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

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)

OnSideUpDownTest (Plane r)

Defined in Data.Geometry.HyperPlane

Methods

onSideUpDown :: forall (d :: Nat) r0. (d ~ Dimension (Plane r), r0 ~ NumType (Plane r), Ord r0, Num r0) => Point d r0 -> Plane r -> SideTestUpDown

(Arity d, Eq r, Fractional 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

(Num r, Eq r, Arity d) => IsIntersectableWith (Point d r) (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

Methods

intersect :: Point d r -> HyperPlane d r -> Intersection (Point d r) (HyperPlane d r)

intersects :: Point d r -> HyperPlane d r -> Bool

nonEmptyIntersection :: proxy (Point d r) -> proxy (HyperPlane d r) -> Intersection (Point d r) (HyperPlane d r) -> Bool

type Rep (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

type Rep (HyperPlane d r) = D1 ('MetaData "HyperPlane" "Data.Geometry.HyperPlane" "hgeometry-0.12.0.2-IMXeR0PuShPEjPCARytEWE" '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 IntersectionOf (Point d r) (HyperPlane d r)

Defined in Data.Geometry.HyperPlane

type IntersectionOf (Point d r) (HyperPlane d r) = '[NoIntersection, Point d r]

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

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

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

Produces a plane. If r lies counter clockwise of q w.r.t. p then the normal vector of the resulting plane is pointing "upwards".

>>> from3Points origin (Point3 1 0 0) (Point3 0 1 0)
HyperPlane {_inPlane = Point3 0 0 0, _normalVec = Vector3 0 0 1}

Lines

_asLine :: Num r => Iso' (HyperPlane 2 r) (Line 2 r)

Convert between lines and hyperplanes

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))

planeCoordinatesWith :: Fractional r => Plane r -> Vector 3 r -> Point 3 r -> Point 2 r

Given * a plane, * a unit vector in the plane that will represent the y-axis (i.e. the "view up" vector), and * a point in the plane,

computes the plane coordinates of the given point, using the inPlane point as the origin, the normal vector of the plane as the unit vector in the "z-direction" and the view up vector as the y-axis.

>>> planeCoordinatesWith (Plane origin (Vector3 0 0 1)) (Vector3 0 1 0) (Point3 10 10 0)
Point2 10.0 10.0

planeCoordinatesTransform :: Num r => Plane r -> Vector 3 r -> Transformation 3 r