Doing Math in Java part 2:Functions

The basics of math in Java using operators was covered in Part 1: Operators. There I went over the standard operations built into the language itself, rather than in its APIs (libraries).

But that's hardly the end of useful math operations. Especially when doing graphics, where all those geometric and trigonometric functions come in so useful. Square root, cosine, absolute values, etc.

If you're wandering into the Java APIs unguided, the java.math package might catch your eye right away. Unfortunately, it's a false trail when what you're looking for is a simple general purpose math package (it's a nice special-purpose math package for particular sorts of calculation, however.)

What you really want is the java.lang.Math class, in the java.lang package.

This has most of the standard math functions you're used to. They're defined as static methods, so you don't need to create a Math object to use them. You just call them like this:

    float distance = Math.sqrt(dx*dx + dy*dy);
    float speed = Math.abs(velocity);

These call the square root function Math.sqrt() and absolute value function Math.abs(). There are a slew of others like degree to radian conversion, the standard trig functions, and so on.

Date Calculations

Calculations with dates are another standard sort of math that's not covered by standard operators. In the package java.util we've got the Calendar class. The Calendar class itself is an abstract class. This means that it's a class used to build other classes with, not to use directly. The GregorianCalendar class is a concrete implementation of Calendar that you can use directly. The Calendar object's add() method will add or subtract some amount of time--days, minutes, hours, etc.--to or from a given date (the date that the object is set to:

1. Create a GregorianCalendar Object


2. Set its date


3. Use its add() method to add or subtract the time difference.

Example:

GregorianCalendar myDate;
myDate = new GregorianCalendar(2011, 6, 7); //set the date to 07 June 2011.
myDate.add(Calendar.Date, 165); // add 165 days to that date.

before(), after() and compareTo will return whether one date occurs before or after another. Computing the number of days between two dates is a bit more complex, unfortunately, as are similar calculations. Basically, the procedure is to use getTime() to convert both dates to time values, get the difference, then divide that by the time units you want to see the difference in (e.g. divide by 24 hours periods to get the difference in days.)

Unfortunately, the Calendar class demonstrates one of the problems with much of Java. It's an overly generalized class that prevents simple solutions to many simple and obvious problems. The older Date class took a more direct approach, but it has been deprecated in favor of the Calendar based classes. Unfortunately, even obtaining a printable date value according to the system's current locale takes a fair bit of set up in Java. A better solution would have been a very general class like Calendar behind a more usable class for solving conventional problems, but Java's development got it backward. We got the simple class first, it's inflexibility for solving certain problems resulted in criticism, then came a general class, which is no good at doing simple and obvious things for most users. The extra layer that we should have to make Calendar more usable has not yet appeared in the standard API (and possibly never will.)

So it takes a lot of code to do what should only take a line or two, when working with dates.

Still, give the Calendar and GregorianCalendar class a look-over. Even though it takes some extra code and set-up to do some simple tasks, the solutions to these problems are well established and many examples are available. It's just not as simple as System.out.println(myDate);

I'll be adding articles dealing specifically with dates myself at a future date.

Doing Math in Java part 1: Operators

One of the most valuable uses of a computer is...computing. That is, acting as a mathematical calculator. Java has a plethora of tools for doing computation.

Operators

The standard math functions that are built into the Java language are called operators. These are the sort of math functions you would expect to find on a simple calculator, plus some extras:

+ - * / % ++ --

There are other operators used for comparisons, these are the math operators. You can learn more about them in the Java Language Specification, specifically in Integer Operations, Floating-Point Operations, and more extensively through Chapter 15, Expressions.

+ and - do what you would expect, they add and subtract one value from another. * is the symbol used for multiplication, instead of the × used in math class. * is used because it's easier for the computer to recognize it as a math operator, × just looks like a letter 'x' to the computer. Similarly, / is used for division. The ÷ sign isn't on most keyboards, but / has been common on keyboards even before they were attached to computers.

The % sign doesn't do what you might, at first, expect. It doesn't calculate a percentage, as it does on most calculators. It returns the remainder of a division. For example, if you do 10/3 (ten divided by three), the result will be 3. But what if you want to get the remainder? That's what % does. 10%3 will return a value of 1. '%' is sometimes called "modulo". It's a bit of a misnomer, mathematically, but the use of the term is common and well understood, so it's not unusual to pronounce 10%3 as "ten modulo three". This is a very valuable function for keeping a value within a certain range, such as keeping an object located onscreen in graphics by having it "wrap" from one side of the screen to the other when it reaches an edge.

++ and -- are the "increment" and "decrement" operators. Increment means "go up by one unit", and decrement "go down by one unit". So if you've got a variable like:

int i = 5;

And you do i++, the value of i will become 6. Doing i-- will take away 1. ++ and -- can be placed either before or after the value they act on, for example:

number = i++;
count = --j;

There will be different effects on your program depending on whether they come before or after the value. You can find information on that in the Java Language Specification as well, in sections 15.14 and 15.15 which cover the two ways of using these operators. In general, it's best to stick to using them after your value until you understand the differences.

Assignment Operators

You can also do math as part of assigning a value. For example, let's say we want to add three to a value in our program. The obvious way to do this would be:

i = i + 3;

This takes the prior value of i, adds 3 to it, then puts the result back into variable i. With an assignment operator we can do the same thing more tersely:

i += 3;

We've combined the + with = to create an operator. This does the same thing as i = i + 3;. Your program doesn't care which way you type it. The same thing can be done with the other operators that take two values:

i *= 4; // Multiply i by four, store result back in i.
i /= 2; // Divide i in half.
i %= 3; // Put the remainder of i/3 in i.
i -= 7; //Subtract seven from i.

More Complex Math

This is what we can do with the basic math operators built into the language. To get more operations, like those found on a scientific or programmer's calculator, we use methods of some of the standard packages of Java. Which I'll cover in a future article.

Until then, have a look at java.lang.Math.

More Collision Detection: Bouncing the Right Way

A common result of a collision between two objects in a video game is a bounce. To do this right, we have to know which direction to make things bounce. Here's one way to do that easily in Java. I've got a ball that's going to bounce in one of eight directions depending on how it hits a brick.


I've marked the changes to the ball's velocity that will occur as a result of each possible type of collision. The three arrows on the left side all show that the xVel (x velocity) is a negative value, the three arrows on the bottom all show that yVel (y velocity) should become a positive value.

In the cases of the corners, both the x and y velocities are set. The bounces off the middles of the sides all cause one velocity to be set, but the other is left alone. For example, a bounce off the right side of the brick sets the xVel to a positive value, but the yVel is unchanged. So if yVel was a positive value before (meaning the ball is travelling down on screen) then it will keep travelling down. If it was negative--moving up--then it will keep moving up. Only the x direction of movement will change. It will start moving from left to right instead of right to left.

It's really easy to detect a collision, but now we need to know the relationship between the two colliding objects so that we can make the ball bounce in the correct direction. As we learned in Stopping Jonathan Livingston Seagull, the effect of how much we move an object before we check a collision can cause problems if we don't understand the limits of how we detect them.

In this program, our ball's movement is presently set at one quarter of its width. We could go as high as one half its width and still have our collision detection routines work properly here. Fortunately, we want to keep the distance the ball moves each turn short to make the movement look smoother.

When we hit the brick, we want to see where it hits the ball. This will tell the ball which way to bounce, just like a real ball. In the drawing above, we have a red brick on a cyan (blue-green) playfield. The ball is dark blue. Where the ball is intersecting, or overlapping, the brick is shown in yellow. Now we just need to know which side of the ball is getting "pushed in" this way. Then we bounce the opposite way.

Here's the program, the key code we're talking about is highlighted:

/* A simple video game style kernel, revision 4.
   by Mark Graybill, August 2010
   Has a ball bouncing off a brick.
   Because the ball moves at a fixed speed,
   slow enough we won't miss a collision,
   we can use simple colliision detection.

   Uses the Brick class from the article
   "Multiple Constructor Methods"
*/

import java.util.*;
import java.awt.*;
import javax.swing.*;
import java.lang.Math;

public class VidBrick extends JPanel{

public Rectangle screen, bounds; // The screen area and boundary.
public JFrame frame; // A JFrame to put the graphics into.
public VGTimerTask vgTask; // The TimerTask that runs the game.
public VGBall ball; // The game ball, a subclass of Rectangle.
private Brick brick; // A brick for the ball to interact with.

/* This sets up the screen area, and creates instances of
 the JFrame, VGBall, VGTimerTask, etc that we'll need. */
  public VidBrick(){
    super();
    screen = new Rectangle(0, 0, 600, 400);
    bounds = new Rectangle(0, 0, 600, 400); // Give some temporary values.
    ball = new VGBall();
    frame = new JFrame("VidBrick");
    vgTask = new VGTimerTask();
    brick = new Brick();
}

  class VGTimerTask extends TimerTask{
    public void run(){
      ball.move();
      frame.repaint();
    }
  }

  class VGBall extends Rectangle{
    int xVel, yVel; // The ball's velocity.
    Color ballColor; // The color of the ball.

/* Create a VGBall with default location of upper left
  corner, size of 20x20 pixels, moving at one quarter
  its height and width per turn--plus it's blue. */
    public VGBall(){
      super(0, 0, 20, 20);
      xVel = width/4;
      yVel = height/4;
      ballColor=new Color(0, 0, 128);
    }

/* Move the Ball. */
    public void move(){
      // Move the ball according to the game rules.
      x+=xVel; // Move horizontally.
      y+=yVel; // Move vertically.

      // Detect edges and bounce if necessary.
      if (x > (bounds.width - width)){
        xVel = -xVel; // reverse movement.
        x = bounds.width -  width; // Set location to screen edge.
      }
      if (y > (bounds.height - height)){
        yVel = -yVel; // reverse movement.
        y = bounds.height - height;
      }
      if (x <= 0) { xVel = -xVel; x = 0; }
      if (y <= 0) { yVel = -yVel; y = 0; }

     // Detect Brick and bounce if necessary.
      if (intersects(brick)) {
        // Get the intersection rectangle to find out which way to bounce.
        Rectangle iRect = intersection(brick);
        // If we hit on the left side, go left (negative x velocity).
        if ((x+(width/2))<(iRect.x+(iRect.width/2))){xVel=(0-Math.abs(xVel));}
        // If we hit on the right side, go right (positive x velocity).
        if ((x+(width/2))>(iRect.x+(iRect.width/2))){xVel=Math.abs(xVel);}
        // If we hit on the top, go up.
        if ((y+(height/2))<(iRect.y+(iRect.height/2))){yVel=(0-Math.abs(yVel));}
        // If we hit on the bottom, go down.
        if ((y+(height/2))>(iRect.y+(iRect.height/2))){yVel=Math.abs(yVel);}
      } // if intersects
    }

/* Draw the ball into the provided graphics context. Preserves
   the context's drawing color setting. */

    public void draw(Graphics g){
    // the ball draws itself in the graphics context given.
      Color gcColor = g.getColor(); // Preserve the present color.
      g.setColor(ballColor); // Use the ball's color for the ball.
      g.fillRect(x, y, width, height); // Draw the ball.
      g.setColor(gcColor); // Restore prior color.
    } // end draw()
  } // end of class VGBall

  public void paintComponent(Graphics g){
    // Get the drawing area bounds for game logic.
    bounds = g.getClipBounds();
    // Clear the drawing area.
    g.clearRect(screen.x, screen.y, screen.width, screen.height);
    // Draw the brick.
    g.setColor(brick.getColor());
    g.fillRect(brick.x, brick.y, brick.width, brick.height);
    // Draw the ball.
    ball.draw(g);
  }

/* Main program loop. */
  public static void main(String arg[]){

    java.util.Timer vgTimer = new java.util.Timer();  // Create a Timer object
    VidBrick panel = new VidBrick(); 
    
    panel.frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    panel.frame.setSize(panel.screen.width, panel.screen.height);

    panel.frame.setContentPane(panel); 
    panel.frame.setVisible(true);

    // Set up the brick.
    panel.brick.x = panel.screen.width/3;
    panel.brick.y = panel.screen.height/3;
    panel.brick.width = panel.screen.width/3;
    panel.brick.height = panel.screen.height/3;

    // Set up a timer to do the vgTask regularly.
    vgTimer.schedule(panel.vgTask, 0, 33);
  }
}

The way we figure out which way to bounce is to find the center of the ball and the center of the intersection rectangle (the yellow box in the picture, where the ball and the brick overlap.) Then if the center of the intersection (shown as an orange dot on the pic) is to the right of the center of the ball (a white dot) we bounce left. If it's to the left, we bounce right, if it's above we bounce down, below we bounce up.

This way we don't have to worry about the size or shape of the brick itself. All we care about is the bit that strikes the ball. Then the ball bounces the correct way.

If we had wanted to get really fancy, we could have made the ball bounce at different angles depending on the angle between the center of the ball and the center of the intersection rectangle. If you're familiar with trigonometry, take a look at the Math class in Java and see if you can implement this.