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

The provided code is a Ruby implementation for calculating the area of a polygon using the shoelace formula. Here's a breakdown of what the code does:

1. Point Struct:

   • The code defines a Point struct using the Struct.new method, which allows us to create structured data objects with named fields. The Point struct has two fields, x and y, representing the coordinates of a point in a 2D plane.

2. Shoelace Method:

   • The Point struct defines a shoelace method. The shoelace formula is often used to calculate the area of a polygon. It takes another Point object as input and calculates the cross-product of the point's x and y coordinates. The result of the shoelace method is effectively x1 * y2 - x2 * y1.

3. Polygon Class:

   • The code defines a Polygon class to represent a polygon with multiple vertices.

   • The initialize method of the Polygon class takes a variable number of coordinate pairs ([x, y]) and creates Point objects for each pair. These Point objects are stored in the @points instance variable.

4. Area Method:

   • The area method of the Polygon class calculates the area of the polygon using the shoelace formula.

   • It first creates a modified list of points by adding the first point to the end of the list. This is done to close the polygon and avoid the need to handle any special cases at the end of the loop.

   • The area method then uses the each_cons(2) method on the modified points list. This method iterates over consecutive pairs of points in the list.

   • For each pair of points (p1 and p2), it calls the shoelace method on p1 with p2 as an argument to compute the cross-product of their coordinates.

   • The results of the shoelace operations are accumulated in a sum. The absolute value of this sum is then divided by 2 to obtain the area of the polygon.

5. Usage:

   • The last line of the code creates a Polygon object with five vertices and then calls the area method on this polygon. The result, 30.0, is printed to the console.

Overall, this code provides a way to calculate the area of a polygon using the shoelace formula, which is a common method for determining the area of simple and complex polygons.

Point = Struct.new(:x,:y) do

  def shoelace(other)
    x * other.y - y * other.x
  end

end

class Polygon

  def initialize(*coords)
    @points = coords.map{|c| Point.new(*c) } 
  end

  def area
    points = @points + [@points.first]
    points.each_cons(2).sum{|p1,p2| p1.shoelace(p2) }.abs.fdiv(2)
  end

end

puts Polygon.new([3,4], [5,11], [12,8], [9,5], [5,6]).area  # => 30.0