Axis Aligned Rectangle Collision Detection - Java

Question

I have some problem checking if the 2 rectangles has a collision given with 4 points, so I have a rect1 with p1(x,y) for lower left corner and p2(x,y) for upper right corner, same as rect2.

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So this is my graph illustration:

This is my sample code so far:

    int[][] rect1 = {{2,0},{3,1}};
    int[][] rect2 = {{0,0},{1,2}};
    if(rect1[1][0] >= rect2[0][0] && rect1[1][1] >= rect2[0][1] && rect1[0][0] <= rect2[1][0] && rect1[0][1] <= rect2[1][1])
    {
        System.out.println("Collision");
    } else {
        System.out.println("No Collision");
    }

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I'm not pretty sure if I got it correctly with this code, can anyone give my some idea? (I'm beginner!)

Answer 1

First, your code do not compiles in the if block. There is an unmatched opening parenthesis. I will remove it.

So, lets add some intermediate variables to better see the meaning of the code:

int[][] rect1 = {{2,0},{3,1}};
int[][] rect2 = {{0,0},{1,2}};

int rect1X1 = rect1[0][0];
int rect1X2 = rect1[1][0];
int rect1Y1 = rect1[0][1];
int rect1Y2 = rect1[1][1];

int rect2X1 = rect2[0][0];
int rect2X2 = rect2[1][0];
int rect2Y1 = rect2[0][1];
int rect2Y2 = rect2[1][1];

if (rect1X2 >= rect2X1 && rect1Y2 >= rect2Y1 && rect1X1 <= rect2X2 && rect1Y1 <= rect2Y2)
{
    System.out.println("Collision");
} else {
    System.out.println("No Collision");
}

Now, lets separate the logic of each axis:

int[][] rect1 = {{2,0},{3,1}};
int[][] rect2 = {{0,0},{1,2}};

int rect1X1 = rect1[0][0];
int rect1X2 = rect1[1][0];
int rect1Y1 = rect1[0][1];
int rect1Y2 = rect1[1][1];

int rect2X1 = rect2[0][0];
int rect2X2 = rect2[1][0];
int rect2Y1 = rect2[0][1];
int rect2Y2 = rect2[1][1];

boolean xCollides = rect1X2 >= rect2X1 && rect1X1 <= rect2X2;
boolean yCollides = rect1Y2 >= rect2Y1 && rect1Y1 <= rect2Y2;

if (xCollides && yCollides)
{
    System.out.println("Collision");
} else {
    System.out.println("No Collision");
}

How can we get a collision for one axis? There are 15 forms of how the two objects are positioned along an axis in relation to each other:

Case 1 - Full coincident collision:

X-----X
X-----X

Cases 2, 3, 4, 5, 6 and 7 - Full non-coincident collision:

X---X              X---X          X-----X
X-----X          X-----X            X---X


X-----X            X-X            X-----X
  X-X            X-----X          X---X

Cases 8 and 9 - Partial collision:

X---X              X---X
  X---X          X---X

Cases 10 and 11 - Barely colliding:

X--X                X--X
   X--X          X--X

Cases 12 and 13 - Just touching (not colliding):

X--X                 X-X
    X-X          X--X

Cases 14 and 15 - Far apart (not colliding):

X-X                  X-X
    X-X          X-X

Your code should separate the cases 1 to 11 from the cases 12 to 15 in each axis. Lets see what it does:

boolean xCollides = rect1X2 >= rect2X1 && rect1X1 <= rect2X2;

• Case 1: true and true -> true
• Case 2: true and true -> true
• Case 3: true and true -> true
• Case 4: true and true -> true
• Case 5: true and true -> true
• Case 6: true and true -> true
• Case 7: true and true -> true
• Case 8: true and true -> true
• Case 9: true and true -> true
• Case 10: true and true -> true
• Case 11: true and true -> true
• Case 12: false and true -> false
• Case 13: true and false -> false
• Case 14: false and true -> false
• Case 15: true and false -> false

So, your code is able to separate the cases 1 to 11 from cases 12 to 15, and thus it is correct for axis X. The code for axis Y is equivalent to the code to axis X (just under a different axis), so it is also correct. Finally, we conclude that your entire code is correct.