Gravity Applet 1.3

//Code by Grey Hugentobler, March 31st, 2011 through April 3rd, 2011

package GravityApplet;

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

public class GravityApplet extends JApplet implements Runnable {
	// G is the gravitational constant for the depicted universe
	public final float gravitationalConstant = 10;
	// t is the time since the simulation started
	public float time = 0;
	// dt is the increment of time we will advance the simulation by each step
	public final float deltaTime = .02f;
	// number of particles
	public int numberOfPlanets = 1000;
	// total mass of the system
	public float totalMass = 0;
	// inverse total mass of the system
	public float inverseTotalMass = 0;
	// center of mass of the system (mechanism to check that the net momentum is
	// in fact 0)
	public Vector centerOfMass = new Vector(0, 0);

	// Mass stores the masses of the particles
	public ArrayList<Float> mass = new ArrayList<Float>();
	// inverseMass stores the inverse mass of each particle
	public ArrayList<Float> inverseMass = new ArrayList<Float>();
	// Position is a collection of the particles position Vectors
	public ArrayList<Vector> position = new ArrayList<Vector>();
	// Velocity is a collection of the particles velocity Vectors
	public ArrayList<Vector> velocity = new ArrayList<Vector>();
	// Acceleration is derived from NetForce using Mass.
	public ArrayList<Vector> acceleration = new ArrayList<Vector>();
	// Color is where the random colors are stored
	public ArrayList<Color> color = new ArrayList<Color>();
	// size stores the radius of each blob determined by mass
	public ArrayList<Float> size = new ArrayList<Float>();

	// bufferGraphics is the Graphics buffer
	public Graphics bufferGraphics;
	// offscreen is the image being put together offscreen
	public Image offscreen;
	// dim is the current dimensions of the applet
	public Dimension dimensions;

	// Show center or not
	public boolean showCenter = true;
	// Show time or not
	public boolean showTime = true;
	//Collide or not
	public boolean collisionOn = true;
	//show number of planets or not
	public boolean showNumberOfPlanets = true;

	// Random number Generator
	public Random randomNumberGenerator = new Random();

	// initiate Applet
	public void init() {

		// standard deviation of the radius
		double sigmaR = 800;
		// standard deviation of the velocity
		double sigmaV = 100;
		// maximum mass
		float maxMass = 20;
		// minimum mass
		float minMass = 20;

		// generate our distribution of particles
		for (int i = 0; i < numberOfPlanets; i++) {
			mass.add(i,	minMass + (maxMass - minMass) * randomNumberGenerator.nextFloat());
			inverseMass.add(i, 1 / mass.get(i));

			double random1 = sigmaR * randomNumberGenerator.nextGaussian();
			double random2 = 2 * Math.PI * randomNumberGenerator.nextDouble();

			position.add( i, new Vector(Math.round(random1 * Math.sin(random2)), Math.round(random1 * Math.cos(random2))));

			double random3 = sigmaV * randomNumberGenerator.nextGaussian();
			double random4 = 2 * Math.PI * randomNumberGenerator.nextDouble();

			velocity.add(i, new Vector(Math.round(random3 * Math.sin(random4)), Math.round(random3 * Math.cos(random4))));
			acceleration.add(i, new Vector(0, 0));

			float randomRed = randomNumberGenerator.nextFloat();
			float randomGreen = randomNumberGenerator.nextFloat();
			float randomBlue = randomNumberGenerator.nextFloat();

			color.add(i, new Color(randomRed, randomGreen, randomBlue));
			size.add(i, (float) Math.sqrt(mass.get(i)));
		}

		// correct for net momentum so that the system doesn't go off screen
		// create Vector representing net momentum
		Vector netMomentum = new Vector(0, 0);

		// find total momentum and total mass
		for (int i = 0; i < numberOfPlanets; i++) {
			netMomentum = netMomentum.add(velocity.get(i).multiply(mass.get(i)));
			totalMass += mass.get(i);
		}

		inverseTotalMass = 1 / totalMass;

		// create vector representing net velocity
		Vector netVelocity = netMomentum.multiply(inverseTotalMass);

		// modify all the velocities to cancel the net momentum
		for (int i = 0; i < numberOfPlanets; i++) {
			velocity.set(i, velocity.get(i).subtract(netVelocity));
		}

		// intermediate between the properties of the particles and the center of mass
		Vector massPosition = new Vector(0, 0);

		// add up the masses multiplied by the positions, the masses
		// have already been added up
		for (int i = 0; i < numberOfPlanets; i++) {
			massPosition = massPosition.add(position.get(i).multiply(mass.get(i)));
		}

		// calculate the center of mass
		centerOfMass = massPosition.multiply(inverseTotalMass);

		//shift all the planets so that the center of mass is the center
		for (int i = 0; i < numberOfPlanets; i++) {
			position.set(i, position.get(i).subtract(centerOfMass));
		}

		// set the background to black, like space
		setBackground(Color.black);

		// start a new thread to run the simulation
		Thread newThread;
		newThread = new Thread(this);
		newThread.start();
	}

	public void paint(Graphics onscreenGraphics) {
		// change dimensions to the current size of the Applet
		dimensions = getSize();

		// change the offscreen image to the dimensions of the Applet
		offscreen = createImage(dimensions.width, dimensions.height);
		bufferGraphics = offscreen.getGraphics();

		// Draw all the little dots
		for (int i = 0; i < numberOfPlanets; i++) {
			bufferGraphics.setColor(color.get(i));
			bufferGraphics.fillOval((int) (position.get(i).x() - size.get(i) + 0.5*dimensions.width), (int) (position.get(i).y() - size.get(i) + 0.5 * dimensions.height), (int) (2 * size.get(i)), (int) (2 * size.get(i)));
		}

		// draw the time to the screen in a green serif bold font
		if (showTime) {
			bufferGraphics.setFont(new Font("serif", Font.BOLD, 12));
			bufferGraphics.setColor(Color.green);
			bufferGraphics.drawString(((int) time + ""), 0, bufferGraphics.getFont().getSize());
		}

		//draw the number of Planets to the screen
		if (showNumberOfPlanets) {
			bufferGraphics.setFont(new Font("serif", Font.BOLD, 12));
			bufferGraphics.setColor(Color.green);
			bufferGraphics.drawString(((int) mass.size() + ""), 0, dimensions.height);
		}

		// draw the center of mass
		if (showCenter) {
			bufferGraphics.setColor(Color.white);
			bufferGraphics.fillRect((int) (centerOfMass.x() - 1 + 0.5 * dimensions.width), (int) (centerOfMass.y() - 1 + 0.5 * dimensions.height), 2, 2);
		}

		// draw it all to the applet
		onscreenGraphics.drawImage(offscreen, 0, 0, this);
	}

	public void run() {
		while (true) {
			// check the system time
			long time1 = System.currentTimeMillis();

			// create some storage variables to make the calculations
			// NetForce is where we store the force of all the particles on each individual particle
			Vector[] netForce = new Vector[numberOfPlanets];
			// Force is where we store the force of each particle on each of the other particles
			Vector[][] force = new Vector[numberOfPlanets][numberOfPlanets];
			// radius is the Vector that will point at the next planet
			Vector radius;
			// divisor is the magnitude of radius squared
			float radiusSquared;

			if(collisionOn)
			{
				// size of the radiuses of the planets added together
				float addedSize;

				for (int i = 0; i < numberOfPlanets; i++) {
					for (int j = i + 1; j < numberOfPlanets; j++) {
						radius = (position.get(j).subtract(position.get(i)));
						radiusSquared = radius.dot(radius);
						addedSize = size.get(i) + size.get(j);
						if (radiusSquared <= addedSize * addedSize) {
							velocity.set(i, velocity.get(i).multiply(mass.get(i)).add(velocity.get(j).multiply(mass.get(j))).multiply(1 / (mass.get(i) + mass.get(j))));
							position.set(i, position.get(i).multiply(mass.get(i)).add(position.get(j).multiply(mass.get(j))).multiply(1 / (mass.get(i) + mass.get(j))));

							int red = Math.round((mass.get(i) * color.get(i).getRed() + mass.get(j)	* color.get(j).getRed()) / (mass.get(i) + mass.get(j)));
							int green = Math.round((mass.get(i) * color.get(i).getGreen() + mass.get(j)	* color.get(j).getGreen()) / (mass.get(i) + mass.get(j)));
							int blue = Math.round((mass.get(i) * color.get(i).getBlue() + mass.get(j) * color.get(j).getBlue()) / (mass.get(i) + mass.get(j)));

							color.set(i, new Color(red, green, blue));
							mass.set(i, mass.get(i) + mass.get(j));
							inverseMass.set(i, 1 / mass.get(i));
							size.set(i, ((float) Math.sqrt(mass.get(i))));
							mass.remove(j);
							inverseMass.remove(j);
							position.remove(j);
							velocity.remove(j);
							acceleration.remove(j);
							color.remove(j);
							size.remove(j);
							numberOfPlanets--;
							j--;
						}
					}
				}
			}

			// find all the forces of each planet on each other planet
			for (int i = 0; i < numberOfPlanets; i++) {
				for (int j = numberOfPlanets - 1; j >= i; j--) {
					radius = (position.get(i).subtract(position.get(j)));
					radiusSquared = radius.dot(radius);
					if (radiusSquared <= .01) {
						force[i][j] = new Vector(0, 0);
					} else {
						force[i][j] = radius.multiply(-gravitationalConstant * mass.get(i) * mass.get(j) / radiusSquared);
					}
					force[j][i] = force[i][j].negative();
				}
			}

			// set the net force to zero
			for (int i = 0; i < numberOfPlanets; i++) {
				netForce[i] = new Vector(0, 0);
			}

			// sum up the forces to find the total force
			for (int i = 0; i < numberOfPlanets; i++) {
				for (int j = 0; j < numberOfPlanets; j++) {
					netForce[i] = netForce[i].add(force[i][j]);
				}
			}

			// convert force to acceleration
			for (int i = 0; i < numberOfPlanets; i++) {
				acceleration.set(i, netForce[i].multiply(inverseMass.get(i)));
			}

			// integrate the position and velocity
			for (int i = 0; i < numberOfPlanets; i++) {
				position.set(i, position.get(i).add(velocity.get(i).multiply(deltaTime)));
				velocity.set(i,	velocity.get(i).add(acceleration.get(i).multiply(deltaTime)));
			}

			// increment the time variable
			if (showTime) {
				time += deltaTime;
			}

			if (showCenter) {
				// intermediate between the properties of the particles and the center of mass
				Vector massPosition = new Vector(0, 0);

				// add up the masses multiplied by the positions, the masses have already been added up
				for (int i = 0; i < numberOfPlanets; i++) {
					massPosition = massPosition.add(position.get(i).multiply(mass.get(i)));
				}

				// calculate the center of mass
				centerOfMass = massPosition.multiply(inverseTotalMass);
			}

			// check the systme time again
			long time2 = System.currentTimeMillis();
			//find out how much time we have used
			int timeUsed = (int) (time2 - time1);
			//figure out how much time is left to use
			int timeRemaining = (int) (1000 * deltaTime) - timeUsed;
			//if we have used up our time just move on
			if (timeRemaining < 0) {
				timeRemaining = 0;
			}
			// sleep the thread until we are ready
			try {
				Thread.sleep(timeRemaining);
			} catch (InterruptedException e) {
			}
			repaint();
		}
	}
}