Safe Haskell	Safe
Language	Haskell98

Data.SG.Geometry.ThreeDim

Description

A module with types to use in a 3D system, and various helper functions. Several more functions are available for use in the Data.SG.Geometry module.

Synopsis

Documentation

newtype Point3' a Source #

A point in 3D space.

Constructors

Point3 (a, a, a)

Instances

Functor Point3' Source #
Methods fmap :: (a -> b) -> Point3' a -> Point3' b # (<$) :: a -> Point3' b -> Point3' a #
Applicative Point3' Source #
Methods pure :: a -> Point3' a # (<>) :: Point3' (a -> b) -> Point3' a -> Point3' b # (>) :: Point3' a -> Point3' b -> Point3' b # (<*) :: Point3' a -> Point3' b -> Point3' a #
Foldable Point3' Source #
Methods fold :: Monoid m => Point3' m -> m # foldMap :: Monoid m => (a -> m) -> Point3' a -> m # foldr :: (a -> b -> b) -> b -> Point3' a -> b # foldr' :: (a -> b -> b) -> b -> Point3' a -> b # foldl :: (b -> a -> b) -> b -> Point3' a -> b # foldl' :: (b -> a -> b) -> b -> Point3' a -> b # foldr1 :: (a -> a -> a) -> Point3' a -> a # foldl1 :: (a -> a -> a) -> Point3' a -> a # toList :: Point3' a -> [a] # null :: Point3' a -> Bool # length :: Point3' a -> Int # elem :: Eq a => a -> Point3' a -> Bool # maximum :: Ord a => Point3' a -> a # minimum :: Ord a => Point3' a -> a # sum :: Num a => Point3' a -> a # product :: Num a => Point3' a -> a #
Traversable Point3' Source #
Methods traverse :: Applicative f => (a -> f b) -> Point3' a -> f (Point3' b) # sequenceA :: Applicative f => Point3' (f a) -> f (Point3' a) # mapM :: Monad m => (a -> m b) -> Point3' a -> m (Point3' b) # sequence :: Monad m => Point3' (m a) -> m (Point3' a) #
VectorNum Point3' Source #
Methods fmapNum1 :: Num b => (a -> b) -> Point3' a -> Point3' b Source # fmapNum2 :: Num c => (a -> b -> c) -> Point3' a -> Point3' b -> Point3' c Source # fmapNum1inv :: Num a => (a -> a) -> Point3' a -> Point3' a Source # simpleVec :: Num a => a -> Point3' a Source #
Coord3 Point3' Source #
Methods getZ :: Point3' a -> a Source #
Coord2 Point3' Source #
Methods getX :: Point3' a -> a Source # getY :: Point3' a -> a Source #
Coord Point3' Source #
Methods getComponents :: Num a => Point3' a -> [a] Source # fromComponents :: Num a => [a] -> Point3' a Source # magSq :: Num a => Point3' a -> a Source # dotProduct :: Num a => Point3' a -> Point3' a -> a Source #
IsomorphicVectors Triple Point3' Source #
Methods iso :: Num a => Triple a -> Point3' a Source #
IsomorphicVectors Rel3' Point3' Source #
Methods iso :: Num a => Rel3' a -> Point3' a Source #
IsomorphicVectors Point3' Triple Source #
Methods iso :: Num a => Point3' a -> Triple a Source #
IsomorphicVectors Point3' Rel3' Source #
Methods iso :: Num a => Point3' a -> Rel3' a Source #
Geometry Rel3' Point3' Line3' Source #
Methods scaleRel :: Num a => a -> Rel3' a -> Rel3' a Source # plusDir :: (Num a, Eq a, Show a) => Point3' a -> Rel3' a -> Point3' a Source # fromPt :: (Num a, Eq a, Show a) => Point3' a -> Point3' a -> Rel3' a Source # getLineVecs :: Num a => Line3' a -> (Point3' a, Rel3' a) Source # makeLine :: Num a => Point3' a -> Rel3' a -> Line3' a Source #
Eq a => Eq (Point3' a) Source #
Methods (==) :: Point3' a -> Point3' a -> Bool # (/=) :: Point3' a -> Point3' a -> Bool #
Ord a => Ord (Point3' a) Source #
Methods compare :: Point3' a -> Point3' a -> Ordering # (<) :: Point3' a -> Point3' a -> Bool # (<=) :: Point3' a -> Point3' a -> Bool # (>) :: Point3' a -> Point3' a -> Bool # (>=) :: Point3' a -> Point3' a -> Bool # max :: Point3' a -> Point3' a -> Point3' a # min :: Point3' a -> Point3' a -> Point3' a #
Read a => Read (Point3' a) Source #
Methods readsPrec :: Int -> ReadS (Point3' a) # readList :: ReadS [Point3' a] # readPrec :: ReadPrec (Point3' a) # readListPrec :: ReadPrec [Point3' a] #
Show a => Show (Point3' a) Source #
Methods showsPrec :: Int -> Point3' a -> ShowS # show :: Point3' a -> String # showList :: [Point3' a] -> ShowS #

data Rel3' a Source #

A relative vector (free vector) in 3D space. The triple is the x, y, z components, and the last item is the squared magnitude of the vector, which is stored with it to speed up various operations. It is suggested you use makeRel3 to create one of these, unless the magnitude is easily apparent, e.g. Rel3 (0, 1, 1) 2

Constructors

Rel3 (a, a, a) a

Instances

Foldable Rel3' Source #
Methods fold :: Monoid m => Rel3' m -> m # foldMap :: Monoid m => (a -> m) -> Rel3' a -> m # foldr :: (a -> b -> b) -> b -> Rel3' a -> b # foldr' :: (a -> b -> b) -> b -> Rel3' a -> b # foldl :: (b -> a -> b) -> b -> Rel3' a -> b # foldl' :: (b -> a -> b) -> b -> Rel3' a -> b # foldr1 :: (a -> a -> a) -> Rel3' a -> a # foldl1 :: (a -> a -> a) -> Rel3' a -> a # toList :: Rel3' a -> [a] # null :: Rel3' a -> Bool # length :: Rel3' a -> Int # elem :: Eq a => a -> Rel3' a -> Bool # maximum :: Ord a => Rel3' a -> a # minimum :: Ord a => Rel3' a -> a # sum :: Num a => Rel3' a -> a # product :: Num a => Rel3' a -> a #
VectorNum Rel3' Source #
Methods fmapNum1 :: Num b => (a -> b) -> Rel3' a -> Rel3' b Source # fmapNum2 :: Num c => (a -> b -> c) -> Rel3' a -> Rel3' b -> Rel3' c Source # fmapNum1inv :: Num a => (a -> a) -> Rel3' a -> Rel3' a Source # simpleVec :: Num a => a -> Rel3' a Source #
Coord3 Rel3' Source #
Methods getZ :: Rel3' a -> a Source #
Coord2 Rel3' Source #
Methods getX :: Rel3' a -> a Source # getY :: Rel3' a -> a Source #
Coord Rel3' Source #
Methods getComponents :: Num a => Rel3' a -> [a] Source # fromComponents :: Num a => [a] -> Rel3' a Source # magSq :: Num a => Rel3' a -> a Source # dotProduct :: Num a => Rel3' a -> Rel3' a -> a Source #
IsomorphicVectors Triple Rel3' Source #
Methods iso :: Num a => Triple a -> Rel3' a Source #
IsomorphicVectors Rel3' Triple Source #
Methods iso :: Num a => Rel3' a -> Triple a Source #
IsomorphicVectors Rel3' Point3' Source #
Methods iso :: Num a => Rel3' a -> Point3' a Source #
IsomorphicVectors Point3' Rel3' Source #
Methods iso :: Num a => Point3' a -> Rel3' a Source #
Geometry Rel3' Point3' Line3' Source #
Methods scaleRel :: Num a => a -> Rel3' a -> Rel3' a Source # plusDir :: (Num a, Eq a, Show a) => Point3' a -> Rel3' a -> Point3' a Source # fromPt :: (Num a, Eq a, Show a) => Point3' a -> Point3' a -> Rel3' a Source # getLineVecs :: Num a => Line3' a -> (Point3' a, Rel3' a) Source # makeLine :: Num a => Point3' a -> Rel3' a -> Line3' a Source #
Eq a => Eq (Rel3' a) Source #
Methods (==) :: Rel3' a -> Rel3' a -> Bool # (/=) :: Rel3' a -> Rel3' a -> Bool #
(Show a, Eq a, Num a) => Num (Rel3' a) Source #
Methods (+) :: Rel3' a -> Rel3' a -> Rel3' a # (-) :: Rel3' a -> Rel3' a -> Rel3' a # (*) :: Rel3' a -> Rel3' a -> Rel3' a # negate :: Rel3' a -> Rel3' a # abs :: Rel3' a -> Rel3' a # signum :: Rel3' a -> Rel3' a # fromInteger :: Integer -> Rel3' a #
Ord a => Ord (Rel3' a) Source #
Methods compare :: Rel3' a -> Rel3' a -> Ordering # (<) :: Rel3' a -> Rel3' a -> Bool # (<=) :: Rel3' a -> Rel3' a -> Bool # (>) :: Rel3' a -> Rel3' a -> Bool # (>=) :: Rel3' a -> Rel3' a -> Bool # max :: Rel3' a -> Rel3' a -> Rel3' a # min :: Rel3' a -> Rel3' a -> Rel3' a #
Read a => Read (Rel3' a) Source #
Methods readsPrec :: Int -> ReadS (Rel3' a) # readList :: ReadS [Rel3' a] # readPrec :: ReadPrec (Rel3' a) # readListPrec :: ReadPrec [Rel3' a] #
Show a => Show (Rel3' a) Source #
Methods showsPrec :: Int -> Rel3' a -> ShowS # show :: Rel3' a -> String # showList :: [Rel3' a] -> ShowS #

makeRel3 :: Num a => (a, a, a) -> Rel3' a Source #

Constructs a Rel3' vector

data Line3' a Source #

A line in 3D space. A line is a point and a free vector indicating direction. A line may be treated by a function as either finite (taking the magnitude of the free vector as the length) or infinite (ignoring the magnitude of the direction vector).

Constructors

Line3
Fields getLineStart3 :: Point3' a getLineDir3 :: Rel3' a

Instances

Geometry Rel3' Point3' Line3' Source #
Methods scaleRel :: Num a => a -> Rel3' a -> Rel3' a Source # plusDir :: (Num a, Eq a, Show a) => Point3' a -> Rel3' a -> Point3' a Source # fromPt :: (Num a, Eq a, Show a) => Point3' a -> Point3' a -> Rel3' a Source # getLineVecs :: Num a => Line3' a -> (Point3' a, Rel3' a) Source # makeLine :: Num a => Point3' a -> Rel3' a -> Line3' a Source #
Eq a => Eq (Line3' a) Source #
Methods (==) :: Line3' a -> Line3' a -> Bool # (/=) :: Line3' a -> Line3' a -> Bool #
Read a => Read (Line3' a) Source #
Methods readsPrec :: Int -> ReadS (Line3' a) # readList :: ReadS [Line3' a] # readPrec :: ReadPrec (Line3' a) # readListPrec :: ReadPrec [Line3' a] #
Show a => Show (Line3' a) Source #
Methods showsPrec :: Int -> Line3' a -> ShowS # show :: Line3' a -> String # showList :: [Line3' a] -> ShowS #