module Queries where

import Test.QuickCheck.Arbitrary

data Point a = Point
           { xCoord :: a
           , yCoord :: a
           }
           deriving(Eq, Ord, Show)

instance Arbitrary a => Arbitrary (Point a) where
    arbitrary = Point <$> arbitrary <*> arbitrary

makesRightTurn :: (Ord a, Num a) => Point a -> Point a -> Point a -> Bool
makesRightTurn (Point x1 y1) (Point x2 y2) (Point x3 y3) =
    let crossProduct = (x2 - x1)*(y3-y1) - (x3 - x1)*(y2 - y1)
    in crossProduct > 0


squaredDistance :: Num a => Point a -> Point a -> a
squaredDistance (Point x1 y1) (Point x2 y2) = (x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1)

data Line a = Line
            { p1 :: Point a
            , p2 :: Point a
            }
            deriving(Eq, Show)

data OpenCircle a = OpenCircle
            { center :: Point a
            , radius :: a
            }
            deriving(Eq, Show)

pointInCircle :: (Ord a, Num a) => Point a -> OpenCircle a -> Bool
pointInCircle p (OpenCircle c r) = (squaredDistance p c) < (r * r)

lineCircleIntersect :: (Ord a, Num a) => OpenCircle a -> Line a -> Bool
lineCircleIntersect c (Line p1 p2) =
    pointInCircle p1 c || pointInCircle p2 c



type Path a = [Line a]

pathToLines :: [Point a] -> [Line a]
pathToLines [] = []
pathToLines [_] = []
pathToLines (p1:p2:ps) = Line p1 p2 : pathToLines (p2:ps)

pathFromPoints :: [Point a] -> Path a
pathFromPoints = pathToLines


removeCircleFromPath :: (Ord a, Num a) => OpenCircle a -> Path a -> Path a
removeCircleFromPath c lines = filter (not . lineCircleIntersect c) lines