{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies #-}
{- $Id: AFRPAffineSpace.hs,v 1.2 2003/11/10 21:28:58 antony Exp $
******************************************************************************
*                                  A F R P                                   *
*                                                                            *
*       Module:         AFRPAffineSpace                                      *
*       Purpose:        Affine space type relation.                          *
*       Authors:        Henrik Nilsson and Antony Courtney                   *
*                                                                            *
*             Copyright (c) Yale University, 2003                            *
*                                                                            *
******************************************************************************
-}

module AFRPAffineSpace where

import AFRPVectorSpace

------------------------------------------------------------------------------
-- Affine Space type relation
------------------------------------------------------------------------------

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

-- Maybe origin should not be a class method, even though an origin
-- can be assocoated with any affine space.
-- Maybe distance should not be a class method, in which case the constraint
-- on the coefficient space (a) could be Fractional (i.e., a Field), which
-- seems closer to the mathematical definition of affine space, provided
-- the constraint on the coefficient space for VectorSpace is also Fractional.

-- Minimal instance: origin, .+^, .^.
class (Floating a, VectorSpace v a) => AffineSpace p v a | p -> v, v -> a where
    origin   :: p
    (.+^)    :: p -> v -> p
    (.-^)    :: p -> v -> p
    (.-.)    :: p -> p -> v
    distance :: p -> p -> a

    p .-^ v = p .+^ (negateVector v)

    distance p1 p2 = norm (p1 .-. p2)