imagick distort keep perspective - php

Question

I have developed a function to distort a PNG-logotype with dragpoints (using this function: http://codepen.io/fta/pen/ifnqH). The logotype itself is an image inside the div with dragpoints.
This logotype can later be generated as an image using PHP + Image Magick using the Imagick module. The logotype could be round, narrow or any kind of shape but the image is always in a 1:1 ratio (ex: 800x800) filled with transparency.
Now to the problem:
I always wan't the logotype to have the ratio 1:1 regarding on how wide or narrow the dragged area is (i don't wan't the logotype itself to be stretched). Although, the image itself can be distorted.
The image on top illustrates how it works now, and the image in the bottom how i wan't it to work
http://i.stack.imgur.com/Ev0H8.jpg
Most importantly, this should work on the generated image using Image Magick + PHP. If it is possible to make it work on the client side using the dragpoints...that is a bonus.
I know how to get the real size of the logotype using $image->trimImage(0);
I should somehow be able to fill the edges of the image with extra transparency (x or y axis) to compensate for the stretch, but that is only so far i have come.
This is my PHP-function to stretch or scale the logotype
public function generate($file, $watermark, $offset = array()) {
$file = rtrim(DIR_IMAGE . str_replace(array('../', '..\\', '..'), '', $file));
$watermark = rtrim(DIR_IMAGE . str_replace(array('../', '..\\', '..'), '', $watermark));
$width = (int)$this->config->get('config_image_popup_width');
$height = (int)$this->config->get('config_image_popup_height');
if (is_file($file) && is_file($watermark)) {
$top = (int)$offset['top'];
$left = (int)$offset['left'];
$opacity = (float)$offset['opacity'];
$new_width = (int)$offset['width'];
$new_height = (int)$offset['height'];
$topleft_y = (float)$offset['transform_topleft_y'];
$topleft_x = (float)$offset['transform_topleft_x'];
$topright_y = (float)$offset['transform_topright_y'];
$topright_x = (float)$offset['transform_topright_x'];
$bottomleft_y = (float)$offset['transform_bottomleft_y'];
$bottomleft_x = (float)$offset['transform_bottomleft_x'];
$bottomright_y = (float)$offset['transform_bottomright_y'];
$bottomright_x = (float)$offset['transform_bottomright_x'];
$image = new ImageMagick($file);
$watermark = new ImageMagick($watermark);
// Resize the product image
$image->resize($width, $height);
// Perspective has not changed, scale only
if ($topleft_y == 0 && $topleft_x == 0 && $topright_y == 0 && $bottomleft_x == 0 && $topright_x == $bottomleft_y && $bottomleft_y == $bottomright_y && $bottomright_y == $bottomright_x) {
$watermark->scale($new_width, $new_height);
} else {
$watermark->perspective($offset);
}
$watermark->opacity($opacity);
$image->composite($watermark->get(), $left, $top);
return $image->base64output(100);
}