-- | The Face module just contains the definition of the 'Face' data
--   type and its two typeclass instances.
module Face
  ( Face(..) )
where

import Point
import ThreeDimensional

data Face = Face { v0 :: Point,
                   v1 :: Point,
                   v2 :: Point,
                   v3 :: Point }
          deriving (Eq)

instance Show Face where
    show f = "Face:\n" ++
             "  v0: " ++ (show (v0 f)) ++ "\n" ++
             "  v1: " ++ (show (v1 f)) ++ "\n" ++
             "  v2: " ++ (show (v2 f)) ++ "\n" ++
             "  v3: " ++ (show (v3 f)) ++ "\n"

-- | The 'Face' type is an instance of 'ThreeDimensional' so that we
--   can call the 'center' function on it. This is useful because the
--   center of a face is always a vertex of a tetrahedron.
instance ThreeDimensional Face where
    -- | Since a face is square, we can just average the four vertices
    --   to find the center.
    center f = ((v0 f) + (v1 f) + (v2 f) + (v3 f)) `scale` (1/4)

    -- | It's possible to implement this, but it hasn't been done
    --   yet. A face will contain a point if the point lies in the same
    --   plane as the vertices of the face, and if it falls on the
    --   correct side of the four sides of the face.
    contains_point _ _ = False