There are 15 functions listed here

A
Affine - Distort the image linearly by moving a list of at least 3 or more sets of control points.
Affine projection - Linearly distort an image using the given Affine Matrix of 6 pre-calculated coefficients.
Arc - Arc the image.

B
Barrel - Given the four coefficients (A,B,C,D) as defined by Helmut Dersch, perform a barrel or pin-cushion distortion.
Barrel inverse - This is very similar to 'Barrel' with the same set of arguments, and argument handling.
Bilinear - Bilinear Distortion, given a minimum of 4 sets of coordinate pairs, or 16 values.

D
Depolar - Uses the same arguments and meanings as a 'Polar' distortion but generates the reverse.

P
Perspective - Perspective distort the images, using a list of 4 or more sets of control points.
Perspective projection - Do a 'Perspective' distortion biased on a set of 8 pre-calculated coefficients.
Polar - Like 'Arc' but do a complete Cartesian to Polar mapping of the image.
Polynomial -

S
Scale rotate translate - Distort image by first scaling and rotating about a given 'center', before translating that 'center' to the new location.
Sentinel -
Shepards - Distort the given list control points (any number) using an Inverse Squared Distance Interpolation Method.

U
Undefined -

These examples were generated using:
Imagick API version 1608
ImageMagick 6.4.8 2010-10-13 Q16

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