Safe Haskell	None
Language	GHC2024

HGeometry.HalfPlane.CommonIntersection

Synopsis

data CommonIntersection halfPlane r
- = SingletonPoint (Point 2 r) (Vector 3 halfPlane)
- | InSubLine (VerticalOrLineEQ r) (Vector 2 halfPlane) (SubLine halfPlane r)
- | Slab halfPlane halfPlane
- | BoundedRegion (ConvexPolygon (Point 2 r :+ halfPlane))
- | UnboundedRegion (Chain Seq r halfPlane)
data SubLine halfPlane r
- = EntireLine
- | InHalfLine (HalfLine (Point 2 r)) halfPlane
- | InSegment (ClosedLineSegment (Point 2 r)) halfPlane halfPlane
newtype Chain (f :: Type -> Type) r halfPlane = Chain (Alternating f (Point 2 r) halfPlane)
commonIntersection :: (Foldable1 f, Functor f, HalfPlane_ halfPlane r, Fractional r, Ord r, HyperPlane_ (BoundingHyperPlane halfPlane 2 r) 2 r, Show halfPlane, Show r) => f halfPlane -> Maybe (CommonIntersection halfPlane r)
boundaries :: (HalfPlane_ halfPlane r, Ord r, Fractional r, Show r, Show halfPlane) => NonVerticals halfPlane r -> These2 (Chain Seq r (LineEQ r :+ halfPlane))
clipUpperByLower :: (Ord r, Num r, HasIntersectionWith (Point 2 r) halfPlane) => Chain Seq r (line :+ halfPlane) -> Chain Seq r (line :+ halfPlane) -> Chain Seq r (line :+ halfPlane)

Documentation

data CommonIntersection halfPlane r Source #

A type represetning the Common intersection of a bunch of halfplanes; assuming this intersection is non-empty.

Constructors

SingletonPoint (Point 2 r) (Vector 3 halfPlane)	Common intersection is a singleton point, defined by the three given halfplanes
InSubLine (VerticalOrLineEQ r) (Vector 2 halfPlane) (SubLine halfPlane r)	The two halfPlanes that define the line, and the other halfplanes furthe restricitng the line.
Slab halfPlane halfPlane	two parallel halfPlanes l and u that form a slab;
BoundedRegion (ConvexPolygon (Point 2 r :+ halfPlane))	each vertex stores the interior halfplane of the CCW-edge it is incident to.
UnboundedRegion (Chain Seq r halfPlane)	each vertex stores the interior halfplane of the CCW-edge it is incident to.

Instances

Instances details

(Show r, Show halfPlane) => Show (CommonIntersection halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection Methods showsPrec :: Int -> CommonIntersection halfPlane r -> ShowS Source # show :: CommonIntersection halfPlane r -> String Source # showList :: [CommonIntersection halfPlane r] -> ShowS Source #
(Eq r, Eq halfPlane) => Eq (CommonIntersection halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection Methods (==) :: CommonIntersection halfPlane r -> CommonIntersection halfPlane r -> Bool Source # (/=) :: CommonIntersection halfPlane r -> CommonIntersection halfPlane r -> Bool Source #

data SubLine halfPlane r Source #

Part of the line

Constructors

EntireLine
InHalfLine (HalfLine (Point 2 r)) halfPlane	the third halfPlane
InSegment (ClosedLineSegment (Point 2 r)) halfPlane halfPlane	the remaining two halfplanes

Instances

Instances details

(Show r, Show halfPlane) => Show (SubLine halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection Methods showsPrec :: Int -> SubLine halfPlane r -> ShowS Source # show :: SubLine halfPlane r -> String Source # showList :: [SubLine halfPlane r] -> ShowS Source #
(Eq r, Eq halfPlane) => Eq (SubLine halfPlane r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection Methods (==) :: SubLine halfPlane r -> SubLine halfPlane r -> Bool Source # (/=) :: SubLine halfPlane r -> SubLine halfPlane r -> Bool Source #

newtype Chain (f :: Type -> Type) r halfPlane Source #

A polygonal chain bounding an unbounded convex region, in CCW order.

Constructors

Chain (Alternating f (Point 2 r) halfPlane)

Instances

Instances details

Foldable f => Bifoldable (Chain f) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods bifold :: Monoid m => Chain f m m -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Chain f a b -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Chain f a b -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Chain f a b -> c Source #
Functor f => Bifunctor (Chain f) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods bimap :: (a -> b) -> (c -> d) -> Chain f a c -> Chain f b d Source # first :: (a -> b) -> Chain f a c -> Chain f b c Source # second :: (b -> c) -> Chain f a b -> Chain f a c Source #
Foldable f => Foldable1 (Chain f r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods fold1 :: Semigroup m => Chain f r m -> m Source # foldMap1 :: Semigroup m => (a -> m) -> Chain f r a -> m Source # foldMap1' :: Semigroup m => (a -> m) -> Chain f r a -> m Source # toNonEmpty :: Chain f r a -> NonEmpty a Source # maximum :: Ord a => Chain f r a -> a Source # minimum :: Ord a => Chain f r a -> a Source # head :: Chain f r a -> a Source # last :: Chain f r a -> a Source # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Chain f r a -> b Source # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Chain f r a -> b Source # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Chain f r a -> b Source # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Chain f r a -> b Source #
Functor f => Functor (Chain f r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods fmap :: (a -> b) -> Chain f r a -> Chain f r b Source # (<$) :: a -> Chain f r b -> Chain f r a Source #
Foldable f => Foldable (Chain f r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods fold :: Monoid m => Chain f r m -> m Source # foldMap :: Monoid m => (a -> m) -> Chain f r a -> m Source # foldMap' :: Monoid m => (a -> m) -> Chain f r a -> m Source # foldr :: (a -> b -> b) -> b -> Chain f r a -> b Source # foldr' :: (a -> b -> b) -> b -> Chain f r a -> b Source # foldl :: (b -> a -> b) -> b -> Chain f r a -> b Source # foldl' :: (b -> a -> b) -> b -> Chain f r a -> b Source # foldr1 :: (a -> a -> a) -> Chain f r a -> a Source # foldl1 :: (a -> a -> a) -> Chain f r a -> a Source # toList :: Chain f r a -> [a] Source # null :: Chain f r a -> Bool Source # length :: Chain f r a -> Int Source # elem :: Eq a => a -> Chain f r a -> Bool Source # maximum :: Ord a => Chain f r a -> a Source # minimum :: Ord a => Chain f r a -> a Source # sum :: Num a => Chain f r a -> a Source # product :: Num a => Chain f r a -> a Source #
Traversable f => Traversable (Chain f r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods traverse :: Applicative f0 => (a -> f0 b) -> Chain f r a -> f0 (Chain f r b) Source # sequenceA :: Applicative f0 => Chain f r (f0 a) -> f0 (Chain f r a) Source # mapM :: Monad m => (a -> m b) -> Chain f r a -> m (Chain f r b) Source # sequence :: Monad m => Chain f r (m a) -> m (Chain f r a) Source #
Traversable f => Traversable1 (Chain f r) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods traverse1 :: Apply f0 => (a -> f0 b) -> Chain f r a -> f0 (Chain f r b) Source # sequence1 :: Apply f0 => Chain f r (f0 b) -> f0 (Chain f r b) Source #
(Show halfPlane, Show (f (Point 2 r, halfPlane))) => Show (Chain f r halfPlane) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods showsPrec :: Int -> Chain f r halfPlane -> ShowS Source # show :: Chain f r halfPlane -> String Source # showList :: [Chain f r halfPlane] -> ShowS Source #
(Eq halfPlane, Eq (f (Point 2 r, halfPlane))) => Eq (Chain f r halfPlane) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods (==) :: Chain f r halfPlane -> Chain f r halfPlane -> Bool Source # (/=) :: Chain f r halfPlane -> Chain f r halfPlane -> Bool Source #
(Ord halfPlane, Ord (f (Point 2 r, halfPlane))) => Ord (Chain f r halfPlane) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain Methods compare :: Chain f r halfPlane -> Chain f r halfPlane -> Ordering Source # (<) :: Chain f r halfPlane -> Chain f r halfPlane -> Bool Source # (<=) :: Chain f r halfPlane -> Chain f r halfPlane -> Bool Source # (>) :: Chain f r halfPlane -> Chain f r halfPlane -> Bool Source # (>=) :: Chain f r halfPlane -> Chain f r halfPlane -> Bool Source # max :: Chain f r halfPlane -> Chain f r halfPlane -> Chain f r halfPlane Source # min :: Chain f r halfPlane -> Chain f r halfPlane -> Chain f r halfPlane Source #
type NumType (Chain f r halfPlane) Source #
Instance details Defined in HGeometry.HalfPlane.CommonIntersection.Chain type NumType (Chain f r halfPlane) = r

commonIntersection :: (Foldable1 f, Functor f, HalfPlane_ halfPlane r, Fractional r, Ord r, HyperPlane_ (BoundingHyperPlane halfPlane 2 r) 2 r, Show halfPlane, Show r) => f halfPlane -> Maybe (CommonIntersection halfPlane r) Source #

Computes the common intersection of a $n$ halfplanes.

running time: $O(n\log n)$

boundaries :: (HalfPlane_ halfPlane r, Ord r, Fractional r, Show r, Show halfPlane) => NonVerticals halfPlane r -> These2 (Chain Seq r (LineEQ r :+ halfPlane)) Source #

Computes the upper boundary of the halfplanes that have negative sign, and the upper boundary of the halfplanes that have negative sign

clipUpperByLower :: (Ord r, Num r, HasIntersectionWith (Point 2 r) halfPlane) => Chain Seq r (line :+ halfPlane) -> Chain Seq r (line :+ halfPlane) -> Chain Seq r (line :+ halfPlane) Source #

given the upper and lower chain, clip the upper thain to retain only the vertices that are above the lower chain.