Shoelace formula for polygonal area: Difference between revisions
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<lang perl6>sub area-by-shoelace(@p) { |
<lang perl6>sub area-by-shoelace(@p) { |
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@p.push: @p[0]; |
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} |
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Revision as of 21:48, 9 August 2017
Shoelace formula for polygonal area is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Write a function/method/routine to use the the Shoelace formula to calculate the area of the polygon described by the ordered points:
(3,4), (5,11), (12,8), (9,5), and (5,6)
Show the answer here, on this page.
ALGOL 68
<lang algol68>BEGIN
# returns the area of the polygon defined by the points p using the Shoelace formula # OP AREA = ( [,]REAL p )REAL: BEGIN [,]REAL points = p[ AT 1, AT 1 ]; # normalise array bounds to start at 1 # IF 2 UPB points /= 2 THEN # the points do not have 2 coordinates # -1 ELSE REAL result := 0; INT n = 1 UPB points; IF n > 1 THEN # there at least two points # []REAL x = points[ :, 1 ]; []REAL y = points[ :, 2 ]; FOR i TO 1 UPB points - 1 DO result +:= x[ i ] * y[ i + 1 ]; result -:= x[ i + 1 ] * y[ i ] OD; result +:= x[ n ] * y[ 1 ]; result -:= x[ 1 ] * y[ n ] FI; ( ABS result ) / 2 FI END # AREA # ;
# test case as per the task # 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 </lang>
- Output:
30.00
Perl 6
<lang perl6>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) ] );</lang>
- Output:
30
Python
<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])) -sum(i * j for i, j in zip(x[1:] + x[:1], y ))) / 2
>>> points = [(3,4), (5,11), (12,8), (9,5), (5,6)] >>> x, y = zip(*points) >>> area_by_shoelace(x, y) 30.0 >>> </lang>