Step by Step solution about How to resolve the algorithm Sutherland-Hodgman polygon clipping step by step in the Ruby programming language

This Ruby code implements the Sutherland-Hodgman algorithm, which is used to clip a polygon (the "subject polygon") against another polygon (the "clip polygon"). Polygon clipping is used in computer graphics to determine which parts of a shape are visible within a given viewing area or window.

Here's a detailed explanation of the code:

1. Point Struct:

   • The code defines a Point struct using Struct.new to represent points in the polygons. Each point has two fields: x and y.
   • The to_s method is defined within the struct to provide a string representation of the point as "(x, y)".

2. sutherland_hodgman Function:

   • This function takes two parameters: subjectPolygon and clipPolygon, which are arrays of Point objects representing the polygons to be clipped.

   • Inside the function, there are a few inner functions defined as procs to reduce the argument passing to "inside" and "intersection":

     • inside: This proc takes a point p as an argument and returns true if the point is inside the current clip edge defined by cp1 and cp2. It uses a cross-product calculation to determine if the point is on the left side of the edge.
     • intersection: This proc takes no arguments and returns the intersection point between the current subject edge defined by s and e and the current clip edge defined by cp1 and cp2. It uses a line-line intersection calculation to find the intersection point.

   • The function initializes outputList with the subjectPolygon and iterates over the clipPolygon vertices.

   • For each cp2 in the clipPolygon, it initializes inputList with the current outputList.

   • It then initializes outputList as an empty array and s with the last point in inputList.

   • It iterates over each e in inputList and checks if e is inside the current clip edge using the inside proc.

   • If e is inside, it adds the intersection point between the current subject edge and the current clip edge to outputList unless s is also inside the current clip edge. It then adds e to outputList.

   • If s is inside the current clip edge, it adds the intersection point between the current subject edge and the current clip edge to outputList.

   • It updates s to e.

   • Finally, it updates cp1 to cp2.

   • The function returns the outputList, which contains the clipped polygon.

3. Sample Polygons and Clipping:

   • The code defines subjectPolygon as an array of points representing a subject polygon with 9 vertices.
   • It defines clipPolygon as an array of points representing a clip polygon with 4 vertices.
   • It calls the sutherland_hodgman function with subjectPolygon and clipPolygon and prints the result, which is an array of Point objects representing the clipped polygon.

Point = Struct.new(:x,:y) do
  def to_s; "(#{x}, #{y})" end
end

def sutherland_hodgman(subjectPolygon, clipPolygon)
  # These inner functions reduce the argument passing to
  # "inside" and "intersection".
  cp1, cp2, s, e = nil
  inside = proc do |p|
    (cp2.x-cp1.x)*(p.y-cp1.y) > (cp2.y-cp1.y)*(p.x-cp1.x)
  end
  intersection = proc do
    dcx, dcy = cp1.x-cp2.x, cp1.y-cp2.y
    dpx, dpy = s.x-e.x, s.y-e.y
    n1 = cp1.x*cp2.y - cp1.y*cp2.x
    n2 = s.x*e.y - s.y*e.x
    n3 = 1.0 / (dcx*dpy - dcy*dpx)
    Point[(n1*dpx - n2*dcx) * n3, (n1*dpy - n2*dcy) * n3]
  end
  
  outputList = subjectPolygon
  cp1 = clipPolygon.last
  for cp2 in clipPolygon
    inputList = outputList
    outputList = []
    s = inputList.last
    for e in inputList
      if inside[e]
        outputList << intersection[] unless inside[s]
        outputList << e
      elsif inside[s]
        outputList << intersection[]
      end
      s = e
    end
    cp1 = cp2
  end
  outputList
end

subjectPolygon = [[50, 150], [200, 50], [350, 150], [350, 300],
                  [250, 300], [200, 250], [150, 350], [100, 250],
                  [100, 200]].collect{|pnt| Point[*pnt]}
 
clipPolygon = [[100, 100], [300, 100], [300, 300], [100, 300]].collect{|pnt| Point[*pnt]}
 
puts sutherland_hodgman(subjectPolygon, clipPolygon)