Source code in the jq programming language

# ccw returns true if the three points make a counter-clockwise turn
def ccw(a; b; c):
  a as [$ax, $ay]
  | b as [$bx, $by]
  | c as [$cx, $cy]
  | (($bx - $ax) * ($cy - $ay)) > (($by - $ay) * ($cx - $ax)) ;

def convexHull:
  if . == [] then []
  else sort as $pts
  # lower hull:
  | reduce $pts[] as $pt ([];
      until (length < 2 or ccw(.[-2]; .[-1]; $pt); .[:-1] )
      | . + [$pt] )
  # upper hull
  | (length + 1) as $t
  | reduce range($pts|length-2; -1; -1) as $i (.;
      $pts[$i] as $pt
      | until (length < $t or ccw(.[-2]; .[-1]; $pt); .[:-1] )
      | . + [$pt])
  | .[:-1]
  end ;

def pts: [
    [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], [12, 10]
];

"Convex Hull: \(pts|convexHull)"