Safe Haskell	None
Language	Haskell2010

Data.Geometry.HyperPlane

Contents

3 Dimensional planes
Supporting Planes

Synopsis

data HyperPlane (d :: Nat) (r :: *) = HyperPlane {
- _inPlane :: !(Point d r)
- _normalVec :: !(Vector d r)
}
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
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
class HasSupportingPlane t where
- supportingPlane :: t -> HyperPlane (Dimension t) (NumType t)

Documentation

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

Hyperplanes embedded in a $d$ dimensional space.

Constructors

HyperPlane
Fields _inPlane :: !(Point d r) _normalVec :: !(Vector d r)

Instances

Arity d => Functor (HyperPlane d) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Geometry.HyperPlane Methods rnf :: HyperPlane d r -> () #
(Arity d, Arity (d + 1), Fractional r) => IsTransformable (HyperPlane d r) Source #
Instance details Defined in Data.Geometry.HyperPlane Methods transformBy :: Transformation (Dimension (HyperPlane d r)) (NumType (HyperPlane d r)) -> HyperPlane d r -> HyperPlane d r Source #
HasSupportingPlane (HyperPlane d r) Source #
Instance details Defined in Data.Geometry.HyperPlane Methods supportingPlane :: HyperPlane d r -> HyperPlane (Dimension (HyperPlane d r)) (NumType (HyperPlane d r)) Source #
(Eq r, Fractional r) => IsIntersectableWith (Line 3 r) (Plane r) Source #
Instance details Defined in Data.Geometry.HyperPlane Methods intersect :: Line 3 r -> Plane r -> Intersection (Line 3 r) (Plane r) Source # intersects :: Line 3 r -> Plane r -> Bool Source # nonEmptyIntersection :: proxy (Line 3 r) -> proxy (Plane r) -> Intersection (Line 3 r) (Plane r) -> Bool Source #
type Rep (HyperPlane d r) Source #
Instance details 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) Source #
Instance details Defined in Data.Geometry.HyperPlane type NumType (HyperPlane d r) = r
type Dimension (HyperPlane d r) Source #
Instance details Defined in Data.Geometry.HyperPlane type Dimension (HyperPlane d r) = d
type IntersectionOf (Line 3 r) (Plane r) Source #
Instance details 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) Source #

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

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

Test if a point lies on a hyperplane.

3 Dimensional planes

type Plane = HyperPlane 3 Source #

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

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

Supporting Planes

class HasSupportingPlane t where Source #

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) Source #

Instances

HasSupportingPlane (HyperPlane d r) Source #
Instance details Defined in Data.Geometry.HyperPlane Methods supportingPlane :: HyperPlane d r -> HyperPlane (Dimension (HyperPlane d r)) (NumType (HyperPlane d r)) Source #
Num r => HasSupportingPlane (Triangle 3 p r) Source #
Instance details Defined in Data.Geometry.Triangle Methods supportingPlane :: Triangle 3 p r -> HyperPlane (Dimension (Triangle 3 p r)) (NumType (Triangle 3 p r)) Source #