Collisions (Separating Axis Theorem)

Question

Hi,
I'm working on a 2D game, it's top-down like GTA2, but I'm havinfgproblems with the collision detector. I know there are a lot of posts about collision already but they didn't help me much. I'm using the separating axis theorem (explained here: http://www.harveycartel.org/metanet/tutorials/tutorialA.html#section1) and most of the code is inspired by http://www.codeproject.com/cs/media/PolygonCollision.asp .
Separating axis theorem:
find all axis perpendicular to all the edges of both objects,
project both objects on the axis,
if there is an axis where the projections do not overlap, then the objects do not overlap.
The problem is that I think my code should work. And guess what, it doesn't. I checked the code 30 times this weekend but maybe there is some tiny mistake I overlook each time..
When I run the program with 6 objects I get this:
1 2 3 4 5 6
1: - 0 0 0 0 0
2: 0 - 1 0 0 0
3: 0 1 - 0 0 0
4: 0 0 0 - 0 0
5: 0 0 0 0 - 0
6: 0 0 0 0 0 - (1=intersect, 0=doesn't intersect)
but this is completely wrong. You can run the program yourself to see the exact locations of the objects.
1 is the triangle at the top,
2 and 3 are the triangles who share an edge
4 is the one on the left intersecting with 3
5 is the triangle on the right
6 is the parallelogram
But it really gets weird when I add a 7th object (the one in the comments):
1 2 3 4 5 6 7
1: - 0 0 0 0 0 0
2: 0 - 0 0 0 0 0
3: 0 0 - 0 0 0 0
4: 0 0 0 - 0 0 0
5: 0 0 0 0 - 0 0
6: 0 0 0 0 0 - 0
7: 0 0 0 0 0 0 -
Now 2 and 3 don't intersect anymore! They didn't change I just added another object.
I'm adding a short explanationof all the classes and the code itself. I know it's a lot of code but I added all the test classes so you can just run Test.Test
I hope someone can help me with this.
Thanks,
El Bandano
_<h5>package CollisionDetector:</h5>_
<h6>CollisionDetector</h6>
The class that is supposed to check for collisions. It will take 2 Props and return a CollisionResult
<h6>CollisionResult</h6>
A small class with 2 public fields. For now only the boolean Intersect matters.
<h6>Interval</h6>
Another small class that represents an interval of floats. It's pretty simple. Distance should return something negative if 2 intervals overlap.
_<h5>package World</h5>_
<h6>MovableProp</h6>
An interface of an object. All objects should be convex.
<h6>Vector2D</h6>
A 2D-vector. It has an x and a y value (floats) and some simple methods. a 2D vector can represent a point or an edge/axis. For a point the x and y are the coordinates. For an axis you need a normalized vector (x^2+y^2=1) and the x and y are coordinates on a parrallell line through (0,0).
_<h5>package Test</h5>_
<h6>Test</h6>
The main class. It makes some objects, prints a matrix showin which intersect eachother and shows a window with all objects.
<h6>TestMovProp</h6>
A basic implementation of MovableProp.
<h6>TestPanel</h6>
A panel that draws MovableProp.
_<h5>package CollisionDetector:</h5>_
<h6>CollisionDetector</h6>
package CollsisionDetector;
import World.MovableProp;
import World.Vector2D;
import java.util.ArrayList;
public class CollisionDetector {
    public CollisionDetector(){
    public CollisionResult DetectCollision(MovableProp propA, MovableProp propB) {
        CollisionResult result = new CollisionResult();
        result.Intersect = true;
        result.WillIntersect = true;
        Vector2D[] edges = UniqueEdges(propA, propB);
        // loop through the edges
        // find an axis perpendicular to the edge
        // project the props on the axis
        // check wether they intersect on that axis
        for (Vector2D edge: edges){
            Vector2D axis = edge.getPerpendicular();
            Interval intA = projectPointsOnAxis(propA.getCoordinates(), axis);
            Interval intB = projectPointsOnAxis(propB.getCoordinates(), axis);
            if (intA.distance(intB) > 0)
                result.Intersect = false;
        return result;
    public Interval projectPointsOnAxis(Vector2D[] points, Vector2D axis){
        Interval i = new Interval();
        for (Vector2D p: points)
            i.add(projectPointOnAxis(p, axis));
        return i;
    public float projectPointOnAxis(Vector2D point, Vector2D axis){
        // axis <-> y=a*x
        float a  = axis.y / axis.x;
        // line <-> y=(-a/1)*x+b
        float a2 = -axis.x / axis.y;
        // b = y-a2*x
        float b = point.y - a2*point.x;
        // y = a *x
        // y = a2*x + b
        // => a*x = a2*x + b
        float x = b/(a-a2);
        float y = a*x;
        // is there a better way to do this?
        return new Float(Math.sqrt(x*x + y*y)).floatValue();
     * Put all edges in 1 array, eliminate doubles (parallels).
    public Vector2D[] UniqueEdges(MovableProp propA,MovableProp propB){
        Vector2D[] aEdges = propA.getEdges();
        Vector2D[] bEdges = propB.getEdges();
        ArrayList<Vector2D> tmp = new ArrayList<Vector2D>();
        for (Vector2D v: aEdges){
            tmp.add(v);
        for (Vector2D v: bEdges){
           if (! tmp.contains(v))
                tmp.add(v);
        return tmp.toArray(new Vector2D[tmp.size()]);
}<h6>CollisionResult</h6>
package CollsisionDetector;
import World.Vector2D;
public class CollisionResult {
    public boolean WillIntersect;
    public boolean Intersect;
    public Vector2D MinimumTranslationVector;
    public CollisionResult() {
}<h6>Interval</h6>
package CollsisionDetector;
public class Interval {
    public float min;
    public float max;
    public Interval() {
        min = Float.MAX_VALUE;
        max = Float.MIN_VALUE;
    public void add(float f){
        // no 'else'! In an empty interval both will be true
        if (f>max)
            max = f;
        if (f<min)
            min = f;
    public float distance(Interval interval){
        if (this.min < interval.min) {
            return interval.min - this.min;
        } else {
            return this.min - interval.min;
}_<h5>package World</h5>_
<h6>MovableProp</h6>
package World;
public interface MovableProp {
    public int getNPoints();
    public Vector2D[] getEdges();
    public Vector2D[] getCoordinates();
}<h6>Vector2D</h6>
package World;
public class Vector2D {
    public float x;
    public float y;
    public Vector2D(float x, float y) {
        this.x = x;
        this.y = y;
    public boolean equals(Object obj){
        if (!(obj instanceof Vector2D)){
            return false;
        }else
            return (this.x == ((Vector2D)obj).x && this.y == ((Vector2D)obj).y);
    public String toString() {
        return ("Vector2D  x=" + x + " ,  y=" + y);
    public void normalize(){
        if (x*x + y*y != 1){
            float x2 = x;
            x /= Math.sqrt(x2*x2+y*y);
            y /= Math.sqrt(x2*x2+y*y);
    public Vector2D getPerpendicular(){
        Vector2D per = new Vector2D(-y,x);
        per.normalize();
        return per;
}_<h5>package Test</h5>_
<h6>Test</h6>
package Test;
import CollsisionDetector.CollisionDetector;
import World.MovableProp;
import java.awt.Polygon;
import java.util.ArrayList;
import java.util.Vector;
import javax.swing.JFrame;
public class Test {
    public static void main(String args[]) {
        CollisionDetector detect = new CollisionDetector();
        float[] x = new float[3];
        float[] y = new float[3];
        ArrayList<MovableProp> list = new ArrayList<MovableProp>();
        x[0] = 200; x[1] = 300; x[2] = 500;
        y[0] = 400; y[1] = 200; y[2] = 300;
        list.add(new TestMovProp(x,y));
        x[0] = 300; x[1] = 500; x[2] = 600;
        y[0] = 400; y[1] = 400; y[2] = 500;
        list.add(new TestMovProp(x,y));
        x[0] = 200; x[1] = 300; x[2] = 600;
        y[0] = 600; y[1] = 400; y[2] = 500;
        list.add(new TestMovProp(x,y));
        x[0] = 100; x[1] = 200; x[2] = 300;
        y[0] = 800; y[1] = 500; y[2] = 700;
        list.add(new TestMovProp(x,y));
        x[0] = 600; x[1] = 600; x[2] = 700;
        y[0] = 400; y[1] = 700; y[2] = 500;
        list.add(new TestMovProp(x,y));
//        x[0] = 100; x[1] = 001; x[2] = 900;
//        y[0] = 001; y[1] = 900; y[2] = 500;
//        list.add(new TestMovProp(x,y));
        x = new float[4];
        y = new float[4];
        x[0] = 450; x[1] = 550; x[2] = 500; x[3] = 400;
        y[0] = 200; y[1] = 250; y[2] = 650; y[3] = 600;
        list.add(new TestMovProp(x,y));
        int n = list.size();
        boolean[][] matrix = new boolean[n][n];
        for (int i=0; i<n; i++){
            for (int j=0; j<n; j++){
                if (i!=j)
                matrix[i][j] = detect.DetectCollision(list.get(i),list.get(j)).Intersect;
        System.out.print("  ");
        for (int i=0; i<n; i++){
            System.out.print("  " + (i+1));
        for (int i=0; i<n; i++){
            System.out.print("\n" + (i+1) + ":  ");
            for (int j=0; j<n; j++){
                if (i==j)
                    System.out.print("-  ");
                else if (matrix[i][j])
                    System.out.print("1  ");
                else
                    System.out.print("0  ");
        System.out.println();
        JFrame window = new JFrame();
        window.setDefaultCloseOperation(window.EXIT_ON_CLOSE);
        window.pack();
        window.setVisible(true);
        window.setContentPane( new TestPanel(list));
        window.pack();
}<h6>TestMovProp</h6>
package Test;
import World.MovableProp;
import World.Vector2D;
public class TestMovProp implements MovableProp{
    float[] X;
    float[] Y;
    Vector2D[] coor;
    public TestMovProp(float[] x, float[] y) {
        X=x; Y=y;
        coor = new Vector2D[getNPoints()];
        for(int i=0; i< getNPoints(); i++){
            coor[i] = new Vector2D(X, Y[i]);
public Vector2D[] getCoordinates(){
return coor;
public int getNPoints() {
return X.length;
public Vector2D[] getEdges() {
int n = getNPoints();
Vector2D[] v = new Vector2D[n];
for (int i=0; i<n-1; i++){
v[i] = new Vector2D(X[i]-X[i+1], Y[i]-Y[i+1]);
v[i].normalize();
v[n-1] = new Vector2D(X[0]-X[n-1], Y[0]-Y[n-1]);
v[n-1].normalize();
return v;
public String toString() {
String s = "\n";
for (Vector2D v: getCoordinates())
s += ("\n" + v);
return s;
<h6>TestPanel</h6>package Test;
import World.MovableProp;
import World.Vector2D;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Polygon;
import java.util.ArrayList;
import javax.swing.JPanel;
public class TestPanel extends JPanel {
public ArrayList<MovableProp> list;
public TestPanel(ArrayList<MovableProp> list) {
super();
this.list = list;
setPreferredSize(new Dimension(1000,850));
public void paint(Graphics g) {
super.paint(g);
for (MovableProp prop:list){
Vector2D[] coor = prop.getCoordinates();
int n = prop.getNPoints();
g.drawLine((int)coor[0].x, (int)coor[0].y, (int)coor[n-1].x, (int)coor[n-1].y);
for (int i=0; i<n-1; i++){
g.drawLine((int)coor[i].x, (int)coor[i].y, (int)coor[i+1].x, (int)coor[i+1].y);

Answer 1

.java wrote:
I have been search for what seems like hours, Nice try, but in less than 15 seconds I found a complete discussion on the subject.
and I still have not managed to find anybody or anything that can clearly answer these three questions:
1. What is SAT?
2. How does it apply to 2D collision detection? (How would it be different with 3D collision detection?)
3. How can this be implemented in Java using Shape objects?
Note: I am easily confused by geometric terminology.This really looks like a question you should have an answer for in your notes from class, or in your book. If not perhaps you need to go ask your teacher what it is and explain why you don't have it in your notes or book.