Matrix transforms in XNA

Question

So in my most recent 2D game I draw objects like so.

_spriteBatch.Draw(_sprite, Center(), null, Color.White, _rotation, new Vector2(_sprite.Width / 2, _sprite.Height / 2), _scale, SpriteEffects.None, 0);

My bounding boxes are generated using a two step algorithm where I make the transform matrix, then apply it to a Rectangle of the sprite's height and width.

    public Rectangle BoundingBoxTransformed
    {
        get
        {
            //Center and rotate our Rectangle

            Matrix m = Matrix.CreateScale(_scale) * 
                Matrix.CreateTranslation(new Vector3(new Vector2((float)-BoundingBox.Width / 2, (float)-BoundingBox.Height / 2), 0.0f)) *
                Matrix.CreateRotationZ(_rotation) *
            //Move our rectangle toward the player, then recenter it by undoing the original translation (now that it's already rotated)

                Matrix.CreateTranslation(new Vector3(_location, 0.0f)) * Matrix.CreateTranslation(new Vector3((float)BoundingBox.Width / 2, (float)BoundingBox.Height / 2, 0.0f));
            return CalculateBoundingRectangle(new Rectangle(0, 0, _sprite.Width, _sprite.Height), m);
        }
    }

This is how I've been finding the new sizes for the scaled bounding boxes.

   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));
    }

I thought that I had the transformations all figured out, but when I run the game, I can see that my bounding boxes do not match up with my sprites.

So what is it that's going on here? Are my transformations out of order? Quick edit: The purple boxes are the original bounding boxes, which are used to determine the height and width of the red (transformed, i.e. scaled and rotated) bounding boxes.

Answer 1

I think this may be your problem:

Matrix.CreateTranslation(new Vector3(new Vector2((float)-BoundingBox.Width / 2, (float)-BoundingBox.Height / 2), 0.0f))

It appears you are trying to create a translation to the point of origin, which is what you should do when creating a rotation matrix, however, you are creating it based on your BoundingBox width and height. This should be your sprites original width and height.

Instead try:

Vector2 origin = new Vector2(_location.X + _sprite.Width / 2, _location.Y + _sprite.Height / 2);

Matrix m = Matrix.CreateTranslation(new Vector3(-origin), 0.0f)) *  
    Matrix.CreateScale(_scale) * 
    Matrix.CreateRotationZ(_rotation) *
    Matrix.CreateTranslation(new Vector3(_location, 0.0f)) * 
    Matrix.CreateTranslation(new Vector3(origin, 0.0f));

And then in your draw code:

_spriteBatch.Draw(_sprite, _location, null, Color.White, _rotation, origin, _scale, SpriteEffects.None, 0);