Trying to make object move parabolically....

Question

Im creating a race track where an object goes around in laps.. So far, the object is moving at straight 90 degree angles when it hits sides.. Im trying, and also wondering how to make the object curve when it turns a corner instead of hitting the edge, then turning a full 90 degree angle.... Im really stumped, first year takin Java :(
Here's what I got so far:
// The "Race" class.
import java.applet.*;
import java.awt.*;
public class Race extends Applet implements Runnable
    Dimension d = getSize ();
    Font f;
    int counter = 0;
    int xchange;
    int ychange;
    int x = 50;
    int y = d.height - 50;
    boolean beg = false;
    boolean slow = false;
    boolean medi = false;
    boolean fast = false;
    Button start, slo, med, fas, stop;
    TextField output;
    Thread t;
    Graphics bufferg;
    Image buffer;
    Image CARu, CARd, CARl, CARr, bakg;
    AudioClip intro, test;
    public void init ()
        test = getAudioClip (getCodeBase (), "1.au");
        intro = getAudioClip (getCodeBase (), "laser.au");
        Dimension d = getSize ();
        buffer = createImage (d.width, d.height);
        bufferg = buffer.getGraphics ();
        start = new Button ("Start");
        start.setBackground (Color.yellow);
        add (start);
        slo = new Button ("Slow");
        slo.setBackground (Color.yellow);
        add (slo);
        med = new Button ("Medium");
        med.setBackground (Color.yellow);
        add (med);
        fas = new Button ("Fast");
        fas.setBackground (Color.yellow);
        add (fas);
        stop = new Button ("Stop");
        stop.setBackground (Color.yellow);
        add (stop);
        CARu = getImage (getCodeBase (), "carUP.jpg");
        CARd = getImage (getCodeBase (), "carDOWN.jpg");
        CARl = getImage (getCodeBase (), "carLEFT.jpg");
        CARr = getImage (getCodeBase (), "carRIGHT.jpg");
        bakg = getImage (getCodeBase (), "bakg.jpg");
    public boolean action (Event e, Object o)
        if (e.target == start)
            beg = true;
            test.loop ();
            intro.play ();
        if (e.target == slo)
            slow = true;
            medi = false;
            fast = false;
        if (e.target == med)
            slow = false;
            medi = true;
            fast = false;
        if (e.target == fas)
            slow = false;
            medi = false;
            fast = true;
        if (e.target == stop)
            beg = false;
            slow = false;
            medi = false;
            fast = false;
            counter = 0;
            x = 50;
            y = d.height - 50;
        return true;
    public void start ()
        if (t == null)
            t = new Thread (this);
            t.start ();
    public void stop ()
        if (t != null)
            t.stop ();
            t = null;
    public boolean keyDown (Event e, int key)
        if (key == 's')
            intro.stop ();
        return true;
    public void run ()
        while (true)
            //Thread sleeps for 15 milliseconds here
            try
                t.sleep (15);
            catch (Exception e)
            Dimension d = getSize ();
            bufferg.setColor (Color.green);
            bufferg.fillRect (0, 0, d.width, d.height);
            // (d.width-50) ((d.height/3) -50)
            bufferg.drawImage (bakg, 0, 0, this);
            bufferg.setColor (Color.red);
            xchange = 0;
            ychange = 0;
            if (beg == true)
                if (x <= (d.width - 50) && y >= (d.height - 50))
                    xchange = 1;
                    if (slow == true)
                        ychange = 1;
                        xchange = 1;
                    if (medi == true)
                        ychange = 2;
                        xchange = 2;
                    if (fast == true)
                        ychange = 6;
                        xchange = 6;
                    bufferg.fillOval (x, d.height - 50, 50, 50);
                    //bufferg.drawImage (car_r, x, 300, this);
                    x += xchange;
                if (x >= (d.width - 50) && y >= ((d.height / 3) - 50))
                    ychange = 1;
                    if (slow == true)
                        ychange = 1;
                        xchange = 1;
                    if (medi == true)
                        ychange = 2;
                        xchange = 2;
                    if (fast == true)
                        ychange = 6;
                        xchange = 6;
                    bufferg.fillOval ((d.width - 50), y, 50, 50);
                    // bufferg.drawImage (car_u, 350, y, this);
                    y -= ychange;
                if (y <= ((d.height / 3) - 50) && x >= 50)
                    xchange = 1;
                    if (slow == true)
                        ychange = 1;
                        xchange = 1;
                    if (medi == true)
                        ychange = 2;
                        xchange = 2;
                    if (fast == true)
                        ychange = 6;
                        xchange = 6;
                    bufferg.fillOval (x, ((d.height / 3) - 50), 50, 50);
                    //bufferg.drawImage (car_l, x, 115, this);
                    x -= xchange;
                if (x <= 50 && y <= (d.height - 50))
                    ychange = 1;
                    if (slow == true)
                        ychange = 1;
                        xchange = 1;
                    if (medi == true)
                        ychange = 2;
                        xchange = 2;
                    if (fast == true)
                        ychange = 6;
                        xchange = 6;
                    bufferg.fillOval (50, y, 50, 50);
                    //bufferg.drawImage (car_d, 50, y, this);
                    y += ychange;
                if ((x <= 50) && (y <= (d.width - 50)) && (x <= (d.width - 50)) && (y >= (d.height - 50)))
                    counter++;
            else
            { //bufferg.drawImage (car_r, 50, 300, this);
                x = 50;
                y = d.height - 50;
                bufferg.fillOval (x, y, 50, 50);
            repaint ();
    public void update (Graphics g)
        paint (g);
    public void paint (Graphics g)
        bufferg.setColor (Color.red);
        f = new Font ("Test", Font.BOLD, 25);
        bufferg.setFont (f);
        bufferg.setColor (Color.blue);
        bufferg.drawString ("Lap " + counter, 300, 300);
        g.drawImage (buffer, 0, 0, this);
    } // paint method
} // Race classCan anyone help me please?

Answer 1

here's a stripped down bounded sprite engine. use the arrows keys. up=accelerate forward. down=accelerate backwards. left=turn left. right=turn right. supply a 32x32 image named "image.jpg" (or write your filename in the code below) to see the picture rotate as it corners. otherwise, you'll just see non rotating colored squares which represent the bounding box of the image. the variable turns is the number of images you will have on the screen at a time. i should have chosen a better variable name.
import java.awt.*;
import java.util.*;
import java.applet.*;
import java.awt.event.*;
import java.awt.geom.*;
import java.awt.image.*;
import java.net.*;
import java.io.*;
public class SpriteEngine extends Applet implements Runnable, KeyListener{
     Graphics2D dbg;
     Image dbImage;
     public int gameSpeed = 100;
     public int turns = 10;
     Thread th;
     boolean forward=false, reverse=false, left=false,right=false;
     Sprite[] sprite = new Sprite[turns];
     public void init(){
          setSize(500,500);
          setBackground(Color.black);
          addKeyListener(this);
          Image image = getImage(getCodeBase(),"image.jpg");
          for(int a=0;a<turns;a++){
               sprite[a]=new Sprite(image, new Color((int)(Math.random()*255),(int)(Math.random()*255),(int)(Math.random()*255)), new Point((int)(Math.random()*500),(int)(Math.random()*500)), Math.random()*360,Math.random()*12-6);
     public void start (){
          th = new Thread (this);
          th.start ();
     public void run ()     {
          Thread.currentThread().setPriority(Thread.MIN_PRIORITY);
          while (true){
               checkControls();
               for(int i=0;i<turns;i++){
                    sprite.move();
               repaint();
               try     {
                    th.sleep (gameSpeed);
               }catch (InterruptedException ex){
     public void paint (Graphics2D g)     {
          for(int a=0;a<turns;a++){
               sprite[a].draw(g);
               g.setColor(Color.black);
     public void update (Graphics g)     {
          if (dbImage == null){
               dbImage = createImage (this.getSize().width, this.getSize().height);
               dbg = (Graphics2D)dbImage.getGraphics();
          dbg.setColor (getBackground ());
          dbg.fillRect (0, 0, this.getSize().width, this.getSize().height);
          dbg.setColor (getForeground());
          paint (dbg);
          g.drawImage (dbImage, 0, 0, this);
     public void keyPressed(KeyEvent e) {
          if (e.getKeyCode()==38){forward=true;}else
          if (e.getKeyCode()==40){reverse=true;}else
          if (e.getKeyCode()==37){left=true;   }else
          if (e.getKeyCode()==39){right=true;  }
     public void keyReleased(KeyEvent e) {
          if (e.getKeyCode()==38){forward=false;}else
          if (e.getKeyCode()==40){reverse=false;}else
          if (e.getKeyCode()==37){left=false;   }else
          if (e.getKeyCode()==39){right=false;  }
     public void keyTyped(KeyEvent e) {}
     public void checkControls(){
          for(int a=0;a<turns;a++){
               if (forward){sprite[a].accel() ;}
               if (reverse){sprite[a].deccel() ;}
               if (left) {sprite[a].turnLeft() ;}
               if (right) {sprite[a].turnRight();}
class Sprite extends Object {
     private Image image;
     AffineTransform imageLocation=new AffineTransform();
     double velocity;
     Rectangle bounds;
     Rectangle refShape=new Rectangle(32,32);
     double MaxSpeed=6;
     double AccelRate=.3;
     public double Rotation=6;
     double posX,posY,angle;
     Color boxColor;
     public boolean keyDown = false;
     double dx,dy;
     public Sprite(Image img, Color color, Point location, double ang, double speed){
          posX=location.x;          posY=location.y;          boxColor = color;
          image=img;                    velocity=speed;               angle=ang;
          bounds=new Rectangle((int)posX,(int)posY,32,32);
     public void draw(Graphics2D g){
          g.setColor(boxColor);
          g.fill((bounds));
          g.setColor(Color.black);
          g.drawImage(image,imageLocation,null); //this draws your image with the AffineTranform applied
     public void setLocation(Point point) {posX=point.x; posY=point.y; }
     public Point getLocation() {return bounds.getLocation();}
     public void setBounds(Rectangle rect){bounds=rect;                }
     public Rectangle getBounds() {return bounds;              }
     public void setSpeed(double speed) {velocity=speed;                 }
     public double getSpeed() {return velocity;            }
     public void setAngle(double theta) {angle=theta;                }
     public double getAngle() {return angle;               }
     public void turnLeft() {angle=angle-Rotation;       }
     public void turnRight() {angle=angle+Rotation;       }
     public AffineTransform getForm() {return imageLocation;          }
     public void setForm(AffineTransform xform){                       }
     public void accel(){if(velocity<MaxSpeed){velocity=velocity+AccelRate;}}
     public void deccel(){if(velocity> -MaxSpeed){velocity=velocity-AccelRate;}}
     public void move(){
          dx=Math.cos(Math.toRadians(angle))*velocity;
          dy=Math.sin(Math.toRadians(angle))*velocity;
          posX=posX+dx;
          posY=posY+dy;
          imageLocation=AffineTransform.getTranslateInstance(posX,posY); //these two line set the affinetransform
          imageLocation.rotate(Math.toRadians(angle)+Math.PI/2,16,16); //to the right place and angle.
          bounds.setLocation((int)posX,(int)posY);
          if(!keyDown){
               if (velocity<0){
                    velocity=velocity+.15; // -drag
               }else if (velocity>0){
                    velocity=velocity - 0.15; // +drag