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(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/
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