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Shoelace formula for polygonal area: Difference between revisions

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Shoelace formula for polygonal area (view source)

Revision as of 14:44, 28 August 2022

2,106 bytes added ,  1 year ago
m
syntax highlighting fixup automation
m (syntax highlighting fixup automation)
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{{trans|Python}}
 
<langsyntaxhighlight lang="11l">F area_by_shoelace(x, y)
R abs(sum(zip(x, y[1..] [+] y[0.<1]).map((i, j) -> i * j))
-sum(zip(x[1..] [+] x[0.<1], y).map((i, j) -> i * j))) / 2
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V y = points.map(p -> p[1])
 
print(area_by_shoelace(x, y))</langsyntaxhighlight>
 
{{out}}
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=={{header|360 Assembly}}==
<langsyntaxhighlight lang="360asm">* SHOELACE 25/02/2019
SHOELACE CSECT
USING SHOELACE,R15 base register
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PG DC CL12' ' buffer
REGEQU
END SHOELACE</langsyntaxhighlight>
{{out}}
<pre>
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{{libheader|Action! Tool Kit}}
{{libheader|Action! Real Math}}
<langsyntaxhighlight Actionlang="action!">INCLUDE "H6:REALMATH.ACT"
 
PROC Area(INT ARRAY xs,ys BYTE count REAL POINTER res)
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Test(xs,ys,5)
RETURN</langsyntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Shoelace_formula_for_polygonal_area.png Screenshot from Atari 8-bit computer]
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{{works with|Ada|Ada|83}}
 
<langsyntaxhighlight Adalang="ada">with Ada.Text_IO;
 
procedure Shoelace_Formula_For_Polygonal_Area
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begin
Ada.Text_IO.Put_Line(Shoelace(my_polygon)'Img);
end Shoelace_Formula_For_Polygonal_Area;</langsyntaxhighlight>
{{out}}
<pre> 3.00000E+01
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=={{header|ALGOL 68}}==
<langsyntaxhighlight lang="algol68">BEGIN
# returns the area of the polygon defined by the points p using the Shoelace formula #
OP AREA = ( [,]REAL p )REAL:
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print( ( fixed( AREA [,]REAL( ( 3.0, 4.0 ), ( 5.0, 11.0 ), ( 12.0, 8.0 ), ( 9.0, 5.0 ), ( 5.0, 6.0 ) ), -6, 2 ), newline ) )
END
</syntaxhighlight>
</lang>
{{out}}
<pre>
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=={{header|APL}}==
{{works with|Dyalog APL}}
<langsyntaxhighlight APLlang="apl">shoelace ← 2÷⍨|∘(((1⊃¨⊢)+.×1⌽2⊃¨⊢)-(1⌽1⊃¨⊢)+.×2⊃¨⊢)</langsyntaxhighlight>
{{out}}
<pre> shoelace (3 4) (5 11) (12 8) (9 5) (5 6)
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=={{header|AutoHotkey}}==
<langsyntaxhighlight AutoHotkeylang="autohotkey">V := [[3, 4], [5, 11], [12, 8], [9, 5], [5, 6]]
 
n := V.Count()
for i, O in V
Sum += V[i, 1] * V[i+1, 2] - V[i+1, 1] * V[i, 2]
MsgBox % result := Abs(Sum += V[n, 1] * V[1, 2] - V[1, 1] * V[n, 2]) / 2</langsyntaxhighlight>
{{out}}
<pre>30.000000</pre>
 
=={{header|BASIC256}}==
<langsyntaxhighlight BASIC256lang="basic256">arraybase 1
dim array = {{3,4}, {5,11}, {12,8}, {9,5}, {5,6}}
 
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sum -= p[1][1] * p[i][2]
return abs(sum) \ 2
end function</langsyntaxhighlight>
 
=={{header|C}}==
Reads the points from a file whose name is supplied via the command line, prints out usage if invoked incorrectly.
<syntaxhighlight lang="c">
<lang C>
#include<stdlib.h>
#include<stdio.h>
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return 0;
}
</syntaxhighlight>
</lang>
Input file, first line specifies number of points followed by the ordered vertices set with one vertex on each line.
<pre>
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=={{header|C sharp|C#}}==
{{trans|Java}}
<langsyntaxhighlight lang="csharp">using System;
using System.Collections.Generic;
 
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}
}
}</langsyntaxhighlight>
{{out}}
<pre>Given a polygon with vertices [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)],
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=={{header|C++}}==
{{trans|D}}
<langsyntaxhighlight lang="cpp">#include <iostream>
#include <tuple>
#include <vector>
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auto ans = shoelace(points);
cout << ans << endl;
}</langsyntaxhighlight>
{{out}}
<pre>30</pre>
 
=={{header|Cowgol}}==
<langsyntaxhighlight lang="cowgol">include "cowgol.coh";
 
typedef Coord is uint16; # floating point types are not supported
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var polygon: Point[] := {{3,4},{5,11},{12,8},{9,5},{5,6}};
print_i16(shoelace(&polygon[0], @sizeof polygon));
print_nl();</langsyntaxhighlight>
{{out}}
<pre>30</pre>
=={{header|D}}==
<langsyntaxhighlight Dlang="d">import std.stdio;
 
Point[] pnts = [{3,4}, {5,11}, {12,8}, {9,5}, {5,6}];
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auto ans = shoelace(pnts);
assert(ans == 30);
}</langsyntaxhighlight>
{{out}}
<pre>30</pre>
 
=={{header|F_Sharp|F#}}==
<langsyntaxhighlight lang="fsharp">
// Shoelace formula for area of polygon. Nigel Galloway: April 11th., 2018
let fN(n::g) = abs(List.pairwise(n::g@[n])|>List.fold(fun n ((nα,gα),(nβ,gβ))->n+(nα*gβ)-(gα*nβ)) 0.0)/2.0
printfn "%f" (fN [(3.0,4.0); (5.0,11.0); (12.0,8.0); (9.0,5.0); (5.0,6.0)])</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|Factor}}==
By constructing a <code>circular</code> from a sequence, we can index elements beyond the length of the sequence, wrapping around to the beginning. We can also change the beginning of the sequence to an arbitrary index. This allows us to use <code>2map</code> to cleanly obtain a sum.
<langsyntaxhighlight lang="factor">USING: circular kernel math prettyprint sequences ;
IN: rosetta-code.shoelace
 
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[ shoelace-sum ] 2bi@ - abs 2 / ;
 
input shoelace-area .</langsyntaxhighlight>
{{out}}
<pre>
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Except for the use of "END FUNCTION ''name'' instead of just END, and the convenient function SUM with array span expressions (so SUM(P) rather than a DO-loop to sum the elements of array P), both standardised with F90, this would be acceptable to F66, which introduced complex number arithmetic. Otherwise, separate X and Y arrays would be needed, but complex numbers seemed convenient seeing as (x,y) pairs are involved. But because the MODULE facility of F90 has not been used, routines invoking functions must declare the type of the function names, especially if the default types are unsuitable, as here. In function AREA, the x and y parts are dealt with together, but in AREASL they might be better as separate arrays, thus avoiding the DIMAG and DBLE functions to extract the x and y parts. Incidentally, the x and y parts can be interchanged and the calculation still works. Comparing the two resulting areas might give some indication of their accuracy.
 
If the MODULE protocol were used, the size of an array parameter is passed as a secret additional parameter accessible via the special function UBOUND, but otherwise it must be passed as an explicit parameter. A quirk of the compiler requires that N be declared before it appears in <code>DOUBLE COMPLEX P(N)</code> so as it is my practice to declare parameters in the order specified, here N comes before P. However, it is not clear whether specifying P(N) does much good (as in array index checking) as an alternative is to specify P(*) meaning merely that the array has one dimension, or even P(12345) to the same effect, with no attention to the actual numerical value. See for example [[Array_length#Fortran]] <langsyntaxhighlight Fortranlang="fortran"> DOUBLE PRECISION FUNCTION AREA(N,P) !Calculates the area enclosed by the polygon P.
C Uses the mid-point rule for integration. Consider the line joining (x1,y1) to (x2,y2)
C The area under that line (down to the x-axis) is the y-span midpoint (y1 + y2)/2 times the width (x2 - x1)
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A2 = AREASL(5,POINT)
WRITE (6,*) "A=",A1,A2
END</langsyntaxhighlight>
 
Output: WRITE (6,*) means write to output unit six (standard output) with free-format (the *). Note the different sign convention.
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===Fortran I===
In orginal FORTRAN 1957:
<langsyntaxhighlight lang="fortran">
C SHOELACE FORMULA FOR POLYGONAL AREA
DIMENSION X(33),Y(33)
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303 FORMAT(F10.2)
 
</syntaxhighlight>
</lang>
{{in}}
<pre>
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=={{header|FreeBASIC}}==
<langsyntaxhighlight lang="freebasic">' version 18-08-2017
' compile with: fbc -s console
 
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Print : Print "hit any key to end program"
Sleep
End</langsyntaxhighlight>
{{out}}
<pre>The area of the polygon = 30</pre>
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=={{header|Go}}==
<langsyntaxhighlight lang="go">package main
 
import "fmt"
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func main() {
fmt.Println(shoelace([]point{{3, 4}, {5, 11}, {12, 8}, {9, 5}, {5, 6}}))
}</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|Haskell}}==
<langsyntaxhighlight Haskelllang="haskell">import Data.Bifunctor (bimap)
 
----------- SHOELACE FORMULA FOR POLYGONAL AREA ----------
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main =
print $
shoelace [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)]</langsyntaxhighlight>
{{out}}
<pre>30.0</pre>
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Implementation:
 
<langsyntaxhighlight Jlang="j">shoelace=:verb define
0.5*|+/((* 1&|.)/ - (* _1&|.)/)|:y
)</langsyntaxhighlight>
 
Task example:
 
<langsyntaxhighlight Jlang="j"> shoelace 3 4,5 11,12 8,9 5,:5 6
30</langsyntaxhighlight>
 
Exposition:
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We start with our list of coordinate pairs
 
<langsyntaxhighlight Jlang="j"> 3 4,5 11,12 8,9 5,:5 6
3 4
5 11
12 8
9 5
5 6</langsyntaxhighlight>
 
But the first thing we do is transpose them so that x coordinates and y coordinates are the two items we are working with:
 
<langsyntaxhighlight lang="j"> |:3 4,5 11,12 8,9 5,:5 6
3 5 12 9 5
4 11 8 5 6</langsyntaxhighlight>
 
We want to rotate the y list by one (in each direction) and multiply the x list items by the corresponding y list items. Something like this, for example:
 
<langsyntaxhighlight lang="j"> 3 5 12 9 5* 1|.4 11 8 5 6
33 40 60 54 20</langsyntaxhighlight>
 
Or, rephrased:
 
<langsyntaxhighlight lang="j"> (* 1&|.)/|:3 4,5 11,12 8,9 5,:5 6
33 40 60 54 20</langsyntaxhighlight>
 
We'll be subtracting what we get when we rotate in the other direction, which looks like this:
 
<langsyntaxhighlight lang="j"> ((* 1&|.)/ - (* _1&|.)/)|:3 4,5 11,12 8,9 5,:5 6
15 20 _72 _18 _5</langsyntaxhighlight>
 
Finally, we add up that list, take the absolute value (there are contexts where signed area is interesting - for example, some graphics application - but that was not a part of this task) and divide that by 2.
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{{trans|Kotlin}}
{{works with|Java|9}}
<langsyntaxhighlight Javalang="java">import java.util.List;
 
public class ShoelaceFormula {
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System.out.printf("its area is %f,%n", area);
}
}</langsyntaxhighlight>
{{out}}
<pre>Given a polygon with vertices [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)],
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=={{header|JavaScript}}==
<langsyntaxhighlight lang="javascript">(() => {
"use strict";
 
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// MAIN ---
return main();
})();</langsyntaxhighlight>
{{Out}}
<pre>Polygonal area by shoelace formula:
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===={{trans|Wren}}====
<langsyntaxhighlight lang="jq"># jq's length applied to a number is its absolute value.
def shoelace:
. as $a
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[ [3, 4], [5, 11], [12, 8], [9, 5], [5, 6] ]
| "The polygon with vertices at \(.) has an area of \(shoelace)."</langsyntaxhighlight>
{{out}}
<pre>
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</pre>
===={{trans|Julia}}====
<langsyntaxhighlight lang="jq">def zip_shoelace:
def sumprod: reduce .[] as [$x,$y] (0; . + ($x * $y));
. as {$x, $y}
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{x: [3, 5, 12, 9, 5], y: [4, 11, 8, 5, 6] }
| zip_shoelace</langsyntaxhighlight>
{{out}}
As above.
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{{trans|Python}}
 
<langsyntaxhighlight lang="julia">"""
Assumes x,y points go around the polygon in one direction.
"""
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x, y = [3, 5, 12, 9, 5], [4, 11, 8, 5, 6]
@show x y shoelacearea(x, y)</langsyntaxhighlight>
 
{{out}}
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=={{header|Kotlin}}==
<langsyntaxhighlight lang="scala">// version 1.1.3
 
class Point(val x: Int, val y: Int) {
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println("Given a polygon with vertices at $v,")
println("its area is $area")
}</langsyntaxhighlight>
 
{{out}}
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=={{header|Lambdatalk}}==
<langsyntaxhighlight lang="scheme">
{def shoelace
{lambda {:pol}
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{shoelace {pol}}
-> 30
</syntaxhighlight>
</lang>
 
=={{header|Lua}}==
<langsyntaxhighlight lang="lua">function shoeArea(ps)
local function det2(i,j)
return ps[i][1]*ps[j][2]-ps[j][1]*ps[i][2]
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for i=1,#ps-1 do sum = sum + det2(i,i+1)end
return math.abs(0.5 * sum)
end</langsyntaxhighlight>
Using an accumulator helper inner function
<langsyntaxhighlight lang="lua">function shoeArea(ps)
local function ssum(acc, p1, p2, ...)
if not p2 or not p1 then
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local p = {{3,4}, {5,11}, {12,8}, {9,5}, {5,6}}
print(shoeArea(p))-- 30 </langsyntaxhighlight>
both version handle special cases of less than 3 point as 0 area result.
 
=={{header|Maple}}==
 
<syntaxhighlight lang="maple">
<lang Maple>
with(ArrayTools):
 
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P1 := Polygon(Array([Point(3,4), Point(5,11), Point(12,8), Point(9,5), Point(5,6)])):
area(P1);
</syntaxhighlight>
</lang>
 
{{out}}<pre>
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=={{header|Mathematica}}/{{header|Wolfram Language}}==
Geometry objects built-in in the Wolfram Language
<langsyntaxhighlight Mathematicalang="mathematica">Area[Polygon[{{3, 4}, {5, 11}, {12, 8}, {9, 5}, {5, 6}}]]</langsyntaxhighlight>
{{out}}
<pre>30</pre>
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=={{header|min}}==
{{works with|min|0.19.3}}
<langsyntaxhighlight lang="min">((((first) map) ((last) map)) cleave) :dezip
(((first) (rest)) cleave append) :rotate
((0 <) (-1 *) when) :abs
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) :shoelace
 
((3 4) (5 11) (12 8) (9 5) (5 6)) shoelace print</langsyntaxhighlight>
{{out}}
<pre>
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=={{header|MiniScript}}==
<langsyntaxhighlight MiniScriptlang="miniscript">shoelace = function(vertices)
sum = 0
points = vertices.len
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print "The polygon area is " + shoelace(verts)
</syntaxhighlight>
</lang>
{{out}}
<pre>
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=={{header|Modula-2}}==
<langsyntaxhighlight lang="modula2">MODULE ShoelaceFormula;
FROM RealStr IMPORT RealToStr;
FROM FormatString IMPORT FormatString;
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ReadChar;
END ShoelaceFormula.</langsyntaxhighlight>
 
=={{header|Nim}}==
<langsyntaxhighlight lang="nim">type
Point = tuple
x: float
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var points = [(3.0, 4.0), (5.0, 11.0), (12.0, 8.0), (9.0, 5.0), (5.0, 6.0)]
 
echo shoelace(points)</langsyntaxhighlight>
 
{{out}}
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=={{header|Perl}}==
<langsyntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
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say area_by_shoelace( [ [3,4], [5,11], [12,8], [9,5], [5,6] ] );
say area_by_shoelace( @poly );
say area_by_shoelace( \@poly );</langsyntaxhighlight>
{{out}}
<pre>30
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=={{header|Phix}}==
<!--<langsyntaxhighlight Phixlang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">enum</span> <span style="color: #000000;">X</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Y</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">test</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">shoelace</span><span style="color: #0000FF;">(</span><span style="color: #000000;">test</span><span style="color: #0000FF;">)</span>
<!--</langsyntaxhighlight>-->
{{out}}
<pre>
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</pre>
An alternative solution, which does not need the X,Y enum, and gives the same output:
<!--<langsyntaxhighlight Phixlang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">shoelace</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">constant</span> <span style="color: #000000;">test</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">}}</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">shoelace</span><span style="color: #0000FF;">(</span><span style="color: #000000;">test</span><span style="color: #0000FF;">)</span>
<!--</langsyntaxhighlight>-->
 
=={{header|PowerBASIC}}==
{{Trans|Visual Basic}}
<langsyntaxhighlight lang="powerbasic">#COMPILE EXE
#DIM ALL
#COMPILER PBCC 6
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CON.PRINT STR$(ShoelaceArea(x(), y()))
CON.WAITKEY$
END FUNCTION</langsyntaxhighlight>
{{out}}
<pre>30</pre>
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=={{header|Python}}==
===Python: Explicit===
<langsyntaxhighlight lang="python">>>> def area_by_shoelace(x, y):
"Assumes x,y points go around the polygon in one direction"
return abs( sum(i * j for i, j in zip(x, y[1:] + y[:1]))
Line 1,452:
30.0
>>>
</syntaxhighlight>
</lang>
 
===Python: numpy===
<langsyntaxhighlight lang="python">
# Even simpler:
# In python we can take an advantage of that x[-1] refers to the last element in an array, same as x[N-1].
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# before applying the Shoelace formula.
 
</syntaxhighlight>
</lang>
 
===Python: Defined in terms of reduce and cycle===
{{Trans|Haskell}}
{{Works with|Python|3.7}}
<langsyntaxhighlight lang="python">'''Polygonal area by shoelace formula'''
 
from itertools import cycle, islice
Line 1,522:
 
if __name__ == '__main__':
main()</langsyntaxhighlight>
{{Out}}
<pre>Polygonal area by shoelace formula:
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===Python: Alternate===
This adopts the ''indexing'' used in the numpy example above, but does not require the numpy library.
<langsyntaxhighlight lang="python">>>> def area_by_shoelace2(x, y):
return abs(sum(x[i-1]*y[i]-x[i]*y[i-1] for i in range(len(x)))) / 2.
 
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>>> area_by_shoelace2(x, y)
30.0
>>> </langsyntaxhighlight>
 
=={{header|Racket}}==
<langsyntaxhighlight lang="racket">#lang racket/base
 
(struct P (x y))
Line 1,552:
 
(module+ main
(area (P 3 4) (P 5 11) (P 12 8) (P 9 5) (P 5 6)))</langsyntaxhighlight>
 
{{out}}
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{{works with|Rakudo|2017.07}}
 
<syntaxhighlight lang="raku" perl6line>sub area-by-shoelace(@p) {
(^@p).map({@p[$_;0] * @p[($_+1)%@p;1] - @p[$_;1] * @p[($_+1)%@p;0]}).sum.abs / 2
}
 
say area-by-shoelace( [ (3,4), (5,11), (12,8), (9,5), (5,6) ] );</langsyntaxhighlight>
{{out}}
<pre>30</pre>
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===Slice and rotation===
{{works with|Rakudo|2017.07}}
<syntaxhighlight lang="raku" perl6line>sub area-by-shoelace ( @p ) {
my @x := @p».[0];
my @y := @p».[1];
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say area-by-shoelace( [ (3,4), (5,11), (12,8), (9,5), (5,6) ] );
</syntaxhighlight>
</lang>
{{out}}
<pre>30</pre>
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<!--
===endpoints as exceptions===
<langsyntaxhighlight lang="rexx">/*REXX program uses a Shoelace formula to calculate the area of an N-sided polygon. */
parse arg pts; $polygon = 'polygon area of ' /*get optional args from the CL.*/
if pts='' then pts= '(3,4),(5,11),(12,8),(9,5),(5,6)' /*Not specified? Use default. */
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A=A + x.j * (y.jp - y.jm) /*compute a part of the area. */
end /*j*/
say $polygon # " points: " pts ' is ───► ' abs(A/2) /*stick a fork in it, we're done*/</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default input:}}
<pre>
Line 1,610:
 
=== wrap-around endpoints ===
<langsyntaxhighlight lang="rexx">/*REXX program uses a Shoelace formula to calculate the area of an N─sided polygon.*/
parse arg $; if $='' then $= "(3,4),(5,11),(12,8),(9,5),(5,6)" /*Use the default?*/
A= 0; @= space($, 0) /*init A; elide blanks from pts.*/
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do j=1 for #; jm= j-1; jp= j+1; A= A + x.j*(y.jm - y.jp) /*portion of area*/
end /*j*/ /*stick a fork in it, we're done*/
say 'polygon area of ' # " points: " $ ' is ───► ' abs(A/2)</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default input:}}
<pre>
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===somewhat simplified===
reformatted and suitable for ooRexx. (x.0 etc. not needed)
<syntaxhighlight lang="text">/*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. */
Line 1,642:
end
A=abs(A/2) /*obtain half of the ¦ A ¦ sum*/
say 'polygon area of' n 'points:' pts 'is --->' A</langsyntaxhighlight>
{{out}}
<pre>polygon area of 5 points: (3,4),(5,11),(12,8),(9,5),(5,6) is ---> 30</pre>
Line 1,648:
===even simpler===
Using the published algorithm
<syntaxhighlight lang="text">/*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. */
Line 1,662:
a=a+x.n*y.1-x.1*y.n
a=abs(a)/2
say 'polygon area of' n 'points:' pts 'is --->' a</langsyntaxhighlight>
{{out}}
<pre>polygon area of 5 points: (3,4),(5,11),(12,8),(9,5),(5,6) is ---> 30</pre>
 
=={{header|Ring}}==
<langsyntaxhighlight lang="ring">
# Project : Shoelace formula for polygonal area
 
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sum = sum - p[1][1] * p[i][2]
return fabs(sum) / 2
</syntaxhighlight>
</lang>
Output:
<pre>
Line 1,689:
 
=={{header|Ruby}}==
<langsyntaxhighlight lang="ruby">
Point = Struct.new(:x,:y) do
 
Line 1,712:
 
puts Polygon.new([3,4], [5,11], [12,8], [9,5], [5,6]).area # => 30.0
</syntaxhighlight>
</lang>
 
=={{header|Scala}}==
<langsyntaxhighlight lang="scala">case class Point( x:Int,y:Int ) { override def toString = "(" + x + "," + y + ")" }
 
case class Polygon( pp:List[Point] ) {
Line 1,742:
println( "Area of " + p + " = " + p.area )
}
</syntaxhighlight>
</lang>
{{out}}
<pre>Area of Polygon( (3,4), (5,11), (12,8), (9,5), (5,6) ) = 30.0</pre>
Line 1,748:
=={{header|Sidef}}==
{{trans|Raku}}
<langsyntaxhighlight lang="ruby">func area_by_shoelace (*p) {
var x = p.map{_[0]}
var y = p.map{_[1]}
Line 1,760:
}
 
say area_by_shoelace([3,4], [5,11], [12,8], [9,5], [5,6])</langsyntaxhighlight>
{{out}}
<pre>
Line 1,770:
{{trans|Scala}}
 
<langsyntaxhighlight lang="swift">import Foundation
 
struct Point {
Line 1,812:
])
 
print("\(poly) area = \(poly.area)")</langsyntaxhighlight>
 
{{out}}
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=={{header|TI-83 BASIC}}==
{{works with|TI-83 BASIC|TI-84Plus 2.55MP}}
<langsyntaxhighlight lang="ti83b">[[3,4][5,11][12,8][9,5][5,6]]->[A]
Dim([A])->N:0->A
For(I,1,N)
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A+[A](I,1)*[A](J,2)-[A](J,1)*[A](I,2)->A
End
Abs(A)/2->A</langsyntaxhighlight>
{{out}}
<pre>
Line 1,833:
 
=={{header|VBA}}==
{{trans|Phix}}<langsyntaxhighlight lang="vb">Option Base 1
Public Enum axes
u = 1
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Next i
Debug.Print shoelace(tcol)
End Sub</langsyntaxhighlight>{{out}}
<pre>30</pre>
 
=={{header|VBScript}}==
<langsyntaxhighlight lang="vb">' Shoelace formula for polygonal area - VBScript
Dim points, x(),y()
points = Array(3,4, 5,11, 12,8, 9,5, 5,6)
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Next 'i
area = Abs(area)/2
msgbox area,,"Shoelace formula" </langsyntaxhighlight>
{{out}}
<pre>
Line 1,890:
{{works with|VBA|6.5}}
{{works with|VBA|7.1}}
<langsyntaxhighlight lang="vb">Option Explicit
 
Public Function ShoelaceArea(x() As Double, y() As Double) As Double
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Next i
Debug.Print ShoelaceArea(x(), y())
End Sub</langsyntaxhighlight>
{{out}}
<pre>30</pre>
Line 1,923:
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<langsyntaxhighlight lang="vbnet">Option Strict On
 
Imports Point = System.Tuple(Of Double, Double)
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End Sub
 
End Module</langsyntaxhighlight>
{{out}}
<pre>Given a polygon with vertices [(3, 4), (5, 11), (12, 8), (9, 5), (5, 6)],
Line 1,957:
 
=={{header|Wren}}==
<langsyntaxhighlight lang="ecmascript">var shoelace = Fn.new { |pts|
var area = 0
for (i in 0...pts.count-1) {
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var pts = [ [3, 4], [5, 11], [12, 8], [9, 5], [5, 6] ]
System.print("The polygon with vertices at %(pts) has an area of %(shoelace.call(pts)).")</langsyntaxhighlight>
 
{{out}}
Line 1,974:
 
=={{header|XPL0}}==
<langsyntaxhighlight XPL0lang="xpl0">proc real Shoelace(N, X, Y);
int N, X, Y;
int S, I;
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];
 
RlOut(0, Shoelace(5, [3, 5, 12, 9, 5], [4, 11, 8, 5, 6]))</langsyntaxhighlight>
 
{{out}}
Line 1,993:
=={{header|zkl}}==
By the "book":
<langsyntaxhighlight lang="zkl">fcn areaByShoelace(points){ // ( (x,y),(x,y)...)
xs,ys:=Utils.Helpers.listUnzip(points); // (x,x,...), (y,y,,,)
( xs.zipWith('*,ys[1,*]).sum(0) + xs[-1]*ys[0] -
xs[1,*].zipWith('*,ys).sum(0) - xs[0]*ys[-1] )
.abs().toFloat()/2;
}</langsyntaxhighlight>
or an iterative solution:
<langsyntaxhighlight lang="zkl">fcn areaByShoelace2(points){ // ( (x,y),(x,y)...)
xs,ys:=Utils.Helpers.listUnzip(points); // (x,x,...), (y,y,,,)
N:=points.len();
N.reduce('wrap(s,n){ s + xs[n]*ys[(n+1)%N] - xs[(n+1)%N]*ys[n] },0)
.abs().toFloat()/2;
}</langsyntaxhighlight>
<langsyntaxhighlight lang="zkl">points:=T(T(3,4), T(5,11), T(12,8), T(9,5), T(5,6));
areaByShoelace(points).println();
areaByShoelace2(points).println();</langsyntaxhighlight>
{{out}}
<pre>
Thundergnat
10,333

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