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

Data.Geometry.HyperPlane

Contents

3 Dimensional planes
Lines
Supporting Planes

Description

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)
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
_asLine :: Num r => Iso' (HyperPlane 2 r) (Line 2 r)
class HasSupportingPlane t where
- supportingPlane :: t -> HyperPlane (Dimension t) (NumType t)
planeCoordinatesWith :: Fractional r => Plane r -> Vector 3 r -> Point 3 r -> Point 2 r
planeCoordinatesTransform :: Num r => Plane r -> Vector 3 r -> Transformation 3 r

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

Instances details

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 # 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) #
OnSideUpDownTest (Plane r) Source #
Instance details 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 Source #
(Arity d, Eq r, Fractional 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) # 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) Source #
Instance details 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) Source #
Instance details Defined in Data.Geometry.HyperPlane type Rep (HyperPlane d r) = D1 ('MetaData "HyperPlane" "Data.Geometry.HyperPlane" "hgeometry-0.12.0.1-744QXwUb5uS54emseMX1Co" '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 IntersectionOf (Point d r) (HyperPlane d r) Source #
Instance details 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) Source #

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

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 #

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) Source #

Convert between lines and hyperplanes

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

Instances details

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 #

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

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 Source #