Convex hull

Find the points which form a convex hull from a set of arbitrary two dimensional points.

For example, given the points (16,3), (12,17), (0,6), (-4,-6), (16,6), (16,-7), (16,-3), (17,-4), (5,19), (19,-8), (3,16), (12,13), (3,-4), (17,5), (-3,15), (-3,-9), (0,11), (-9,-3), (-4,-2) and (12,10) the convex hull would be (-9,-3), (-3,-9), (19,-8), (17,5), (12,17), (5,19) and (-3,15).

J

Restated from the implementation at http://kukuruku.co/hub/funcprog/introduction-to-j-programming-language-2004

<lang J>counterclockwise =: ({. , }. /: 12 o. }. - {.) @ /:~ crossproduct =: 11"_ o. [: (* +)/ }. - {. removeinner =: #~ 1 , 0 > 3 crossproduct\ ] , 1: hull =: [: removeinner^:_ counterclockwise</lang>

Example use:

<lang J> hull 16j3 12j17 0j6 _4j_6 16j6 16j_7 16j_3 17j_4 5j19 19j_8 3j16 12j13 3j_4 17j5 _3j15 _3j_9 0j11 _9j_3 _4j_2 12j10 _9j_3 _3j_9 19j_8 17j5 12j17 5j19 _3j15</lang>