{-# OPTIONS_GHC -Wall #-} {-# LANGUAGE Safe #-} {- | Module : Physics.Learn.CommonVec Copyright : (c) Scott N. Walck 2012-2019 License : BSD3 (see LICENSE) Maintainer : Scott N. Walck <walck@lvc.edu> Stability : experimental This module defines some common vector operations. It is intended that this module not be imported directly, but that its functionality be gained by importing either 'SimpleVec' or 'CarrotVec', but not both. Choose 'SimpleVec' for vector operations (such as vector addition) with simple concrete types, which work only with the type 'Vec' of three-dimensional vectors. Choose 'CarrotVec' for vector operations that work with any type in the appropriate type class. -} -- The definitions that are common to SimpleVec and CarrotVec. -- We need to export the data constructor Vec for both SimpleVec and CarrotVec. module Physics.Learn.CommonVec ( Vec(..) , R , vec , (><) , iHat , jHat , kHat ) where infixl 7 >< type R = Double -- | A type for vectors. data Vec = Vec { xComp :: R -- ^ x component , yComp :: R -- ^ y component , zComp :: R -- ^ z component } deriving (Eq) instance Show Vec where show (Vec x y z) = "vec " ++ showDouble x ++ " " ++ showDouble y ++ " " ++ showDouble z showDouble :: Double -> String showDouble x | x < 0 = "(" ++ show x ++ ")" | otherwise = show x -- | Form a vector by giving its x, y, and z components. vec :: R -- ^ x component -> R -- ^ y component -> R -- ^ z component -> Vec vec = Vec -- | Cross product. (><) :: Vec -> Vec -> Vec Vec ax ay az >< Vec bx by bz = Vec (ay*bz - az*by) (az*bx - ax*bz) (ax*by - ay*bx) iHat, jHat, kHat :: Vec -- | Unit vector in the x direction. iHat = vec 1 0 0 -- | Unit vector in the y direction. jHat = vec 0 1 0 -- | Unit vector in the z direction. kHat = vec 0 0 1