Affine

<?php 
$image = new imagick( "opossum.jpg" ); 
$points = array( 
                0,0, 25,25,   
               100,0, 100,50 
               );
$image->setimagebackgroundcolor("#fad888");
$image->setImageVirtualPixelMethod( imagick::VIRTUALPIXELMETHOD_BACKGROUND );
$image->distortImage(  Imagick::DISTORTION_AFFINE, $points, TRUE ); 
header( "Content-Type: image/jpeg" ); 
echo $image;
?>

Affine Projection

<?php 
$image = new imagick( "opossum.jpg" ); 
$points = array( 0.9,0.3,
                -0.2,0.7,
                 20,15 );
$image->setimagebackgroundcolor("#fad888");
$image->setImageVirtualPixelMethod( imagick::VIRTUALPIXELMETHOD_BACKGROUND );
$image->distortImage( Imagick::DISTORTION_AFFINEPROJECTION, $points, TRUE ); 
header( "Content-Type: image/jpeg" ); 
echo $image;
?>

Arc

<?php 
$image = new imagick( "opossum.jpg" ); 
$draw = new imagickdraw(); 
$degrees = array( 180 );
$image->setimagebackgroundcolor("#fad888");
$image->setImageVirtualPixelMethod( imagick::VIRTUALPIXELMETHOD_BACKGROUND );
$image->distortImage( Imagick::DISTORTION_ARC, $degrees, TRUE ); 
header( "Content-Type: image/jpeg" ); 
echo $image;
?>

Rotated Arc

<?php 
$image = new imagick( "opossum.jpg" ); 
$draw = new imagickdraw(); 
$degrees = array( 180, 45, 100, 20 );
$image->setimagebackgroundcolor("#fad888");
$image->setImageVirtualPixelMethod( imagick::VIRTUALPIXELMETHOD_BACKGROUND );
$image->distortImage( Imagick::DISTORTION_ARC, $degrees, TRUE ); 
header( "Content-Type: image/jpeg" ); 
echo $image;
?>

Bilinear

<?php 
$image = new imagick( "opossum.jpg" ); 
$points = array( 
                0,0, 25,25, # top left  
                176,0, 126,0, # top right
                0,135, 0,105, # bottom right 
                176,135, 176,135 # bottum left
                );
$image->setimagebackgroundcolor("#fad888");
$image->setImageVirtualPixelMethod( imagick::VIRTUALPIXELMETHOD_BACKGROUND );
$image->distortImage( Imagick::DISTORTION_BILINEAR, $points, TRUE ); 
header( "Content-Type: image/jpeg" ); 
echo $image;
?>

Perspective

<?php 
$image = new imagick( "opossum.jpg" ); 
$points = array( 
                0,0, 25,25, # top left  
                176,0, 126,0, # top right
                0,135, 0,105, # bottom right 
                176,135, 176,135 # bottum left
                );
$image->setimagebackgroundcolor("#fad888");
$image->setImageVirtualPixelMethod( imagick::VIRTUALPIXELMETHOD_BACKGROUND );
$image->distortImage( Imagick::DISTORTION_PERSPECTIVE, $points, TRUE ); 
header( "Content-Type: image/jpeg" ); 
echo $image;
?>

Scale Rotate Translate

<?php 
$image = new imagick( "opossum.jpg" ); 
$points = array( 
                 1.5, # scale 150%
                 150 # rotate
               );
$image->setimagebackgroundcolor("#fad888");
$image->setImageVirtualPixelMethod( imagick::VIRTUALPIXELMETHOD_BACKGROUND );
$image->distortImage( imagick::DISTORTION_SCALEROTATETRANSLATE, $points, TRUE ); 
header( "Content-Type: image/jpeg" ); 
echo $image;
?>

It is worth nothing that details on distorts as well as arguments can be found at http://www.imagemagick.org/Usage/distorts/ - the PHP manual doesn't give much, if any, detail on arguments.

I found this very useful when I had to do a translated rotation on an image - i.e. rotating around a point in the image that was not square in the center. This can be achieved by using distortImage with Imagick::DISTORTION_SCALEROTATETRANSLATE like this:

<?php

$imagick = new Imagick('/path/to/image');
$args = array(
    20, # x point to rotate around
    20, # y point to rotate around
    1, # scaling factor - 1 means no scaling
    90, # angle to rotate
);

$imagick->setImageVirtualPixelMethod(Imagick::VIRTUALPIXELMETHOD_TRANSPARENT);
$imagick->distortImage(Imagick::DISTORTION_SCALEROTATETRANSLATE, $args, true);

?>

Note that this type of distort takes from 1 to 7 arguments, depending on what you want to do exactly - there is a lot of flexibility here.

Control Points for DISTORTION_PERSPECTIVE are pairs of x0, y0, x1, y1 coordinates, where x0/y0 is the original point and x1/y1 is the destination point, 

e.g. for a four point distortion:

    <?php 

    $im = new imagick( $fn); 

    $w=$im->getImageWidth();
    $h=$im->getImageHeight();
    $im->setImageFormat('png');

    $controlPoints = array(
                    $tLx, $tLy, 0, 0,  // top left
                    $tRx, $tRy, $w, 0, // top right
                    $bRx, $bRy, $w, $h, // bottom right
                    $bLx, $bLy, 0, $h // bottom left
                );

    /* Perform the distortion */
    $im->distortImage(Imagick::DISTORTION_PERSPECTIVE, $controlPoints, false);

    // Output the image
    $output = $im->getimageblob();
    $outputtype = $im->getFormat();

    header("Content-type: $outputtype");
    echo $output;
     
    ?>

Slide image with shadow using distortImage

<?php

$slideValue = 150;

// Create new object 
$im = new Imagick("grnhrs.jpg");

// Resize 
$im->thumbnailImage(500,400);

// Set the image format to png 
$im->setImageFormat('png');

//Clone the current object
$shadow = $im->clone();

//Set image background color to black (this is the color of the shadow)
$shadow->setImageBackgroundColor( new ImagickPixel( 'black' ) );
 
 //Create the shadow 
$shadow->shadowImage( 80, 10, 5, 5 );

// Fill background area with transparent for image
//VIRTUALPIXELMETHOD_TRANSPARENT
$im->setImageVirtualPixelMethod(Imagick::VIRTUALPIXELMETHOD_ TRANSPARENT);

// Activate matte 
$im->setImageMatte(true);

//Control points for the distortion 
$controlPoints = array( 0, 0,
                        $slideValue, 0,
                        
                        0, $im->getImageHeight(),
                        0, $im->getImageHeight(),
                        
                        $im->getImageWidth(), 0,
                        $im->getImageWidth(), 0,
                        
                        $im->getImageWidth(), $im->getImageHeight(),
                        $im->getImageWidth()-$slideValue, $im->getImageHeight());
                        
// Perform the distortion 
$im->distortImage(Imagick::DISTORTION_PERSPECTIVEPROJECTION, $controlPoints, true);

// Perform the distortion in shadow image
$shadow->distortImage(Imagick::DISTORTION_PERSPECTIVEPROJECTION, $controlPoints, true);

// Imagick::shadowImage only creates the shadow.
// That is why the original image is composited over it 
$shadow->compositeImage( $im, Imagick::COMPOSITE_OVER, 0, 0 );

/* Ouput the image */
header("Content-Type: image/png");
echo $shadow;

?>