Shoelace formula for polygonal area: Difference between revisions

===version 1===

parse var @ '(' x.n "," y.n ')' "," @ /*obtain X and Y coördinates*/

===version 2===

This REXX version uses a different method to define the &nbsp; <big>'''X₀, &nbsp; Y₀'''</big>, &nbsp; and &nbsp; <big>'''X_n+1''', &nbsp; <big>'''Y_n+1'''</big> &nbsp; data points &nbsp; (and not treat them as exceptions).

When calculating the area for many polygons &nbsp; (or where the number of polygon sides is large), &nbsp; this method would be faster.

<lang rexx>/*REXX program uses a Shoelace formula to calculate the area of an N-sided polygon. */

parse arg pts /*obtain optional arguments from the CL*/

if pts='' then pts= '(3,4),(5,11),(12,8),(9,5),(5,6)' /*Not specified? Use default. */

pts=space(pts, 0); @=pts /*elide extra blanks; save pts.*/

do n=1 until @='' /*perform destructive parse on @*/

parse var @ '(' x.n "," y.n ')' "," @ /*obtain X and Y coördinates*/

end /*n*/

np=n+1 /*a variable to hold N+1 value*/

parse value x.1 y.1 x.n y.n with x.np y.np x.0 y.0 /*define X.0 & X.n+1 points.*/

A=0 /*initialize the area to zero.*/

do j=1 for n; jp=j+1; jm=j-1 /*adjust for J for overflow. */

A=A + x.j * (y.jp - y.jm) /*compute a part of the area. */

end /*j*/

A=abs(A/2) /*obtain half of the │ A │ sum*/

say 'polygon area of ' n " points: " pts ' is ───► ' A /*stick a fork in it, we're done*/</lang>

{{out|output|text=&nbsp; is the same as the 1^st REXX version.}} <br><br>