Richard Suchenwirth 2004-12-08 - The corners of a polygon can come in clockwise or counter-clockwise order. The latter is to be preferred, but Tk's canvas displays both without problems. However, a clockwise-ordered polygon may indicate that a transformation (e.g. mirroring) has to take place. So I modified KBK's ccw code from convex hull, so that given a polygon as an {x y x y x y ...} list returns 1 if the polygon is counterclockwise, else 0. Should the first three points be collinear, the second to fourth are taken instead. By the way, the ccw code returned -1 for counterclockwise, 1 for clockwise, if I did not do a subtle mistake...
proc counterclockwise polygon {
foreach { x0 y0 x1 y1 x2 y2} $polygon break
set dx1 [expr { $x1 - $x0 }]
set dy1 [expr { $y1 - $y0 }]
set dx2 [expr { $x2 - $x0 }]
set dy2 [expr { $y2 - $y0 }]
set prod1 [expr { $dx1 * $dy2 }]
set prod2 [expr { $dy1 * $dx2 }]
if { $prod1 > $prod2 } {return 0}
if { $prod1 < $prod2 } {return 1}
if { $dx1*$dx2 < 0 || $dy1*$dy2 < 0 } {return 1}
if { $dx1*$dx1 + $dy1*$dy1 < $dx2*$dx2 + $dy2*$dy2 } {return 0}
counterclockwise [lrange $polygon 2 end]
}