Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	Haskell2010

Data.Geometry.HalfSpace

Description

$d$-dimensional HalfSpaces

Synopsis

newtype HalfSpace d r = HalfSpace {
- _boundingPlane :: HyperPlane d r
}
boundingPlane :: forall d r d r. Iso (HalfSpace d r) (HalfSpace d r) (HyperPlane d r) (HyperPlane d r)
type HalfPlane = HalfSpace 2
leftOf :: Num r => Line 2 r -> HalfPlane r
rightOf :: Num r => Line 2 r -> HalfPlane r
above :: Num r => Line 2 r -> HalfPlane r
below :: Num r => Line 2 r -> HalfPlane r
inHalfSpace :: (Num r, Ord r, Arity d) => Point d r -> HalfSpace d r -> PointLocationResult

Documentation

>>> :{
let myVector :: Vector 3 Int
    myVector = Vector3 1 2 3
    myPoint = Point myVector
:}

newtype HalfSpace d r Source #

A Halfspace in $d$ dimensions. Note that the intended side of the halfspace is already indicated by the normal vector of the bounding plane.

Constructors

HalfSpace
Fields _boundingPlane :: HyperPlane d r

Instances

Arity d => Functor (HalfSpace d) Source #
Instance details Defined in Data.Geometry.HalfSpace Methods fmap :: (a -> b) -> HalfSpace d a -> HalfSpace d b # (<$) :: a -> HalfSpace d b -> HalfSpace d a #
Arity d => Foldable (HalfSpace d) Source #
Instance details Defined in Data.Geometry.HalfSpace Methods fold :: Monoid m => HalfSpace d m -> m # foldMap :: Monoid m => (a -> m) -> HalfSpace d a -> m # foldr :: (a -> b -> b) -> b -> HalfSpace d a -> b # foldr' :: (a -> b -> b) -> b -> HalfSpace d a -> b # foldl :: (b -> a -> b) -> b -> HalfSpace d a -> b # foldl' :: (b -> a -> b) -> b -> HalfSpace d a -> b # foldr1 :: (a -> a -> a) -> HalfSpace d a -> a # foldl1 :: (a -> a -> a) -> HalfSpace d a -> a # toList :: HalfSpace d a -> [a] # null :: HalfSpace d a -> Bool # length :: HalfSpace d a -> Int # elem :: Eq a => a -> HalfSpace d a -> Bool # maximum :: Ord a => HalfSpace d a -> a # minimum :: Ord a => HalfSpace d a -> a # sum :: Num a => HalfSpace d a -> a # product :: Num a => HalfSpace d a -> a #
Arity d => Traversable (HalfSpace d) Source #
Instance details Defined in Data.Geometry.HalfSpace Methods traverse :: Applicative f => (a -> f b) -> HalfSpace d a -> f (HalfSpace d b) # sequenceA :: Applicative f => HalfSpace d (f a) -> f (HalfSpace d a) # mapM :: Monad m => (a -> m b) -> HalfSpace d a -> m (HalfSpace d b) # sequence :: Monad m => HalfSpace d (m a) -> m (HalfSpace d a) #
(Arity d, Eq r, Fractional r) => Eq (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace Methods (==) :: HalfSpace d r -> HalfSpace d r -> Bool # (/=) :: HalfSpace d r -> HalfSpace d r -> Bool #
(Arity d, Show r) => Show (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace Methods showsPrec :: Int -> HalfSpace d r -> ShowS # show :: HalfSpace d r -> String # showList :: [HalfSpace d r] -> ShowS #
Generic (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace Associated Types type Rep (HalfSpace d r) :: Type -> Type # Methods from :: HalfSpace d r -> Rep (HalfSpace d r) x # to :: Rep (HalfSpace d r) x -> HalfSpace d r #
(Arity d, Arity (d + 1), Fractional r) => IsTransformable (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace Methods transformBy :: Transformation (Dimension (HalfSpace d r)) (NumType (HalfSpace d r)) -> HalfSpace d r -> HalfSpace d r Source #
(Num r, Ord r, Arity d) => IsIntersectableWith (Point d r) (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace Methods intersect :: Point d r -> HalfSpace d r -> Intersection (Point d r) (HalfSpace d r) # intersects :: Point d r -> HalfSpace d r -> Bool # nonEmptyIntersection :: proxy (Point d r) -> proxy (HalfSpace d r) -> Intersection (Point d r) (HalfSpace d r) -> Bool #
(Fractional r, Ord r) => IsIntersectableWith (Line 2 r) (HalfSpace 2 r) Source #
Instance details Defined in Data.Geometry.HalfSpace Methods intersect :: Line 2 r -> HalfSpace 2 r -> Intersection (Line 2 r) (HalfSpace 2 r) # intersects :: Line 2 r -> HalfSpace 2 r -> Bool # nonEmptyIntersection :: proxy (Line 2 r) -> proxy (HalfSpace 2 r) -> Intersection (Line 2 r) (HalfSpace 2 r) -> Bool #
type Rep (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace type Rep (HalfSpace d r) = D1 (MetaData "HalfSpace" "Data.Geometry.HalfSpace" "hgeometry-0.11.0.0-5Q7X7STHtn33ZJbJEL0QVy" True) (C1 (MetaCons "HalfSpace" PrefixI True) (S1 (MetaSel (Just "_boundingPlane") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (HyperPlane d r))))
type NumType (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace type NumType (HalfSpace d r) = r
type Dimension (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace type Dimension (HalfSpace d r) = d
type IntersectionOf (Point d r) (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace type IntersectionOf (Point d r) (HalfSpace d r) = NoIntersection ': (Point d r ': ([] :: [Type]))
type IntersectionOf (Line d r) (HalfSpace d r) Source #
Instance details Defined in Data.Geometry.HalfSpace type IntersectionOf (Line d r) (HalfSpace d r) = NoIntersection ': (HalfLine d r ': (Line d r ': ([] :: [Type])))

boundingPlane :: forall d r d r. Iso (HalfSpace d r) (HalfSpace d r) (HyperPlane d r) (HyperPlane d r) Source #

type HalfPlane = HalfSpace 2 Source #

leftOf :: Num r => Line 2 r -> HalfPlane r Source #

Get the halfplane left of a line (i.e. "above") a line

>>> leftOf $ horizontalLine 4
HalfSpace {_boundingPlane = HyperPlane {_inPlane = Point2 [0,4], _normalVec = Vector2 [0,1]}}

rightOf :: Num r => Line 2 r -> HalfPlane r Source #

Get the halfplane right of a line (i.e. "below") a line

>>> rightOf $ horizontalLine 4
HalfSpace {_boundingPlane = HyperPlane {_inPlane = Point2 [0,4], _normalVec = Vector2 [0,-1]}}

above :: Num r => Line 2 r -> HalfPlane r Source #

below :: Num r => Line 2 r -> HalfPlane r Source #

inHalfSpace :: (Num r, Ord r, Arity d) => Point d r -> HalfSpace d r -> PointLocationResult Source #

Test if a point lies in a halfspace