Transparent area goes black after copying/cropping PNG image using PHP GD library

Recently I was working on a project in which I needed to do some image manipulations using PHP GD library. Specifically I needed to crop some areas from PNG images. I was able to crop the images pretty easily, but there was a problem in the resulting images: the transparent areas were going black which was making the resulting images unusable. To solve this problem I had to do the following:

$cropped_image = ImageCreateTrueColor($crop_width, $crop_height);
imagealphablending( $cropped_image, false );
imagesavealpha( $cropped_image, true );
$transparent = imagecolorallocatealpha($cropped_image, 0, 0, 0, 127);
imagefill($cropped_image, 0, 0, $transparent);
$original_image = ImageCreateFromPNG($image_to_crop);
imagealphablending( $original_image, false );
imagesavealpha( $original_image, true );
ImageCopy($cropped_image, $original_image, 0, 0, $left, $top, $width, $height);
ImagePNG($cropped_image, $save_path);

Here $image is the cropped image. $width and $height are the width and height of the original image respectively. $left and $top are the left and top location of the rectangular portion of the original image which should be cropped. And $save_path is the location where the cropped image should be saved.

Hope this helps someone.