{-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE NoMonomorphismRestriction #-} {-# LANGUAGE OverlappingInstances #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TypeFamilies #-} {-# LANGUAGE UndecidableInstances #-} module Math.Coordinate.UV where import Data.Typeable (Typeable) import Control.Applicative import Data.Array.Accelerate import Data.Array.Accelerate.Smart import Data.Array.Accelerate.Tuple import Data.Array.Accelerate.Array.Sugar import Data.Complex import qualified Data.Foldable as F import qualified Math.Coordinate.Cartesian as Cartesian import Math.Coordinate.Cartesian (Cartesian) import Math.Coordinate.Coordinate (CoordConversion(..), ManualConversion(..), convertCoord) import qualified Math.Space.Space as Space import Math.Space.Space (Space2) data UV = UV deriving (Show) data Point1 a = Point1 !a deriving (Eq, Ord, Show, Read, Typeable) data Point2 a = Point2 !a !a deriving (Eq, Ord, Show, Read, Typeable) data Point3 a = Point3 !a !a !a deriving (Eq, Ord, Show, Read, Typeable) toUV = convertCoord UV -------------------------------------------------------------------------------- -- Classes -------------------------------------------------------------------------------- class UVCoord1 coord where u :: coord a -> a class UVCoord1 coord => UVCoord2 coord where v :: coord a -> a class UVCoord2 coord => UVCoord3 coord where w :: coord a -> a -------------------------------------------------------------------------------- -- Instances -------------------------------------------------------------------------------- instance UVCoord1 Point1 where u (Point1 u) = u instance UVCoord1 Point2 where u (Point2 u _) = u instance UVCoord2 Point2 where v (Point2 _ v) = v instance UVCoord1 Point3 where u (Point3 u _ _) = u instance UVCoord2 Point3 where v (Point3 _ v _) = v instance UVCoord3 Point3 where w (Point3 _ _ w) = w instance (Space2 space, Num a, a~b) => CoordConversion ManualConversion Cartesian (space b) (Point2 a) (Cartesian.Point2 a) where convertCoordBase _ _ space (Point2 u v) = Cartesian.Point2 (u*w) (v*h) where w = Space.width space h = Space.height space instance (Space2 space, Fractional a, a~b) => CoordConversion ManualConversion UV (space b) (Cartesian.Point2 a) (Point2 a) where convertCoordBase _ sys space (Cartesian.Point2 x y) = Point2 (x/w) (y/h) where w = Space.width space h = Space.height space -------------------------------------------------------------------------------- -- Point1 -------------------------------------------------------------------------------- instance Functor Point1 where fmap f (Point1 a) = Point1 (f a) instance Applicative Point1 where pure a = Point1 a {-# INLINE pure #-} Point1 a <*> Point1 d = Point1 (a d) {-# INLINE (<*>) #-} instance Num a => Num (Point1 a) where (+) = liftA2 (+) {-# INLINE (+) #-} (-) = liftA2 (-) {-# INLINE (-) #-} (*) = liftA2 (*) {-# INLINE (*) #-} negate = fmap negate {-# INLINE negate #-} abs = fmap abs {-# INLINE abs #-} signum = fmap signum {-# INLINE signum #-} fromInteger = pure . fromInteger {-# INLINE fromInteger #-} instance Fractional a => Fractional (Point1 a) where recip = fmap recip {-# INLINE recip #-} (/) = liftA2 (/) {-# INLINE (/) #-} fromRational = pure . fromRational {-# INLINE fromRational #-} type instance EltRepr (Point1 a) = EltRepr a type instance EltRepr' (Point1 a) = EltRepr' a instance Elt a => Elt (Point1 a) where eltType _ = eltType (undefined :: a) toElt = Point1 . toElt fromElt (Point1 a) = fromElt a eltType' _ = eltType' (undefined :: a) toElt' = Point1 . toElt' fromElt' (Point1 a) = fromElt' a instance IsTuple (Point1 a) where type TupleRepr (Point1 a) = ((), a) fromTuple (Point1 x) = ((), x) toTuple ((), x) = Point1 x instance (Lift Exp a, Elt (Plain a)) => Lift Exp (Point1 a) where type Plain (Point1 a) = Point1 (Plain a) lift (Point1 x) = Exp . Tuple \$ NilTup `SnocTup` lift x instance (Elt a, e ~ Exp a) => Unlift Exp (Point1 e) where unlift t = Point1 \$ Exp \$ ZeroTupIdx `Prj` t -------------------------------------------------------------------------------- -- Point2 -------------------------------------------------------------------------------- instance Functor Point2 where fmap f (Point2 a b) = Point2 (f a) (f b) instance Applicative Point2 where pure a = Point2 a a {-# INLINE pure #-} Point2 a b <*> Point2 d e = Point2 (a d) (b e) {-# INLINE (<*>) #-} instance Num a => Num (Point2 a) where (+) = liftA2 (+) {-# INLINE (+) #-} (-) = liftA2 (-) {-# INLINE (-) #-} (*) = liftA2 (*) {-# INLINE (*) #-} negate = fmap negate {-# INLINE negate #-} abs = fmap abs {-# INLINE abs #-} signum = fmap signum {-# INLINE signum #-} fromInteger = pure . fromInteger {-# INLINE fromInteger #-} instance Fractional a => Fractional (Point2 a) where recip = fmap recip {-# INLINE recip #-} (/) = liftA2 (/) {-# INLINE (/) #-} fromRational = pure . fromRational {-# INLINE fromRational #-} type instance EltRepr (Point2 a) = EltRepr (a, a) type instance EltRepr' (Point2 a) = EltRepr' (a, a) instance Elt a => Elt (Point2 a) where eltType _ = eltType (undefined :: (a,a)) toElt p = case toElt p of (x, y) -> Point2 x y fromElt (Point2 x y) = fromElt (x, y) eltType' _ = eltType' (undefined :: (a,a)) toElt' p = case toElt' p of (x, y) -> Point2 x y fromElt' (Point2 x y) = fromElt' (x, y) instance IsTuple (Point2 a) where type TupleRepr (Point2 a) = TupleRepr (a,a) fromTuple (Point2 x y) = fromTuple (x,y) toTuple t = case toTuple t of (x, y) -> Point2 x y instance (Lift Exp a, Elt (Plain a)) => Lift Exp (Point2 a) where type Plain (Point2 a) = Point2 (Plain a) --lift = Exp . Tuple . F.foldl SnocTup NilTup lift (Point2 x y) = Exp \$ Tuple \$ NilTup `SnocTup` lift x `SnocTup` lift y instance (Elt a, e ~ Exp a) => Unlift Exp (Point2 e) where unlift t = Point2 (Exp \$ SuccTupIdx ZeroTupIdx `Prj` t) (Exp \$ ZeroTupIdx `Prj` t) -------------------------------------------------------------------------------- -- Point3 -------------------------------------------------------------------------------- instance Functor Point3 where fmap f (Point3 a b c) = Point3 (f a) (f b) (f c) instance Applicative Point3 where pure a = Point3 a a a {-# INLINE pure #-} Point3 a b c <*> Point3 d e f = Point3 (a d) (b e) (c f) {-# INLINE (<*>) #-} instance Num a => Num (Point3 a) where (+) = liftA2 (+) {-# INLINE (+) #-} (-) = liftA2 (-) {-# INLINE (-) #-} (*) = liftA2 (*) {-# INLINE (*) #-} negate = fmap negate {-# INLINE negate #-} abs = fmap abs {-# INLINE abs #-} signum = fmap signum {-# INLINE signum #-} fromInteger = pure . fromInteger {-# INLINE fromInteger #-} instance Fractional a => Fractional (Point3 a) where recip = fmap recip {-# INLINE recip #-} (/) = liftA2 (/) {-# INLINE (/) #-} fromRational = pure . fromRational {-# INLINE fromRational #-} type instance EltRepr (Point3 a) = EltRepr (a, a, a) type instance EltRepr' (Point3 a) = EltRepr' (a, a, a) instance Elt a => Elt (Point3 a) where eltType _ = eltType (undefined :: (a,a,a)) toElt p = case toElt p of (x, y, z) -> Point3 x y z fromElt (Point3 x y z) = fromElt (x, y, z) eltType' _ = eltType' (undefined :: (a,a,a)) toElt' p = case toElt' p of (x, y, z) -> Point3 x y z fromElt' (Point3 x y z) = fromElt' (x, y, z) instance IsTuple (Point3 a) where type TupleRepr (Point3 a) = TupleRepr (a,a,a) fromTuple (Point3 x y z) = fromTuple (x,y,z) toTuple t = case toTuple t of (x, y, z) -> Point3 x y z instance (Lift Exp a, Elt (Plain a)) => Lift Exp (Point3 a) where type Plain (Point3 a) = Point3 (Plain a) --lift = Exp . Tuple . F.foldl SnocTup NilTup lift (Point3 x y z) = Exp \$ Tuple \$ NilTup `SnocTup` lift x `SnocTup` lift y `SnocTup` lift z instance (Elt a, e ~ Exp a) => Unlift Exp (Point3 e) where unlift t = Point3 (Exp \$ SuccTupIdx (SuccTupIdx ZeroTupIdx) `Prj` t) (Exp \$ SuccTupIdx ZeroTupIdx `Prj` t) (Exp \$ ZeroTupIdx `Prj` t)