{-# LANGUAGE FlexibleInstances      #-}
{-# LANGUAGE FunctionalDependencies #-}
-- |
-- Module      :  Data.AffineSpace
-- Copyright   :  (c) Antony Courtney and Henrik Nilsson, Yale University, 2003
-- License     :  BSD-style (see the LICENSE file in the distribution)
--
-- Maintainer  :  ivan.perez@keera.co.uk
-- Stability   :  provisional
-- Portability :  non-portable (GHC extensions)
--
-- Affine space type relation.
module Data.AffineSpace where

-- Internal imports
import Data.VectorSpace

infix 6 .+^, .-^, .-.

-- | Affine Space type relation.
--
-- An affine space is a set (type) @p@, and an associated vector space @v@ over
-- a field @a@.
class (Floating a, VectorSpace v a) => AffineSpace p v a | p -> v, v -> a where

  -- | Origin of the affine space.
  origin :: p

  -- | Addition of affine point and vector.
  (.+^) :: p -> v -> p

  -- | Subtraction of affine point and vector.
  (.-^) :: p -> v -> p
  p .-^ v = p .+^ negateVector v

  -- | Subtraction of two points in the affine space, giving a vector.
  (.-.) :: p -> p -> v

  -- | Distance between two points in the affine space, same as the 'norm' of
  -- the vector they form (see '(.-.)'.
  distance :: p -> p -> a
  distance p1 p2 = norm (p1 .-. p2)