AABB of rotated sprite?

Question

Say I have a sprite. Its axis-aligned bounding box (AABB) is easy to find since I know the width and height. Say I rotate it 45 degrees, I don\'t think the AABB would be big

Answer 1

Answer 2

If you want a single box that covers all angles, just take the half-diagonal of your existing box as the radius of a circle. The new box has to contain this circle, so it should be a square with side-length equal to twice the radius (equiv. the diagonal of the original AABB) and with the same center as the original.

In general the object will be rotated around an arbitrary point, so you have to compute the new location of the center and translate this box to the right place.

Answer 3

I don't know if this is the most efficient method, but I would just calculate the new positions of the vertices and based on that data find out the AABB. So for example,

Vertex v0, v1, v2, v3;
// in the local coordinates of the rectangle
// so for example v0 is always 0,0 and width and height define the others
// put some values to v0..v3

glLoadIdentity();
glTranslatef(the position of the rectangle);
glTranslatef(center_point);
glRotatef(angle, 0,0,1);
glTranslatef(-center_point);

GLfloat matrix[16];
glGetFloatv(GL_MODELVIEW_MATRIX, matrix);

v0 = multiply_matrix_by_vector(matrix, v0);
v1 = multiply_matrix_by_vector(matrix, v1);
v2 = multiply_matrix_by_vector(matrix, v2);
v3 = multiply_matrix_by_vector(matrix, v3);

AABB = find_the_minimums_and_maximums(v0, v1, v2, v3);

If you don't know how to multiply a matrix by vector, try googling it.

Also note that since the matrix dimensions are 4x4, the vectors for the vertices also need to be 4-dimensional. You can convert a 2D vector to a 4D vector by adding a third component 0 (zero) and a fourth component 1 (one). After the multiplication has been done, you can convert the resulting 4D vector back to 2D by dividing the x and y components by the fourth component and simply by ignoring the third component because you don't need a third dimension.

Since matrix multiplications might be a quite processor-heavy operation, this approach might be good only, if you don't need to update a lot of AABBs very often.