += axm*dt;            // velocity at end of interval
      vy += aym*dt;
      x += vxm*dt;           // position at end of interval
      y += vym*dt;
      ax = f.getfx(x,y,vx,vy,this)/mass;  // acceleration at end of interval
      ay = f.getfy(x,y,vx,vy,this)/mass;
   }
}

public class Force
   {
   private final static double g = 9.8; // not convention
   double b = 0;   // used in drag force

   public void setb(double b)
   {
      this.b = b;
   }

   public double getfx(double x, double y, double vx, double vy, Particle p)
   {
      return -b*vx;
   }

   public double getfy(double x, double y, double vx, double vy, Particle p)
   {
      return -b*vy - g*p.getMass();
   }
}

Note that {\tt If} statements are the same as in C/C++ except that Java uses a boolean value to condition the execution. Summary of relational operators. The step method implements the Euler-Richardson integration algorithm. We need to compute the acceleration at the beginning of the interval the first time the algorithm is used. Then we can use the acceleration computed at the end of the previous interval. Note how this is used in the step method to refer to the Particle itself; in Force we use the argument Particle to get the particle's mass. The class that draws the trajectory is given below.

import java.awt.*;
public class Simulation extends Frame
{
   public static void main(String[] args)
   {
      Simulation sim = new Simulation();   // set up window for application
   }

   public Simulation()
     {
        setSize(512,342);
        setVisible(true);
    }

}

   public void paint(Graphics g)
   {
      setBackground(Color.white);
      calculateTrajectory(g);
   }

   private void calculateTrajectory(Graphics g)
   {
      final double tmax = 10.0;
      final double dt = 0.5;
      Particle p = new Particle(0.0, 200.0, 40.0, 25.0);
      Force f = new Force();
      g.setColor(Color.blue);
      double time = 0.0;
      while (time < tmax)
      {
      // draw circle of diameter 10 pixels. note use of casting
         g.drawOval((int)p.getX(), getSize().height - (int)p.getY(), 10, 10);  
         p.step(dt,f);
         time += dt;
      }
   }
}

The Simulation class extends the Frame class. The paint method is called when the Frame is first shown and anytime Frame is brought to the front.

Java uses a coordinate system whose origin is at the upper left-hand corner with positive x values to the right and positive y values down. Because of this choice of screen coordinate system, we need to convert world coordinates to screen coordinates when drawing an oval to represent the particle. Because the last two arguments of drawOval are the same, the oval is a circle. (Note that drawOval requires integers.)

Note the use of the while statement which allows all the statements within the braces of the while statement to be executed again and again as long as the argument of the while statement (time < tmax) is true.

An alternative to the while loop is the for loop which looks like

for (int i = 0; i < 10; i++)
   statement;

or

for (int i = 0; i < 10; i++)
{
   statement 1;
   ...
   statement n;
}

Semicolons are used to separate the fields inside the parenthesis. The first field initializes a variable. Usually, the variable is also declared here. The second field determines under what condition the loop will continue. The third field lists how the variable in the first field changes at the end of each pass through the loop.

Offscreen buffers

When the window of another application covers the frame, Java automatically calls paint when the user returns to our original program. This action allows us to see the contents of the original window. However, in the above program it means that the trajectory must be recomputed. A better approach is to first draw the trajectory to an offscreen image buffer and then blast the latter to the screen. As long as the buffer is saved, no new calculations need to be done.

First we will show how this is done for the Simulation class and then we will show an example where it is more useful. // Image and Graphics do not use constructors.

import java.awt.*;
public class Simulation extends Frame
{
   Image offscreen;   // make image class variable so available to all methods

   public static void main(String[] args)
   {
       Simulation sim = new Simulation();   // set up window for application
   }

   public Simulation()
   {
      setSize(512, 342);
      setVisible(true);
      offscreen = createImage(getSize().width, getSize().height);
      calculateTrajectory();
   }

   public void paint(Graphics g)
   {
      setBackground(Color.white);
      g.drawImage(offscreen, 0, 0, this);  // draw image onto screen
   }

   public void calculateTrajectory()
   {
      final double tmax = 10.0;
      final double dt = 0.5;
      Graphics g = offscreen.getGraphics();
      g.setColor(Color.blue);
      Particle p = new Particle(0.0, 200.0, 40.0, 25.0);
      Force f = new Force();
      double time = 0.0;
      while (time < tmax)
      {
         g.drawOval((int)p.getX(), getSize().height - (int)p.getY(), 10, 10);
         p.step(dt,f);
         time += dt;
      }
   }
}

The Graphics class is used here to provide drawing methods for offscreen, which is an instantiation of the Image class. Both Graphics and Image cannot be instantiated directly with a constructor, instead we can use the getGraphics and createImage methods, respectively. The Image class represents a displayable image.

Note how we declare offscreen outside of any method, and instantiate it with the createImage method in the constructor. This is a common technique for making objects accessible to all the methods of a class, and to insure that they continue to exist after a method returns.

User Interaction

Offscreen buffers are useful when we want to draw more than one trajectory without running the program over again. To do so we want the user to interact with the program. This feature is very easy to accomplish using components such as Buttons, TextFields, and Menus. Below we show how to use a TextField to receive a number from the user. We put the TextField on a separate frame and use an actionListener to detect whether the user has entered a number in the TextField. The number entered will be the friction coefficient, b, used in a drag force of the form -bv.

import java.awt.*;
import java.awt.event.*;   // needed for actionListener

class ParameterInput extends Frame
{
   TextField tf;
   Label lb;
   Simulation sim;

   public FrictionInput (Simulation sim)  // pass address of object
   {
      this.sim = sim;
      setUpFrame();
   }

   public void setUpFrame()
   {
      setTitle("Friction Input");
      setSize(200,100);
      setLocation(400,50);  // location for frame
      setLayout(null);   // not using any layout manager
      lb = new Label("Friction Coefficient"); // new label for textfield
      lb.setSize(150,20);
      lb.setLocation(30,70);
      add(lb);                                 // add label
      tf = new TextField();  // new textfield
      tf.addActionListener(new actionTF());   // add listener
      tf.setSize(50,20);
      tf.setLocation(30,40);
      add(tf);                                  // add textfield
      setVisible(true);
   }

   class actionTF implements ActionListener   // example of Internal class
   // user has to tell ActionLister what to do so have to implement it.
   {    

      public void actionPerformed(ActionEvent e)
      {
         Double R = new Double(tf.getText().trim());  // convert text to number
         // trim gets rid of extra zeros 
         sim.calculateTrajectory(R.doubleValue());
      }
   }
}

There are two objects attached to the Frame. Label lb represents some text that will be placed under the TextField tf. The size and location of each of these components is specified. There are layout managers that automatically decide these specifications for you, but they frequently do not look good.

One of the features of Java is the use of the actionListener which is implemented by using the addActionListener method and an internal class which implements the ActionListener interface. An interface is like a class except none of the methods have implementations. Instead the user must supply these as we have done above for the method actionPerformed(ActionEvent e). The beauty of the above event model is that the user does not have to write code to check for an occurence of an event in other parts of the program. Whenever, a number is entered into the TextField, the actionPerformed method will be executed. Here we extract the number by converting the string in the TextField to a number using the Double class, and then call the calculateTrajectory method of the object sim.

import java.awt.*;

public class Simulation extends Frame
{
   private Image offscreen;
   private int counter = 0;  // used to change color for each trajecto
   public static void main(String[] args)
   {
      Simulation sim = new Simulation();   // set up window for application
      FrictionInput fi = new FrictionInput(sim);   // set up second window
   }

   public Simulation()    // constructor
   {
      setSize(512, 342);
      setVisible(true);
      offscreen = createImage(getSize().width, getSize().height);
   }

   public void paint(Graphics g)
   {
      setBackground(Color.white);
      g.drawImage(offscreen, 0, 0, this);   // draw image on screen
   }

   public void calculateTrajectory(double b)
   {
      final double tmax = 10.0;
      final double dt = 0.5;
      Graphics g = offscreen.getGraphics();   // create buffer
      changeColor(g);
      Particle p = new Particle(0.0, 200.0, 40.0, 25.0);
      Force f = new Force();
      f.setb(b);
      double time = 0.0;
      while (time < tmax)
      {
         g.drawOval((int)p.getX(), getSize().height - (int)p.getY(), 10, 10);
         p.step(dt,f);
         time += dt;
      }
      repaint();
   }

   public void changeColor(Graphics g)
   {
      switch(counter++)
      {
         case 0:
            g.setColor(Color.red);
            break;
         case 1:
            g.setColor(Color.blue);
            break;
         case 2:
            g.setColor(Color.green);
            break;
         case 3:
            g.setColor(Color.yellow);
            break;
         case 4:
            g.setColor(Color.magenta);
            break;
         case 5:
            g.setColor(Color.orange);
            break;
         case 6:
            g.setColor(Color.cyan);
            break;
         case 7:
            g.setColor(Color.pink);
            break;
         default:
            g.setColor(Color.black);
       }
   }
}

Note the use of the method repaint which clears the Frame and calls paint. However, all the trajectories are still on on the offscreen buffer so that they will all appear on the screen.

We have added a method, changeColor, which uses a different color each time a new trajectory is drawn, up to 8 trajectories. Any more trajectories are colored black. Note the use of the switch statement. Each time a trajectory is drawn, the value of counter is checked and then incremented (using counter++. (Note that counter++; means that the current value of counter is used in the switch statement before it is incremented by 1. If we used ++counter; instead, counter would be incremented by 1 first.) The value checked then determines which statement to execute. Also note the use of the break statement. Without it every case would be executed.

The switch statement is useful if there are many possible choices. If there are only a few choices or if the choices cannot be encoded as an integer, then the if statement can be used. Examples of the latter are as follows:

if (x < 0)
{
   y = 20;
   x = 10;
}

if (x < 0)
   y = 10;     // braces not needed for single statement
else
   y = 20;

if (x < 0)
   y = 10;
else if (x > 0)
   y = 20;
else
   y = 30;

Animation

We now return to a single trajectory and discuss animation. Instead of showing the trajectory we will simply show a ball as it moves. The following code does this so that there is very little flicker. We have reduced the time step so that the motion of the ball will be slowed down.

import java.awt.*;

public class Simulation extends Frame
{
   Image offscreen;

   public static void main(String[] args)
   {
      Simulation sim = new Simulation();   // set up window for application
      sim.calculateTrajectory();
   }

   public Simulation()
   {  // constructor
      setSize(512, 342);
      setVisible(true);
      offscreen = createImage(getSize().width, getSize().height);
   }

   public void paint(Graphics g)
   {
      setBackground(Color.white);
      g.drawImage(offscreen,0,0,this);
   }

   public void calculateTrajectory()
   {
      final double tmax = 10.0;
      final double dt = 0.005;
      Graphics b = offscreen.getGraphics();
      Particle p = new Particle(0.0, 200.0, 40.0, 25.0);
      Force f = new Force();
      double time = 0.0;
      while (time < tmax)
      {
         Rectangle oldRect = new Rectangle((int)p.getX(),getSize().height -(int)p.getY(),11,11);
         p.step(dt,f);
         time += dt;
         Rectangle newRect = new Rectangle((int)p.getX(),getSize().height -(int)p.getY(),11,11);
         // new region of ball
         Rectangle r = newRect.union(oldRect); // new plus old region
         // b is buffer. key to avoid flicker is not to call repaint
         b.clearRect(r.x,r.y,r.width,r.height);    // clear new plus old region on buffer
         b.fillOval((int)p.getX(), getSize().height - (int)p.getY(), 10, 10);
         Graphics g = getGraphics();
         g.drawImage(offscreen,0,0,this);
      }
   }
}

The basic strategy used above is to define three rectangles. One containing the old position of the ball, one containing the new position, and one which is the union of the two. Then we clear the buffer of this latter rectangle, and draw our new ball. We then draw our image to the screen. Note how we grab the Graphics object for the screen within calculateTrajectory instead of using repaint. This avoids some of the flickering that would occur from clearing the Frame.

Threads

Often we want the user to be able to interrupt a simulation while it is running, and then start it going again. For example, we might want to know the coordinates of our ball at some instant while we are watching it. One can use Threads to accomplish this. Basically, a Thread is a process which is running parallel to another process. Below we set up a Thread and use a MouseListener to interrupt the program. The interface Runnable contains the methods we need to start, stop, and run the Thread.

import java.awt.*;
import java.awt.event.*;

public class Simulation extends Frame implements MouseListener, Runnable
{
   Image offscreen;
   Graphics gb;   // graphics buffer
   Particle p;
   Force f;
   boolean running = false;
   Thread runner;

   public static void main(String[] args)
   {
      Simulation sim = new Simulation();  // set up window for application
   }

   public Simulation()
   { // constructor
     setSize(512, 342);
     setVisible(true);
     offscreen = createImage(getSize().width, getSize().height);
     p = new Particle(0.0, 200.0, 40.0, 25.0);
     f = new Force();
     gb = offscreen.getGraphics();
     start();  // method associated with thread
     addMouseListener(this);   // this refer to frame class
   }

   public void paint(Graphics g)
   {
      setBackground(Color.white);
      g.drawImage(offscreen,0,0,this);
   }

   public void start()
   {
      runner = new Thread(this);   // this refers to frame
     runner.start();
   }

   public void stop()
   {
      runner.stop();
   }

   public void run()
   {
      while(true)
      {
         try {Thread.sleep(5);}  // delay 5 msec between updates
         catch (InterruptedException e){};   // would catch the moue click
         if(running) calculateTrajectory();
      }
   }

   public void mouseClicked(MouseEvent e)
   {
      // see coordinates
      Graphics g = getGraphics();
     g.clearRect(0,0,getSize().width, getSize().height);
     g.fillOval((int)p.getX(), getSize().height - (int)p.getY(), 10, 10);
     g.drawString("x = " + String.valueOf(p.getX()),e.getX(),e.getY());
     g.drawString("y = " + String.valueOf(p.getY()),e.getX(),e.getY() + 30);
  running = false;
   }

   public void mouseEntered(MouseEvent e) {running = true;}
   // move inside frame, runs; otherwise stops
   public void mouseExited(MouseEvent e) {running = false;}
   public void mousePressed(MouseEvent e) {}
   public void mouseReleased(MouseEvent e) {}

   public void calculateTrajectory()
   {
      // should be draw trajectory
     private final double dt = 0.005;
     Rectangle oldRect = new Rectangle((int)p.getX(),getSize().height -(int)p.getY(),11,11);
  p.step(dt, f);
     time += dt;
     Rectangle newRect = new Rectangle((int)p.getX(),getSize().height -(int)p.getY(),11,11);
     Rectangle r = newRect.union(oldRect);
     gb.clearRect(r.x,r.y,r.width,r.height);
     gb.fillOval((int)p.getX(), getSize().height - (int)p.getY(), 10, 10);
     Graphics g = getGraphics();
     g.drawImage(offscreen,0,0,this);
   }
}

We have modified calculateTrajectory so that it only computes and draws one step. We have eliminated the while statement. Instead control of the trajectory is given to the run method of the Thread runner. The try catch statement is used to interrupt the Thread for 5 milliseconds to check to see if any event occurred. The MouseListener checks for events. In this case we can stop the motion by moving the mouse outside the Frame, and start it again by moving it into the Frame and start it again by moving it into the Frame. If the mouse is clicked, we write the x and y coordinates of the ball at the locatiuon of the mouse click, redraw the ball, and stop the motion. Note that the interface methods mousePressed and mouseReleased must be defined even though they do not do anything in this example.