Data.SG.Geometry.ThreeDim

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.

Documentation

newtype Point3' a

A point in 3D space.

Constructors

Point3 (a, a, a)

Instances

Functor Point3'

Methods

fmap :: (a -> b) -> Point3' a -> Point3' b

(<$) :: a -> Point3' b -> Point3' a

Applicative Point3'

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'

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'

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'

Methods

fmapNum1 :: Num b => (a -> b) -> Point3' a -> Point3' b

fmapNum2 :: Num c => (a -> b -> c) -> Point3' a -> Point3' b -> Point3' c

fmapNum1inv :: Num a => (a -> a) -> Point3' a -> Point3' a

simpleVec :: Num a => a -> Point3' a

Coord3 Point3'

Methods

getZ :: Point3' a -> a

Coord2 Point3'

Methods

getX :: Point3' a -> a

getY :: Point3' a -> a

Coord Point3'

Methods

getComponents :: Num a => Point3' a -> [a]

fromComponents :: Num a => [a] -> Point3' a

magSq :: Num a => Point3' a -> a

dotProduct :: Num a => Point3' a -> Point3' a -> a

IsomorphicVectors Triple Point3'

Methods

iso :: Num a => Triple a -> Point3' a

IsomorphicVectors Rel3' Point3'

Methods

iso :: Num a => Rel3' a -> Point3' a

IsomorphicVectors Point3' Triple

Methods

iso :: Num a => Point3' a -> Triple a

IsomorphicVectors Point3' Rel3'

Methods

iso :: Num a => Point3' a -> Rel3' a

Geometry Rel3' Point3' Line3'

Methods

scaleRel :: Num a => a -> Rel3' a -> Rel3' a

plusDir :: (Num a, Eq a, Show a) => Point3' a -> Rel3' a -> Point3' a

fromPt :: (Num a, Eq a, Show a) => Point3' a -> Point3' a -> Rel3' a

getLineVecs :: Num a => Line3' a -> (Point3' a, Rel3' a)

makeLine :: Num a => Point3' a -> Rel3' a -> Line3' a

Eq a => Eq (Point3' a)

Methods

(==) :: Point3' a -> Point3' a -> Bool

(/=) :: Point3' a -> Point3' a -> Bool

Ord a => Ord (Point3' a)

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)

Methods

readsPrec :: Int -> ReadS (Point3' a)

readList :: ReadS [Point3' a]

readPrec :: ReadPrec (Point3' a)

readListPrec :: ReadPrec [Point3' a]

Show a => Show (Point3' a)

Methods

showsPrec :: Int -> Point3' a -> ShowS

show :: Point3' a -> String

showList :: [Point3' a] -> ShowS

data Rel3' a

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'

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'

Methods

fmapNum1 :: Num b => (a -> b) -> Rel3' a -> Rel3' b

fmapNum2 :: Num c => (a -> b -> c) -> Rel3' a -> Rel3' b -> Rel3' c

fmapNum1inv :: Num a => (a -> a) -> Rel3' a -> Rel3' a

simpleVec :: Num a => a -> Rel3' a

Coord3 Rel3'

Methods

getZ :: Rel3' a -> a

Coord2 Rel3'

Methods

getX :: Rel3' a -> a

getY :: Rel3' a -> a

Coord Rel3'

Methods

getComponents :: Num a => Rel3' a -> [a]

fromComponents :: Num a => [a] -> Rel3' a

magSq :: Num a => Rel3' a -> a

dotProduct :: Num a => Rel3' a -> Rel3' a -> a

IsomorphicVectors Triple Rel3'

Methods

iso :: Num a => Triple a -> Rel3' a

IsomorphicVectors Rel3' Triple

Methods

iso :: Num a => Rel3' a -> Triple a

IsomorphicVectors Rel3' Point3'

Methods

iso :: Num a => Rel3' a -> Point3' a

IsomorphicVectors Point3' Rel3'

Methods

iso :: Num a => Point3' a -> Rel3' a

Geometry Rel3' Point3' Line3'

Methods

scaleRel :: Num a => a -> Rel3' a -> Rel3' a

plusDir :: (Num a, Eq a, Show a) => Point3' a -> Rel3' a -> Point3' a

fromPt :: (Num a, Eq a, Show a) => Point3' a -> Point3' a -> Rel3' a

getLineVecs :: Num a => Line3' a -> (Point3' a, Rel3' a)

makeLine :: Num a => Point3' a -> Rel3' a -> Line3' a

Eq a => Eq (Rel3' a)

Methods

(==) :: Rel3' a -> Rel3' a -> Bool

(/=) :: Rel3' a -> Rel3' a -> Bool

(Show a, Eq a, Num a) => Num (Rel3' a)

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)

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)

Methods

readsPrec :: Int -> ReadS (Rel3' a)

readList :: ReadS [Rel3' a]

readPrec :: ReadPrec (Rel3' a)

readListPrec :: ReadPrec [Rel3' a]

Show a => Show (Rel3' a)

Methods

showsPrec :: Int -> Rel3' a -> ShowS

show :: Rel3' a -> String

showList :: [Rel3' a] -> ShowS

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

Constructs a Rel3' vector

data Line3' a

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'

Methods

scaleRel :: Num a => a -> Rel3' a -> Rel3' a

plusDir :: (Num a, Eq a, Show a) => Point3' a -> Rel3' a -> Point3' a

fromPt :: (Num a, Eq a, Show a) => Point3' a -> Point3' a -> Rel3' a

getLineVecs :: Num a => Line3' a -> (Point3' a, Rel3' a)

makeLine :: Num a => Point3' a -> Rel3' a -> Line3' a

Eq a => Eq (Line3' a)

Methods

(==) :: Line3' a -> Line3' a -> Bool

(/=) :: Line3' a -> Line3' a -> Bool

Read a => Read (Line3' a)

Methods

readsPrec :: Int -> ReadS (Line3' a)

readList :: ReadS [Line3' a]

readPrec :: ReadPrec (Line3' a)

readListPrec :: ReadPrec [Line3' a]

Show a => Show (Line3' a)

Methods

showsPrec :: Int -> Line3' a -> ShowS

show :: Line3' a -> String

showList :: [Line3' a] -> ShowS