(info:dir determine direction for polygon described by ordered points)
(minimum 3 points, up to 6 points)

(return: #<_dir:> == 2 for CW, 3 for CCW, -1 for undetermined)
(return: #<_dir:area>)
(return: #<_dir:cx>, #<_dir:cy> centroid)

o<dir> sub
#<n>  =  #1 (=4 N neg:verbose)
#<x1> =  #2
#<y1> =  #3
#<x2> =  #4
#<y2> =  #5
#<x3> =  #6
#<y3> =  #7
#<x4> =  #8 (=0)
#<y4> =  #9 (=0)
#<x5> = #10 (=0)
#<y5> = #11 (=0)
#<x6> = #12 (=0)
#<y6> = #13 (=0)

        #<verbose> = 0
o<i0>   if [#<n> LT 0]
          #<n> = [ABS[#<n>]]
          #<verbose> = 1
o<i0>   endif

o<i1>   if [[#<n> GE 7] or [#<n> LE 2]]
           (print, dir: problem bad n=#<n>)
           (debug, dir: problem bad n=#<n>)
           #<_dir:> = -1 ;undetermined with message, caller must handle
o<i1>   endif

        #<a>  = 0
        #<cx> = 0
        #<cy> = 0

        #<del> = [#<x1> * #<y2> - #<x2> * #<y1>]
        #<a>   = [#<a>  + #<del>]
        #<cx>  = [#<cx> + [#<x2> + #<x1>] * #<del>]
        #<cy>  = [#<cy> + [#<y2> + #<y1>] * #<del>]

        #<del> = [#<x2> * #<y3> - #<x3> * #<y2>]
        #<a>   = [#<a>  + #<del>]
        #<cx>  = [#<cx> + [#<x3> + #<x2>] * #<del>]
        #<cy>  = [#<cy> + [#<y3> + #<y2>] * #<del>]

o<if3>  if [#<n> eq 3]
          #<del> = [#<x3> * #<y1> - #<x1> * #<y3>]
          #<a>   = [#<a>  + #<del>]
          #<cx>  = [#<cx> + [#<x1> + #<x3>] * #<del>]
          #<cy>  = [#<cy> + [#<y1> + #<y3>] * #<del>]
o<if3>  endif
o<if4>  if [#<n> eq 4]
          #<del> = [#<x3> * #<y4> - #<x4> * #<y3>]
          #<a>   = [#<a>  + #<del>]
          #<cx>  = [#<cx> + [#<x4> + #<x3>] * #<del>]
          #<cy>  = [#<cy> + [#<y4> + #<y3>] * #<del>]

          #<del> = [#<x4> * #<y1> - #<x1> * #<y4>]
          #<a>   = [#<a>  + #<del>]
          #<cx>  = [#<cx> + [#<x1> + #<x4>] * #<del>]
          #<cy>  = [#<cy> + [#<y1> + #<y4>] * #<del>]
o<if4>  endif
o<if5>  if [#<n> eq 5]
          #<del> = [#<x3> * #<y4> - #<x4> * #<y3>]
          #<a>   = [#<a>  + #<del>]
          #<cx>  = [#<cx> + [#<x4> + #<x3>] * #<del>]
          #<cy>  = [#<cy> + [#<y4> + #<y3>] * #<del>]

          #<del> = [#<x4> * #<y5> - #<x5> * #<y4>]
          #<a>   = [#<a>  + #<del>]
          #<cx>  = [#<cx> + [#<x5> + #<x4>] * #<del>]
          #<cy>  = [#<cy> + [#<y5> + #<y4>] * #<del>]

          #<del> = [#<x5> * #<y1> - #<x1> * #<y5>]
          #<a>   = [#<a>  + #<del>]
          #<cx>  = [#<cx> + [#<x1> + #<x5>] * #<del>]
          #<cy>  = [#<cy> + [#<y1> + #<y5>] * #<del>]
o<if5>  endif
o<if6>  if [#<n> eq 6]
          #<del> = [#<x3> * #<y4> - #<x4> * #<y3>]
          #<a>   = [#<a>  + #<del>]
          #<cx>  = [#<cx> + [#<x4> + #<x3>] * #<del>]
          #<cy>  = [#<cy> + [#<y4> + #<y3>] * #<del>]

          #<del> = [#<x4> * #<y5> - #<x5> * #<y4>]
          #<a>   = [#<a>  + #<del>]
          #<cx>  = [#<cx> + [#<x5> + #<x4>] * #<del>]
          #<cy>  = [#<cy> + [#<y5> + #<y4>] * #<del>]

          #<del> = [#<x5> * #<y6> - #<x6> * #<y5>]
          #<a>   = [#<a>  + #<del>]
          #<cx>  = [#<cx> + [#<x6> + #<x5>] * #<del>]
          #<cy>  = [#<cy> + [#<y6> + #<y5>] * #<del>]

          #<del> = [#<x6> * #<y1> - #<x1> * #<y6>]
          #<a>   = [#<a>  + #<del>]
          #<cx>  = [#<cx> + [#<x1> + #<x6>] * #<del>]
          #<cy>  = [#<cy> + [#<y1> + #<y6>] * #<del>]
o<if6>  endif

        #<_dir:cx>   = [#<cx> / #<a> / 3] ; signed area reqd here
        #<_dir:cy>   = [#<cy> / #<a> / 3] ; signed area reqd here
        #<_dir:area> = [ABS[#<a>]/2]      ; return unsigned area

o<f0>   if [#<a> GT 0]
          #<_dir:> = 3 (ccw)
o<f0>   else
o<f1>     if [#<a> LT 0]
            #<_dir:> = 2 (cw)
o<f1>     else
            #<_dir:> = -1 ;undetermined
o<f1>     endif
o<f0>   endif

o<f2>   if [#<verbose> GT 0]
o<f3>     if [#<_dir:> eq 2]
            (debug, dir:  CW #<_dir:> area=#<_dir:area> cx=#<_dir:cx> cy=#<_dir:cy>)
o<f3>     else
            (debug, dir: CCW #<_dir:> area=#<_dir:area> cx=#<_dir:cx> cy=#<_dir:cy>)
o<f3>     endif
o<f2>   endif

o<dir> endsub
; ref: many sources for polygons on the web, for example:
; http://paulbourke.net/geometry/polyarea/