Copyright	(C) Frank Staals
License	see the LICENSE file
Maintainer	Frank Staals
Safe Haskell	None
Language	GHC2024

HGeometry.Cone

Description

A Data type to represent Cones

Synopsis

data Cone r point edge = Cone point (Vector 2 r :+ edge) (Vector 2 r :+ edge)
apex :: forall r point1 edge point2 f. Functor f => (point1 -> f point2) -> Cone r point1 edge -> f (Cone r point2 edge)
leftBoundaryVector :: forall r point edge f. Functor f => ((Vector 2 r :+ edge) -> f (Vector 2 r :+ edge)) -> Cone r point edge -> f (Cone r point edge)
rightBoundaryVector :: forall r point edge f. Functor f => ((Vector 2 r :+ edge) -> f (Vector 2 r :+ edge)) -> Cone r point edge -> f (Cone r point edge)
leftBoundary :: (Dimension point ~ 2, NumType point ~ r) => Cone r point edge -> HalfLine point :+ edge
rightBoundary :: (Dimension point ~ 2, NumType point ~ r) => Cone r point edge -> HalfLine point :+ edge
coneBisector :: (Point_ point 2 r, Num r) => Cone r point edge -> HalfLine point
intersectingHalfplanes :: (Point_ point 2 r, Num r, Ord r) => Cone r point edge -> Vector 2 (HalfSpaceF (LinePV 2 r))

Documentation

data Cone r point edge Source #

A Cone

Constructors

Cone point (Vector 2 r :+ edge) (Vector 2 r :+ edge)

Instances

Instances details

Bifoldable (Cone r) Source #
Instance details Defined in HGeometry.Cone Methods bifold :: Monoid m => Cone r m m -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Cone r a b -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Cone r a b -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Cone r a b -> c Source #
Bifunctor (Cone r) Source #
Instance details Defined in HGeometry.Cone Methods bimap :: (a -> b) -> (c -> d) -> Cone r a c -> Cone r b d Source # first :: (a -> b) -> Cone r a c -> Cone r b c Source # second :: (b -> c) -> Cone r a b -> Cone r a c Source #
Bitraversable (Cone r) Source #
Instance details Defined in HGeometry.Cone Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Cone r a b -> f (Cone r c d) Source #
Functor (Cone r point) Source #
Instance details Defined in HGeometry.Cone Methods fmap :: (a -> b) -> Cone r point a -> Cone r point b Source # (<$) :: a -> Cone r point b -> Cone r point a Source #
Foldable (Cone r point) Source #
Instance details Defined in HGeometry.Cone Methods fold :: Monoid m => Cone r point m -> m Source # foldMap :: Monoid m => (a -> m) -> Cone r point a -> m Source # foldMap' :: Monoid m => (a -> m) -> Cone r point a -> m Source # foldr :: (a -> b -> b) -> b -> Cone r point a -> b Source # foldr' :: (a -> b -> b) -> b -> Cone r point a -> b Source # foldl :: (b -> a -> b) -> b -> Cone r point a -> b Source # foldl' :: (b -> a -> b) -> b -> Cone r point a -> b Source # foldr1 :: (a -> a -> a) -> Cone r point a -> a Source # foldl1 :: (a -> a -> a) -> Cone r point a -> a Source # toList :: Cone r point a -> [a] Source # null :: Cone r point a -> Bool Source # length :: Cone r point a -> Int Source # elem :: Eq a => a -> Cone r point a -> Bool Source # maximum :: Ord a => Cone r point a -> a Source # minimum :: Ord a => Cone r point a -> a Source # sum :: Num a => Cone r point a -> a Source # product :: Num a => Cone r point a -> a Source #
Traversable (Cone r point) Source #
Instance details Defined in HGeometry.Cone Methods traverse :: Applicative f => (a -> f b) -> Cone r point a -> f (Cone r point b) Source # sequenceA :: Applicative f => Cone r point (f a) -> f (Cone r point a) Source # mapM :: Monad m => (a -> m b) -> Cone r point a -> m (Cone r point b) Source # sequence :: Monad m => Cone r point (m a) -> m (Cone r point a) Source #
(Point_ point 2 r, Num r, Ord r) => HasIntersectionWith (Point 2 r) (Cone r point edge) Source #
Instance details Defined in HGeometry.Cone Methods intersects :: Point 2 r -> Cone r point edge -> Bool Source #
(Show point, Show r, Show edge) => Show (Cone r point edge) Source #
Instance details Defined in HGeometry.Cone Methods showsPrec :: Int -> Cone r point edge -> ShowS Source # show :: Cone r point edge -> String Source # showList :: [Cone r point edge] -> ShowS Source #
(Eq point, Eq r, Eq edge) => Eq (Cone r point edge) Source #
Instance details Defined in HGeometry.Cone Methods (==) :: Cone r point edge -> Cone r point edge -> Bool Source # (/=) :: Cone r point edge -> Cone r point edge -> Bool Source #
(Ord point, Ord r, Ord edge) => Ord (Cone r point edge) Source #
Instance details Defined in HGeometry.Cone Methods compare :: Cone r point edge -> Cone r point edge -> Ordering Source # (<) :: Cone r point edge -> Cone r point edge -> Bool Source # (<=) :: Cone r point edge -> Cone r point edge -> Bool Source # (>) :: Cone r point edge -> Cone r point edge -> Bool Source # (>=) :: Cone r point edge -> Cone r point edge -> Bool Source # max :: Cone r point edge -> Cone r point edge -> Cone r point edge Source # min :: Cone r point edge -> Cone r point edge -> Cone r point edge Source #
type Dimension (Cone r point edge) Source #
Instance details Defined in HGeometry.Cone type Dimension (Cone r point edge) = 2
type NumType (Cone r point edge) Source #
Instance details Defined in HGeometry.Cone type NumType (Cone r point edge) = r

apex :: forall r point1 edge point2 f. Functor f => (point1 -> f point2) -> Cone r point1 edge -> f (Cone r point2 edge) Source #

leftBoundaryVector :: forall r point edge f. Functor f => ((Vector 2 r :+ edge) -> f (Vector 2 r :+ edge)) -> Cone r point edge -> f (Cone r point edge) Source #

rightBoundaryVector :: forall r point edge f. Functor f => ((Vector 2 r :+ edge) -> f (Vector 2 r :+ edge)) -> Cone r point edge -> f (Cone r point edge) Source #

leftBoundary :: (Dimension point ~ 2, NumType point ~ r) => Cone r point edge -> HalfLine point :+ edge Source #

Get the left boundary as a HalfLine starting at the apex.

rightBoundary :: (Dimension point ~ 2, NumType point ~ r) => Cone r point edge -> HalfLine point :+ edge Source #

Get the left boundary as a HalfLine starting at the apex.

coneBisector :: (Point_ point 2 r, Num r) => Cone r point edge -> HalfLine point Source #

Get the bisector of the cone

intersectingHalfplanes :: (Point_ point 2 r, Num r, Ord r) => Cone r point edge -> Vector 2 (HalfSpaceF (LinePV 2 r)) Source #

Get the two halfplanes so that the cone is the intersection of the two halfplanes. the first halfplane is the plane right of the left boundary, whereas the second halfplane is the plane left of the right boundary.