A simple approach would be to create a new image with the desired size, transform a Graphics2D
of this image according to the selected square region, and then simply paint the original image into this graphics:
private static BufferedImage extractRegion(
BufferedImage source, Point2D center, Point2D size, double angleRad)
{
int w = (int)size.getX();
int h = (int)size.getY();
BufferedImage result =
new BufferedImage(w, h, BufferedImage.TYPE_INT_ARGB);
Graphics2D g = result.createGraphics();
g.setRenderingHint(
RenderingHints.KEY_INTERPOLATION,
RenderingHints.VALUE_INTERPOLATION_BILINEAR);
g.translate(size.getX() / 2, size.getY() / 2);
g.rotate(angleRad);
g.translate(-center.getX(), -center.getY());
g.drawImage(source, 0, 0, null);
g.dispose();
return result;
}