How to check if point intersects AABB for custom 2D physics engine

Question

I've found no way of creating a 2D collision AABB on google, and I was wondering how the maths of it work. I was thinking that I could use some kind of matrix transforms to achieve it but that idea failed epically. So basically, I want to know of any resource that can help me create an Angle-Aligned Bounding Box and check if a point intersects it, or an explanation of the maths and logic of it.

Edit: I don't know if I made it clear, but I need to test collisions with them. Just to make that crystal clear.

I've now ported this: asawicki.info/… but I can't figure out how to make it work. — annonymously
What are you trying to make an AABB around? Is it a simple shape like a rectangle or a circle, or is it something complicated like a sprite? — David Brown
@David I just need to make it for my physics engine. It should encompass anything I want it to when I make my games. But for now I'll keep it to a rotated rectangle — annonymously
That is very vague. To answer your question we need more specifics. Can don't you post a short example of the kind of objects you have and what you've tried so far? — David Brown
@DavidBrown well actually I don't need specifics, just the logic behind how they work and how to find if a point intersects the aabb — annonymously

jgallant jgallant · Accepted Answer · 2011-12-29T13:07:17

An intersection check between two Rectangles does not allow you to check against a rotated rectangle. The as the simple intersects function will not work. Your idea of calculating a Rectangle that encompasses your "actual" rotated Rectangle, and then checking for collisions on the Bounding Rectangles instead.

Here is some code that will return a Rectangle based on another Rectangle and a Rotation Matrix transformation:

public static Rectangle CalculateBoundingRectangle(Rectangle rectangle, Matrix transform)
{
    // Get all four corners in local space
    Vector2 leftTop = new Vector2(rectangle.Left, rectangle.Top);
    Vector2 rightTop = new Vector2(rectangle.Right, rectangle.Top);
    Vector2 leftBottom = new Vector2(rectangle.Left, rectangle.Bottom);
    Vector2 rightBottom = new Vector2(rectangle.Right, rectangle.Bottom);

    // Transform all four corners into work space
    Vector2.Transform(ref leftTop, ref transform, out leftTop);
    Vector2.Transform(ref rightTop, ref transform, out rightTop);
    Vector2.Transform(ref leftBottom, ref transform, out leftBottom);
    Vector2.Transform(ref rightBottom, ref transform, out rightBottom);

    // Find the minimum and maximum extents of the rectangle in world space
    Vector2 min = Vector2.Min(Vector2.Min(leftTop, rightTop),
                                Vector2.Min(leftBottom, rightBottom));
    Vector2 max = Vector2.Max(Vector2.Max(leftTop, rightTop),
                                Vector2.Max(leftBottom, rightBottom));

    // Return that as a rectangle
    return new Rectangle((int)min.X, (int)min.Y, (int)(max.X - min.X), (int)(max.Y - min.Y));
}

Of course, this type of collision detection is fast, but not accurate. Your Bounding rectangle will not be a 1:1 representation of your shape. If you need more accuracy, you could then use a per-pixel collision check after checking with AABB.

This answer might also be of interest to you, particularly the answer on SAT.

How to check if point intersects AABB for custom 2D physics engine

1 Answers