Shoelace formula for polygonal area: Difference between revisions
Shoelace formula for polygonal area (view source)
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{{out}}
<pre>30</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
In keeping with the principles of modularity and reusability, the problem has been broken down into subroutines that can process any polygon. In other words, the subroutines don't just solve the area of one polygon; they can find the area of any polygon.
<syntaxhighlight lang="Delphi">
{Create a 2D vector type}
type T2DVector = record
X, Y: double;
end;
{Test polygon}
var Polygon: array [0..4] of T2DVector =
((X:3; Y:4), (X:5; Y:11), (X:12; Y:8), (X:9; Y:5), (X:5; Y:6));
function GetPolygonArea(Polygon: array of T2DVector): double;
{Return the area of the polygon }
{K = [(x1y2 + x2y3 + x3y4 + ... + xny1) - (x2y1 + x3y2 + x4y3 + ... + x1yn)]/2}
var I,Inx: integer;
var P1,P2: T2DVector;
var Sum1,Sum2: double;
begin
Result:=0;
Sum1:=0; Sum2:=0;
for I:=0 to Length(Polygon)-1 do
begin
{Vector back to the beginning}
if I=(Length(Polygon)-1) then Inx:=0
else Inx:=I+1;
P1:=Polygon[I];
P2:=Polygon[Inx];
Sum1:=Sum1 + P1.X * P2.Y;
Sum2:=Sum2 + P2.X * P1.Y;
end;
Result:=abs((Sum1 - Sum2)/2);
end;
procedure ShowPolygon(Poly: array of T2DVector; Memo: TMemo);
var I: integer;
var S: string;
begin
S:='';
for I:=0 to High(Poly) do
S:=S+Format('(%2.1F, %2.1F) ',[Poly[I].X, Poly[I].Y]);
Memo.Lines.Add(S);
end;
procedure ShowPolygonArea(Memo: TMemo);
var Area: double;
begin
ShowPolygon(Polygon,Memo);
Area:=GetPolygonArea(Polygon);
Memo.Lines.Add('Area: '+FloatToStrF(Area,ffFixed,18,2));
end;
</syntaxhighlight>
{{out}}
<pre>
(3.0, 4.0) (5.0, 11.0) (12.0, 8.0) (9.0, 5.0) (5.0, 6.0)
Area: 30.00
Elapsed Time: 3.356 ms.
</pre>
=={{header|EasyLang}}==
<syntaxhighlight lang="easylang">
proc shoelace . p[][] res .
sum = 0
for i = 1 to len p[][] - 1
sum += p[i][1] * p[i + 1][2]
sum -= p[i + 1][1] * p[i][2]
.
sum += p[i][1] * p[1][2]
sum -= p[1][1] * p[i][2]
res = abs sum / 2
.
data[][] = [ [ 3 4 ] [ 5 11 ] [ 12 8 ] [ 9 5 ] [ 5 6 ] ]
shoelace data[][] res
print res
</syntaxhighlight>
=={{header|Elixir}}==
<syntaxhighlight lang="elixir">
def shoelace(points) do
points
|> Enum.reduce({0, List.last(points)}, fn {x1, y1}, {sum, {x0, y0}} ->
{sum + (y0 * x1 - x0 * y1), {x1, y1}}
end)
|> elem(0)
|> div(2)
end
</syntaxhighlight>
=={{header|F_Sharp|F#}}==
Line 713 ⟶ 811:
=={{header|Fōrmulæ}}==
{{FormulaeEntry|page=https://formulae.org/?script=examples/Shoelace_formula_for_polygonal_area}}
'''Solution'''
[[File:Fōrmulæ - Shoelace formula 01.png]]
'''Test case'''
[[File:Fōrmulæ - Shoelace formula 02.png]]
[[File:Fōrmulæ - Shoelace formula 03.png]]
=={{header|Go}}==
Line 1,714 ⟶ 1,818:
<pre>
The area of the polygon = 30
</pre>
=={{header|RPL}}==
{| class="wikitable"
! RPL code
! Comment
|-
|
≪
DUP 1 GET +
0 2 3 PICK SIZE '''FOR''' j
OVER j GET LAST 1 - GET
OVER RE OVER IM * SWAP RE ROT IM * - +
'''NEXT'''
ABS 2 / SWAP DROP
≫ <span style="color:blue">''''SHOEL''''</span> STO
|
<span style="color:blue">'''SHOEL'''</span> ''( { (vertices) } → area ) ''
append 1st vertice at the end
sum = 0 ; loop
get 2 vertices
sum += determinant
end loop
finalize calculation, clean stack
return area
|}
{(3,4) (5,11) (12,8) (9,5) (5,6)} <span style="color:blue">'''SHOEL'''</span>
{{out}}
<pre>
1: 30
</pre>
Line 1,985 ⟶ 2,119:
=={{header|Wren}}==
<syntaxhighlight lang="
var area = 0
for (i in 0...pts.count-1) {
| |||