Data.Geometry.HyperPlane

Documentation

data HyperPlane (d :: Nat) (r :: *)

Hyperplanes embedded in a \(d\) dimensional space.

Constructors

HyperPlane

Fields

• _inPlane :: !(Point d r)
• _normalVec :: !(Vector d r)

Instances

Arity d => Functor (HyperPlane d)

Defined in Data.Geometry.HyperPlane

Methods

fmap :: (a -> b) -> HyperPlane d a -> HyperPlane d b

(<$) :: a -> HyperPlane d b -> HyperPlane d a

Arity d => Foldable (HyperPlane d)

Defined in Data.Geometry.HyperPlane

Methods

fold :: Monoid m => HyperPlane d m -> m

foldMap :: Monoid m => (a -> m) -> HyperPlane d a -> m

foldr :: (a -> b -> b) -> b -> HyperPlane d a -> b

foldr' :: (a -> b -> b) -> b -> HyperPlane d a -> b

foldl :: (b -> a -> b) -> b -> HyperPlane d a -> b

foldl' :: (b -> a -> b) -> b -> HyperPlane d a -> b

foldr1 :: (a -> a -> a) -> HyperPlane d a -> a

foldl1 :: (a -> a -> a) -> HyperPlane d a -> a

toList :: HyperPlane d a -> [a]

null :: HyperPlane d a -> Bool

length :: HyperPlane d a -> Int

elem :: Eq a => a -> HyperPlane d a -> Bool

maximum :: Ord a => HyperPlane d a -> a

minimum :: Ord a => HyperPlane d a -> a

sum :: Num a => HyperPlane d a -> a

product :: Num a => HyperPlane d a -> a

Arity d => Traversable (HyperPlane d)

Defined in Data.Geometry.HyperPlane

Methods

traverse :: Applicative f => (a -> f b) -> HyperPlane d a -> f (HyperPlane d b)

sequenceA :: Applicative f => HyperPlane d (f a) -> f (HyperPlane d a)

mapM :: Monad m => (a -> m b) -> HyperPlane d a -> m (HyperPlane d b)

sequence :: Monad m => HyperPlane d (m a) -> m (HyperPlane d a)

(Arity d, Eq r) => Eq (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

Methods

(==) :: HyperPlane d r -> HyperPlane d r -> Bool

(/=) :: HyperPlane d r -> HyperPlane d r -> Bool

(Arity d, Show r) => Show (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

Methods

showsPrec :: Int -> HyperPlane d r -> ShowS

show :: HyperPlane d r -> String

showList :: [HyperPlane d r] -> ShowS

Generic (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

Associated Types

type Rep (HyperPlane d r) :: Type -> Type

Methods

from :: HyperPlane d r -> Rep (HyperPlane d r) x

to :: Rep (HyperPlane d r) x -> HyperPlane d r

(NFData r, Arity d) => NFData (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

Methods

rnf :: HyperPlane d r -> ()

(Arity d, Arity (d + 1), Fractional r) => IsTransformable (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

Methods

transformBy :: Transformation (Dimension (HyperPlane d r)) (NumType (HyperPlane d r)) -> HyperPlane d r -> HyperPlane d r

HasSupportingPlane (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

Methods

supportingPlane :: HyperPlane d r -> HyperPlane (Dimension (HyperPlane d r)) (NumType (HyperPlane d r))

(Eq r, Fractional r) => IsIntersectableWith (Line 3 r) (Plane r)

Defined in Data.Geometry.HyperPlane

Methods

intersect :: Line 3 r -> Plane r -> Intersection (Line 3 r) (Plane r)

intersects :: Line 3 r -> Plane r -> Bool

nonEmptyIntersection :: proxy (Line 3 r) -> proxy (Plane r) -> Intersection (Line 3 r) (Plane r) -> Bool

type Rep (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

type Rep (HyperPlane d r) = D1 (MetaData "HyperPlane" "Data.Geometry.HyperPlane" "hgeometry-0.8.0.0-2B18HmKepFxHOPvqiUEkND" False) (C1 (MetaCons "HyperPlane" PrefixI True) (S1 (MetaSel (Just "_inPlane") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Point d r)) :*: S1 (MetaSel (Just "_normalVec") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Vector d r))))

type NumType (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

type NumType (HyperPlane d r) = r

type Dimension (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

type Dimension (HyperPlane d r) = d

type IntersectionOf (Line 3 r) (Plane r)

Defined in Data.Geometry.HyperPlane

type IntersectionOf (Line 3 r) (Plane r) = NoIntersection ': (Point 3 r ': (Line 3 r ': ([] :: [Type])))

normalVec :: forall d r. Lens' (HyperPlane d r) (Vector d r)

inPlane :: forall d r. Lens' (HyperPlane d r) (Point d r)

onHyperPlane :: (Num r, Eq r, Arity d) => Point d r -> HyperPlane d r -> Bool

Test if a point lies on a hyperplane.

3 Dimensional planes

type Plane = HyperPlane 3

pattern Plane :: Point 3 r -> Vector 3 r -> Plane r

from3Points :: Num r => Point 3 r -> Point 3 r -> Point 3 r -> HyperPlane 3 r

Supporting Planes

class HasSupportingPlane t where

Types for which we can compute a supporting hyperplane, i.e. a hyperplane that contains the thing of type t.

Methods

supportingPlane :: t -> HyperPlane (Dimension t) (NumType t)

Instances

HasSupportingPlane (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

Methods

supportingPlane :: HyperPlane d r -> HyperPlane (Dimension (HyperPlane d r)) (NumType (HyperPlane d r))

Num r => HasSupportingPlane (Triangle 3 p r)

Defined in Data.Geometry.Triangle

Methods

supportingPlane :: Triangle 3 p r -> HyperPlane (Dimension (Triangle 3 p r)) (NumType (Triangle 3 p r))