Step by Step solution about How to resolve the algorithm Determine if two triangles overlap step by step in the Haskell programming language

The code you posted checks if two triangles overlap. It does this by checking if any of the vertices of one triangle are inside the other triangle, or if any of the midlines of one triangle intersect the other triangle.

Here's a breakdown of the code:

• The isOverlapping function takes two triangles as input and returns True if they overlap, and False otherwise.
• The vertexInside function checks if any of the vertices of one triangle are inside the other triangle. It does this by calling the isInside function for each vertex of one triangle and each triangle of the other triangle.
• The isInside function checks if a point is inside a triangle. It does this by computing the area of the triangle formed by the point and the three vertices of the triangle. If the area is positive, then the point is inside the triangle.
• The midLineInside function checks if any of the midlines of one triangle intersect the other triangle. It does this by calling the isInside function for each midline of one triangle and each triangle of the other triangle.
• The midPoints function computes the midpoints of the three sides of a triangle.
• The intersections function computes the intersection point of two lines.
• The midLines function computes the three midlines of a triangle.
• The line function computes the equation of a line given three points.

The test function is used to test the isOverlapping function. It does this by applying the isOverlapping function to a list of pairs of triangles.

isOverlapping :: Triangle Double -> Triangle Double -> Bool
isOverlapping t1 t2 = vertexInside || midLineInside
  where
    vertexInside =
      any (isInside t1) (vertices t2) ||
      any (isInside t2) (vertices t1)

    isInside t = (Outside /=) . overlapping t
                   
    midLineInside =
      any (\p -> isInside t1 p && isInside t2 p) midPoints
                    
    midPoints =
      [ intersections l1 l2 | l1 <- midLines t1
                            , l2 <- midLines t2 ]

    intersections (a1,b1,c1) (a2,b2,c2) =
      ( -(-b2*c1+b1*c2)/(a2*b1-a1*b2)
      , -(a2*c1-a1*c2)/(a2*b1-a1*b2) ) 

    midLines (Triangle a b c) =
      [line a b c, line b c a, line c a b]

    line (x,y) (ax, ay) (bx, by) =
      (ay+by-2*y, -ax-bx+2*x, -ay*x-by*x+ax*y+bx*y)

test = map (uncurry isOverlapping)
  [ (Triangle (0,0) (5,0) (0,5), Triangle (0,0) (5,0) (0,6))
  , (Triangle (0,0) (0,5) (5,0), Triangle (0,0) (0,5) (5,0))
  , (Triangle (0,0) (5,0) (0,5), Triangle (-10,0) (-5,0) (-1,6))
  , (Triangle (0,0) (5,0) (2.5,5), Triangle (0,4) (2.5,-1) (5,4))
  , (Triangle (0,0) (1,1) (0,2), Triangle (2,1) (3,0) (3,2))
  , (Triangle (0,0) (1,1) (0,2), Triangle (2,1) (3,-2) (3,4))
  , (Triangle (0,0) (1,0) (0,1), Triangle (1,0) (2,0) (1,1))]