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Shoelace formula for polygonal area: Difference between revisions
Shoelace formula for polygonal area (view source)
Revision as of 06:40, 27 December 2020
, 3 years ago→{{header|Python}}
(Added XPL0 example.) |
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>>> area_by_shoelace(x, y)
30.0
>>>
# 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].
# Introducing the index i=[0,1,2,...,N-1]; i-1=[-1,0,...,N-1]; N is the number of vertices of a polygon.
# Thus x[i] is a sequence of the x-coordinate of the polygon vertices, x[i-1] is the sequence shifted by 1 index.
# Note that the shift must be negative. The positive shift x[i+1] results in an error: x[N] index out of bound.
import numpy as np
# x,y are arrays containing coordinates of the polygon vertices
x=np.array([3,5,12,9,5])
y=np.array([4,11,8,5,6])
i=np.arange(len(x))
#Area=np.sum(x[i-1]*y[i]-x[i]*y[i-1])*0.5 # signed area, positive if the vertex sequence is counterclockwise
Area=np.abs(np.sum(x[i-1]*y[i]-x[i]*y[i-1])*0.5) # one line of code for the shoelace formula
</lang>
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