if 0 {Richard Suchenwirth 2004--07-23 - Given a convex polygon represented as {x y x y ...} list of its corner coordinates, I wanted to calculate its area. This is simple for the special case of the triangle, using the "Heronic formula":}
proc triangle'area coords {
foreach {xa ya xb yb xc yc} $coords break
set a [expr {hypot($yb-$yc, $xb-$xc)}]
set b [expr {hypot($ya-$yc, $xa-$xc)}]
set c [expr {hypot($ya-$yb, $xa-$xb)}]
set s [expr {($a+$b+$c)/2.}]
expr {sqrt($s*($s-$a)*($s-$b)*($s-$c))} ;# Heronic formula
}if 0 {For the general polygon I devised this recursive approach, which de facto does a triangulation, by measuring the area between the first three points, and then calling itself with the second corner's coordinates removed from the list: }
proc polygon::area coords {
expr {
[llength $coords]<6? 0 :
[triangle'area [lrange $coords 0 5]]
+ [area [lreplace $coords 2 3]]
}
}See also Drawing and rotating polygons - Regular polygons - Polygon intersection