{-# OPTIONS_GHC -Wall #-}
{-# LANGUAGE Safe #-}

{- | 
Module      :  Physics.Learn.CoordinateFields
Copyright   :  (c) Scott N. Walck 2012-2018
License     :  BSD3 (see LICENSE)
Maintainer  :  Scott N. Walck <walck@lvc.edu>
Stability   :  experimental

Coordinate fields for Cartesian, cylindrical, and spherical coordinates.
-}

module Physics.Learn.CoordinateFields
    ( x
    , y
    , z
    , s
    , phi
    , r
    , theta
    )
    where

import Physics.Learn.Position
    ( ScalarField
    , cartesianCoordinates
    , cylindricalCoordinates
    , sphericalCoordinates
    )

fst3 :: (a,b,c) -> a
fst3 :: forall a b c. (a, b, c) -> a
fst3 (a
v,b
_,c
_) = a
v

snd3 :: (a,b,c) -> b
snd3 :: forall a b c. (a, b, c) -> b
snd3 (a
_,b
v,c
_) = b
v

thd3 :: (a,b,c) -> c
thd3 :: forall a b c. (a, b, c) -> c
thd3 (a
_,b
_,c
v) = c
v

-- | The x Cartesian coordinate of a position.
x :: ScalarField
x :: ScalarField
x = forall a b c. (a, b, c) -> a
fst3 forall b c a. (b -> c) -> (a -> b) -> a -> c
. Position -> (Double, Double, Double)
cartesianCoordinates

-- | The y Cartesian coordinate of a position.
y :: ScalarField
y :: ScalarField
y = forall a b c. (a, b, c) -> b
snd3 forall b c a. (b -> c) -> (a -> b) -> a -> c
. Position -> (Double, Double, Double)
cartesianCoordinates

-- | The z Cartesian (or cylindrical) coordinate of a position.
z :: ScalarField
z :: ScalarField
z = forall a b c. (a, b, c) -> c
thd3 forall b c a. (b -> c) -> (a -> b) -> a -> c
. Position -> (Double, Double, Double)
cartesianCoordinates

-- | The s cylindrical coordinate of a position.
--   This is the distance of the position from the z axis.
s :: ScalarField
s :: ScalarField
s = forall a b c. (a, b, c) -> a
fst3 forall b c a. (b -> c) -> (a -> b) -> a -> c
. Position -> (Double, Double, Double)
cylindricalCoordinates

-- | The phi cylindrical (or spherical) coordinate of a position.
--   This is the angle from the positive x axis 
--   to the projection of the position onto the xy plane.
phi :: ScalarField
phi :: ScalarField
phi = forall a b c. (a, b, c) -> b
snd3 forall b c a. (b -> c) -> (a -> b) -> a -> c
. Position -> (Double, Double, Double)
cylindricalCoordinates

-- | The r spherical coordinate of a position.
--   This is the distance of the position from the origin.
r :: ScalarField
r :: ScalarField
r = forall a b c. (a, b, c) -> a
fst3 forall b c a. (b -> c) -> (a -> b) -> a -> c
. Position -> (Double, Double, Double)
sphericalCoordinates

-- | The theta spherical coordinate of a position.
--   This is the angle from the positive z axis to the position.
theta :: ScalarField
theta :: ScalarField
theta = forall a b c. (a, b, c) -> b
snd3 forall b c a. (b -> c) -> (a -> b) -> a -> c
. Position -> (Double, Double, Double)
sphericalCoordinates