6 responses to “Exercise 8.6”

1. I surrender. Correct text is at
   http://www.mroweczka.pl/exerc806.hs

   polygon ver = 
       foldl Intersect Empty [HalfPlane a b| (a,b)<-zip ver (tail ver++[head ver])] 
   

   or if you don't like Empty constructor

   polygon' ver = 
      let zipped = [HalfPlane a b| (a,b)<-zip ver (tail ver++[head ver])] 
      in foldl Intersect (head zipped) (tail zipped)
   

   [Edited by admin to add code from the above URL]

2. I’ve removed your false starts and added the code. Try using <pre> tags around the code – that should preserve it.

3. Hi Wieslaw, I think this is no correct
   polygon ver =
   foldl Intersect Empty [HalfPlane a b| (a,b)<-zip ver (tail ver++[head ver])]

   it should be
   polygon ver =
   foldl Intersect (Complement Empty) [HalfPlane a b| (a,b)<-zip ver (tail ver++[head ver])]

   beacause “anything `Intersect` Empty” is “Empty”. You should Intersect it with all the space which is “Complement Empty”. I wrote the same solution with “Complement Empty” and it is working.

4. No. There is no such thing as a polygon with one or two sides. There needs to be a check, on the length of the list of coordinates, and if less than 3 it should be Empty. Then proceed as folding the Intersection into these planes.

5. Fero,Jon you are both right. Thanks.
   Jon – assuming there is no polygon with less than 3 sides then the check should return error and not Empty.

6. The solution given does not guard against the case of a 2-point list. The region will then become the extended infinite line created from the 2 points. I suggest to modify it as follows:

   polygon :: [Coordinate] -> Region
   polygon x
   | (length x) < 3 = error "polygon: requires at least 3 points"
   | otherwise = halfPlane (head x) (tail x ++ [head x])
   where halfPlane x1 (x2:xs) = HalfPlane x1 x2 `Intersect` halfPlane x2 xs
   halfPlane _ [] = Complement Empty