{-# LANGUAGE MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances #-} ----------------------------------------------------------------------------------------- -- | -- Module : FRP.Yampa.AffineSpace -- Copyright : (c) Antony Courtney and Henrik Nilsson, Yale University, 2003 -- License : BSD-style (see the LICENSE file in the distribution) -- -- Maintainer : nilsson@cs.yale.edu -- Stability : provisional -- Portability : non-portable (GHC extensions) -- -- Affine space type relation. -- ----------------------------------------------------------------------------------------- module FRP.Yampa.AffineSpace where import FRP.Yampa.VectorSpace 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. -- | 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)