Step by Step solution about How to resolve the algorithm Shoelace formula for polygonal area step by step in the Julia programming language

This Julia code snippet calculates the area of a polygon using the shoelace formula. It assumes that the x and y coordinates of the polygon's vertices are given as vectors and that the vertices go around the polygon in one direction.

The shoelacearea function takes two vectors x and y representing the x and y coordinates of the polygon's vertices. It calculates the area of the polygon using the shoelace formula, which is given by:

area = (1/2) * abs(sum(x[i] * y[i+1] for i in 1:length(x)) - sum(x[i+1] * y[i] for i in 1:length(x)))

The function first calculates the sum of the products of the x coordinates of the vertices with the y coordinates of the next vertices (i.e., x[i] * y[i+1] for i from 1 to the length of x). It then calculates the sum of the products of the x coordinates of the next vertices with the y coordinates of the vertices (i.e., x[i+1] * y[i] for i from 1 to the length of x). The difference between these two sums is multiplied by 1/2 to get the area of the polygon.

The function returns the absolute value of the area, since the area of a polygon can be negative if the vertices are entered in the wrong direction.

The code then defines two vectors x and y representing the x and y coordinates of the vertices of a polygon. It then calls the shoelacearea function with x and y as arguments and prints the result using the @show macro.

"""
Assumes x,y points go around the polygon in one direction.
"""
shoelacearea(x, y) =
    abs(sum(i * j for (i, j) in zip(x, append!(y[2:end], y[1]))) -
        sum(i * j for (i, j) in zip(append!(x[2:end], x[1]), y))) / 2

x, y = [3, 5, 12, 9, 5], [4, 11, 8, 5, 6]
@show x y shoelacearea(x, y)